This paper proposes an analytical model that clarifies the relationship between specific place and human emotions as well as the cause of the emotions using tweet data with location information. In addition, Twitter data with location information are analyzed to show the effectiveness of our proposed model. First, geotags are provided to collect Twitter data and increase the number of data for analysis. Second, training data with emotion labels based on the emotion expression dictionary are created and used, and supervised learning is done using fastText to obtain the emotion estimates. Finally, by using the result, topic extraction is performed to estimate the causes of the emotions. As a result, the transition of emotion in time and space as well as its cause is obtained.

<p>本研究は, 一般廃棄物の焼却処理で発生する熱エネルギーを有効利用するため, 千葉県を事例にとり, 可燃ごみの発生要因から発生熱量を予測する手法として二段階重回帰分析を提案した．重回帰分析にはパネルデータを用い, 固定効果, 変量効果の有意性についても検証した．その結果, 固定効果に有意性は見られず, プールドOLS, および変量効果モデルを採用し, 重回帰分析を行った．重回帰分析で得られた回帰式の妥当性を確かめるため, その回帰式で得られた発生熱量から低位発熱量を算出し, 低位発熱量の公表実測値との比較を相関係数と対応のあるt検定を用いて検証した．その結果, 相関係数は0.4216となり, 相関があるとされる0.4を上回った．また, 対応のあるt検定のP値は0.5548となり, 5%の有意水準で平均に差はないという帰無仮説は棄却されなかった．以上のことから, 本研究の目的である, 可燃ごみの発生要因から発生熱量を予測手法の成果は得られた．</p>

This research focuses on the two purposes of maximizing the amount of heat generated by incineration and minimizing the collection distance of waste, in determining allocations and locations of general waste incineration facilities as a case study of Chiba northwest bay area. For these purposes, we propose the multi-objective optimization with Voronoi diagram and genetic algorithm (MOVGA). As for the maximization of the amount of generated heat, we predict the amount by using regression equation of multiple linear regression analysis and formulate it as the set partitioning problem (SPP) to maximize the prediction value. As for the minimization of waste collection distances, we formulate it as the multi-Weber problem. To solve these two problems, we use MOVGA, which has the seeds of the Voronoi diagram as a gene. As a result of the survey using data of 2015 year of Chiba northwest bay area, in the case of 3 facilities it was found that the calorific value increased enough to cover the power of 4,205 households (converted to housing complex) per year despite the increase of 3% t-km per year.

This paper proposes an investor-friendly random fuzzy portfolio selection model considering both robustness and adjustment of future asset returns derived from investor's forecasts for financial tendency using a fuzzy inference method. It is important to predict the price or the return of each asset appropriately considering current market trends in portfolio optimization. In this paper, a standard multi-factor model, namely Arbitrage Pricing Theory (APT), is introduced as an asset pricing model. In addition, in order to extend standard APT by integrating important rules of current markets trends derived from technical analysis and fundamental analysis, each factor of APT is assumed to be a random fuzzy variable whose mean is adjusted by the fuzzy reasoning method, particularly product-sum-gravity method. Furthermore, it is also important for the investor to reduce the worst case of the total loss in terms of risk-averse. Therefore, worst-case conditional Value-at-Risk, which is a robust programming approach without assuming some specific random distribution, is considered. Since the proposed model is formulated as a biobjective programming problem both minimizing the value of worst-case conditional Value-at-Risk and maximizing the total expected return, it is equivalently transformed into the deterministic nonlinear programming problem using the satisficing trade-off method, and the efficient algorithm to obtain the optimal portfolio is developed. By solving our proposed model, the investor can obtain the risk-averse optimal portfolio with the large total return complying with current market trends.

<p>To introduce the renewable energy in regional communities, it is necessary to select a sustainable energy mix on the basis of evaluation from multiple viewpoints including complex environmental impacts. The purpose of this study is to develop a tool for multi-objective optimization and evaluation of renewable energy composition in municipalities considering multiple environmental criteria. This tool was developed by improving Renewable Energy Regional Optimization Utility Tool for Environmental Sustainability, REROUTES. The adjustable variables are the amount of deployed renewable energy resources from solar, wind, small and medium-scale hydro, geothermal and biomass energy. NSGA-II, a kind of genetic algorithms was applied and implemented to REROUTES to solve multiobjective optimization with six objective functions (proportion of developed renewable energy, economic balance, decrease in CO2 emissions, circulation rate of biomass resource, impacted ecosystem area, and diversity index). A case study for two municipalities showed that the developed tool successfully calculated pareto solutions having trade-off with reflecting the natural conditions and varying demand structures of case study areas. In addition, a process of selecting one best solution from the pareto solutions on the basis of local opinions could be demonstrated. In conclusion, this study could develop an useful tool to support decision-making regarding the development of renewable energy resources.</p>

This paper considers optimal production scheduling of an agricultural product to find the best matching between farmers and retailers with contract. It is important to construct the agricultural production system to hold the win-win relationship among all stakeholders in terms of sustainability. Therefore, in this paper, a multiobjective programming problem for the sustainable agricultural supply chain management is formulated to both find the optimal matching between farmers and retailers. It is generally difficult to obtain the best solution for all stakeholders directly. Therefore, Bellman-Zadeh approach is introduced, and the efficient algorithm to obtain these optimal solutions is also developed.

We have investigated the ease of use in terms of the inputting, sharing, and viewing of information over a mobile device (e.g., smartphones). In this paper, we design a new IT tool that connects producers with consumers. Specifically, we have developed a video-based digital signage system for agricultural direct sales station, and the main purpose of this paper is to introduce the outline of this system and its and operation result. We actually have utilized the proposed system to a Michi-no-Eki, Kohan-no-Sato Fukutomi, Higashi-Hiroshima-City, Japan, which is a Japanese-style roadside rest area and contributed to the relationship building between consumers and producers. The proposed system considers a user-friendly interface design, where elderly farmers can operate intuitively, and which enables the continuous use of the system in order to actively realize the application of IT to agriculture. Specifically, the proposed system can support an analysis needed to connect producers and consumers, and a function for acquiring the summary of analysis result is also implemented.

This paper considers the effectiveness of momentum indicators through the prediction of stock price for the large-capital stocks. In recent years, FinTech, which is the integration of finance and technology, has been recently expanding. One of the hot topics in FinTech is whether or not the momentum indications give an effective impact for the financial market. This paper focuses the large-capital stocks in Japanese financial market, particularly two specific stocks. Using real market data, the effectiveness of several momentum factors is discussed multidirectionally.

This paper considers an agricultural supply chain management to find the best matching between farmers and retailers with contract according to their preferences. It is important to construct the agricultural production system to hold the win-win relationship considering transportation costs. Therefore, in this paper, a mathematical programming problem is formulated to find the optimal matching between farmers and retailers under several uncertainties. It is generally difficult to obtain the best solution directly in terms of multiobjectivity and uncertainty. Therefore, the flexible modeling and the efficient algorithm to obtain these optimal solutions are also developed using a data-driven approach using our proposed information system.

Understanding the geographic and environmental factors that affect local criminal activity is important for crime prevention. In this study, we use data from Geo-Twitter to analyze the reasons underlying the occurrence of local criminal activity. In recent years, abundant location-based social network (LBSN )(e.g., Foursquare, Geo-Twitter) data has become easily available at a low cost. Therefore, many studies have used LBSNs data to model and understand human mobile behavior, such as patterns of human travel and activity. However, few studies on local criminal activities have been reported. In this paper, a new methodology is proposed to identify the reasons underlying local criminal activity from the view point of geographic and environmental factors. Our methodology consists of the following steps. First, we collect geo-tagged data from Twitter. In particular, we extract a large corpus with geo-tags, called tweets, from major cities in the United States. Second, we measure the sentiments expressed in tweets posted from a specific area using the fastText model [1]. Third, we apply a simple clustering technique called latent Dirichlet allocation (LDA) to identify the topics that are clustered in each area using sentimental analysis. Lastly, we analyze the reasons for crime by comparing the topics and the information on all crime using the data portal.

In this research, a revised recommendation system to generate recommended items for each user is constructed, such as "recommended for you" on the e-commerce websites. By using both the purchase and the browsing data, sparseness of matrix derived from the user's behavior history data is reduced. The main purpose is to construct a recommendation system that can recommend new items not browsed by users and appropriate items matching user preferences.As a procedure for generating recommended items, a user-item matrix and must-link constraints are first constructed from user's behavior history data. We add rows and columns to represent various item and user information to the user-item matrix. Next, semi-supervised learning is performed using the user-item matrix and the must-link constraint, and a new user-item matrix is generated. From this matrix on the basis of Pearson similarity, item similarity and user similarity are obtained. Finally, item-based collaborative filtering and user-based collaborative filtering are performed to generate recommended items.Experimental results show that the F-measure to represent the recommendation accuracy increases by generating recommended items with the proposed model using must-link constraints, user information and item information. In addition, it can be seen that the proposed model is more likely to purchase recommended items than the model of existing models.

This paper focuses on improving the adaptability of the investor sentiment index introduced by Baker and Wurgler[1] in the Chinese stock market. Considering not all the original proxies for sentiment are suitable for Chinese stock market, a new combination of proxies to form the investor sentiment index is proposed. Based on this investor sentiment index, the relationship between investor sentiment and stock price index in Chinese stock market is found.

This paper proposes a robust model of multi period agricultural supply chain to consider both maximizing the total profit and minimizing the environmental load with random and fuzzy parameters. Our proposed model is formulated as a fuzzy and stochastic, multiobjective and multiperiod programming problem, and hence, it is hard to solve the formulated problem directly without setting a specific random distribution and a specific membership function. Therefore, a distribution-free approach based on sample mean and variance derived from received data, which does not assume any specific random distributions and membership functions, is introduced to apply our proposed model to various uncertain conditions. In addition, deterministic equivalent transformations are also introduced to obtain the optimal solution efficiently using the scenario-based approach.

Hiroshima City is surrounded by mountains on its three sides, the east, north, and west, except the south facing the sea, and besides, its urban area places delta region. The capacity of the urban area in Hiroshima City is limited, so its land prices are exceedingly higher than other areas. Due to these conditions, most of the citizens live in residential estates at the slope of these mountains surrounding the city. However, the living environment of the suburban slope residential estates doesn't seem so suitable for elderly people who are unable to go shopping usually called as "vulnerable road users". Our previous study showed the concept of information sharing system to support the transportation of residents living in a place where public transportation is not sufficiently developed. In this paper, based on the investigation results on residents' traffic attitude in the slope residential estates at Itsukaichi District, Hiroshima City, and also our previous work, we design and develop a web service to support vulnerable road user's daily life in suburban residential estates.

This paper proposes a mathematical programming approach to construct an appropriate membership function extending our previous studies. It is important to set a membership function with both subjectivity and objectivity to obtain a reasonable optimal solution based on decision maker's feelings in real-world decision making. In order to ensure objectivity of obtained membership function as well as subjectivity, an entropy-based approach based on mathematical programming is integrated into interval estimation considered by the decision maker. As a general entropy with fuzziness, fuzzy Harvda-Charvat entropy is introduced, which is a natural extension of fuzzy Shannon entropy. In addition, qualitative and subjective evaluations based on the pairwise comparison are introduced to represent the differences between two membership values. The main step of our revised approach is to solve the proposed mathematical programming problem strictly using nonlinear programming. In this paper, the given membership function is assumed to be a piecewise linear membership function as approximation of nonlinear functions, and each intermediate value of partial linear function is optimally obtained.

To expand the use of renewable energy, it is necessary to optimize energy production at a local level through an appropriate combination of different renewable energy resources. Additionally, the environmental impacts from the use of renewable resources must be considered from different perspectives. Thus, this study aims to develop a decision tool that evaluates and optimizes the renewable energy mix at a regional scale with regard to various environmental impacts. This tool was developed by creating a municipal energy database that includes five renewable energies (solar, wind, small- and medium-scale hydro, geothermal and biomass energy) and six evaluation indicators (proportion of developed renewable energy, economic balance, installed wind power, decrease in CO2 emissions, circulation rate of biomass resource, and impacted ecosystem area). Specifying different constraints in the model allowed investigation of the optimal renewable energy combination in a study area for two different scenarios, with the results highlighting the trade-offs between the scenarios. We also optimized the combination of different renewable energies for every municipality across Japan, while incorporating the natural conditions and varying demand structure. In conclusion, the tool developed in this study could support decision-making regarding the development of renewable energy resources. (C) 2016 Elsevier Ltd. All rights reserved.

This paper proposes an objective approach to the construction of an appropriate membership function that extends to our previous studies. It is important to set a membership function with subjectivity and objectivity to obtain a reasonable optimal solution that complies with the decision maker's feelings in real-world decision making. To ensure objectivity and subjectivity of the obtained membership function, an entropy-based approach based on mathematical programming is integrated into the interval estimation considered by the decision maker. Fuzzy Harvda-Charvat entropy, which is a natural extension of fuzzy Shannon entropy, is introduced as general entropy with fuzziness. The main steps of our proposed approach are to set intervals with membership values 0 and 1 to enable a decision maker to judge confidently, and to solve the proposed mathematical programming problem strictly using nonlinear programming. In this paper, the given membership function is assumed to be a piecewise linear membership function as an approximation of nonlinear functions, and each intermediate value of partial linear function is optimally obtained.

This paper proposes an extended approach to construct an appropriate membership function as objectively as possible. It is important to set an appropriate membership function to obtain a reasonable optimal solution for real-world decision making. The main academic contribution of our proposed approach is to integrate a general continuous and nonlinear function minimizing the subjectivity into an interval estimation by a heuristic method under a given probability density function based on real-world data. Our approach is an extend approach of Civanlar and Trussell's study. One of two main steps of our proposed approach is to set membership values which a decision maker confidently judges whether an element is included in the given set or not. Another is to obtain other values objectively by solving Civanlar and Trussell's mathematical programming problem with a nonlinear membership function. In this paper, the given membership function is approximately transformed into a piecewise linear membership function, and the appropriate values of parameters in the piecewise linear membership function are determined.

This paper proposes a route recommendation system for sightseeing based on a network optimization problem. Sightseeing route planning is not difficult if a tourist initially sets satisfaction values of sightseeing spots numerically. However, it was hard to evaluate the satisfaction values objectively according to the tourist's feelings. The tourist can subjectively do a qualitative and pairwise comparison of sightseeing plans which tourism companies provide. Our proposed approach is to formulate a mathematical programming problem with constraints based on the tourist's comparison and to determine the satisfaction values of sightseeing spots objectively. Our proposed approach can deal with the synergy effect among sightseeing spots. In addition, the framework of personal sightseeing route planning system is proposed.

This paper proposes a strict constructing approach for a reasonable membership function as objectively as possible. It is important to set a reasonable membership function to parameters for real-world decision making interactively and objectively. The main contribution of our proposed approach is to integrate a general continuous function derived from mathematical programming under a given probability density function based on real-world data into subjective interval estimation by a heuristic method. The interval estimation is to set intervals that a decision maker confidently judges whether an element is completely or never included in the given set. The main steps of our proposed approach are to solve the mathematical programming problem in terms of objectivity. It is hard to solve the problem with nonlinear function directly and efficiently. In this paper, the given nonlinear membership function is approximately transformed into a piecewise linear membership function, and the appropriate membership values are determined based on the strict optimal solution.

This paper proposes a framework to recommend personal sightseeing route as well as to objectively obtain the tourist's utility to sightseeing plans and sightseeing spots from subjective comparison. The subjective comparison is qualitatively performed using a scale of measurement such as Likert scale, and the mathematical programming problem including this comparison as constraints is introduced. In the case of route planning, traveling and sightseeing times are randomly changed dependent on current traffic and congestion conditions, and hence, Time-Expanded Network (TEN) to represent these traffic conditions in the underlying static network with each discrete time step is introduced. In addition, the network optimization problem is introduced to obtain the personal appropriate sightseeing route. This problem is formulated as a nonlinear and discrete optimization problem, and it is hard to solve it directly and efficiently. Therefore, an efficient algorithm is also developed based on dynamic programming and transformation of the main problem into the recursive equation.

Hiroshima City is surrounded by mountains on its three sides, the east, north, and west, except the south facing the sea, and besides, its urban area places delta region. For this reason, the population of Hiroshima City is concentrated in the slope residential estates at the surrounding mountains of the city. However, the living environment of the suburban slope residential estates doesn't seem so suitable for vulnerable road users, mainly elderly people. Thus in this paper, based on the traffic attitude survey results for residents in the slope residential estates at Itsukaichi district, Hiroshima City, previously conducted by our previous works, we examine an effective way to support vulnerable road users and to enrich their life. Especially, we develop a prototype system to support the transportation for residents living in a place where public transportation is not sufficiently developed.

There are many problems in Japanese agriculture, and the most critical thing among these is a rapid decrease in the working population due to a growing proportion of elderly people. The cause of the aging in the agricultural field would be small incomes due to the low agricultural productivity. To improve the income level, the authors have developed an information sharing system of food production, marketing, and consumption, named food CMS (Contents Management System). Food CMS aims to promote proper management of food resources in the whole food supply chain. The types of users in Food CMS are farmers, customers, and distributors including retailing stores, brokers, and restaurants, so Food CMS has the capability to give benefits appropriate to the types of users. Concretely, Food CMS provides services such as the direct relationship-building between a customer and a producer, sales opportunity with e-commerce, freshness management of foods, and rationalization of the order placement and acceptance work between distributors. Since the integrated database of Food CMS can store all distribution data of foods, the data will contribute to adjusting the supply to demand and reducing the food loss. This paper shows the effort the authors have addressed, especially the functional design of Food CMS, and the performance.

This paper proposes an interactive approach to obtain an appropriate sightseeing route for the tourist under various uncertain traffic and climate conditions including time-dependent parameters and ambiguous satisfaction values at sightseeing sites. Since the uncertain traffic and climate conditions include time-dependent conditions, Time Expanded Network (TEN) are proposed for each condition. Furthermore, interval numbers for ambiguous satisfaction values are proposed, and hence, the proposed model is formulated as a multiobjective interval programming problem with many constraints derived from network optimization. In order to transform the multiobjective into the single-objective, Minkowski's Lp-metric is introduced as a compromise approach. From the final formulation of our proposed model using the optimistic satisfactory for interval numbers, an interactive algorithm to obtain the appropriate sightseeing route communicating with the tourist is developed.

This paper proposes a route recommendation system for sightseeing based on a network optimization problem. Traveling and sightseeing times are randomly changed dependent on current traffic and congestion conditions, and hence, Time-Expanded Network (TEN) to contain a copy to the set of nodes in the underlying static network for each discrete time step is introduced. In addition, in order to select the next sightseeing site, conditional probabilities are introduced, which are calculated by current conditions, statistical and Web data. Our proposed model is formulated as a nonlinear and discrete optimization problem, and it is hard to solve it directly and efficiently. Therefore, an efficient algorithm is also developed based on dynamic programming and transformation of the main problem into the recursive equation.

This paper proposes a constructing algorithm for an appropriate membership function to integrate the fuzzy Shannon entropy with a piecewise linear function into subjective intervals estimation by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in real-world decision making. The main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the initial mathematical programming problem efficiently using previous constructing approaches. In this paper, introducing some natural assumptions in the real-world and performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each appropriate membership value is developed. (C) 2015 The Authors. Published by Elsevier B.V.

This paper develops a constructing algorithm for an appropriate membership function as objectively as possible. It is important to set an appropriate membership function for real-world decision making. The main academic contribution of our proposed algorithm is to integrate a general continuous and nonlinear function with fuzzy Shannon entropy into subjective interval estimation by a heuristic method under a given probability density function based on real-world data. Two main steps of our proposed approach are to set membership values a decision maker confidently judges whether an element is included in the given set or not and to obtain other values objectively by solving a mathematical programming problem with fuzzy Shannon entropy. It is difficult to solve the problem efficiently using previous constructing approaches due to nonlinear function. In this paper, the given nonlinear membership function is approximately transformed into a piecewise linear membership function, and the appropriate values are determined. Furthermore, by introducing natural assumptions in the real-world and interactively adjusting the membership values, an algorithm to obtain the optimal condition of each appropriate membership value is developed. (C) 2015 The Authors. Published by Elsevier B.V.

This paper proposes a sightseeing route planning problem by electric vehicle with time-dependency of traveling times between any two sightseeing sites. In order to represent the time-dependency, Time-Expanded Network (TEN), which contains a copy to the set of nodes in the underlying static network for each discrete time step, is introduced. In addition, it is hard for the tourist to set satisfaction values at sightseeing sites numerically, but it is not difficult to classify sightseeing sites into several groups. Therefore, the objective function of our proposed model is set to maximize the total visiting sightseeing sites in each group. The problem is a multiobjective programming problem, and hence, a principle of compromise is introduced to solve our proposed problem in network optimization. Furthermore, the main constrained network optimization problem is equivalently transformed into a recursive equation, and an exact and greedy algorithm is developed.

Solving transportation problems is essential in engineering and supply chain management, where profitability depends on optimal traffic flow. This study proposes risk-control approaches for two bottleneck transportation problems with random variables and preference levels to objective functions with risk parameters. Each proposed model is formulated as a multiobjective programming problem using robust-based optimization derived from stochastic chance constraints. Since it is impossible to obtain a transportation pattern that optimizes all objective functions, our proposed models are numerically solved by introducing an aggregation function for the multiobjective problem. An exact algorithm that performs deterministic equivalent transformations and introduces auxiliary problems is also developed.

This paper proposes a route planning problem for sightseeing with fuzzy random variables for traveling times and satisfaction of sightseeing activities under general sightseeing constraints and various conditions. In general, traveling times among sightseeing places and satisfactions of activities depend on weather and climate conditions. Furthermore, the satisfactions also depend on the tourist's tiredness. Therefore, not only fuzzy random variables for traveling times and satisfactions but also the tiredness-dependency is introduced. In addition, the tourist will like to do a route planning without drastically changing from the optimal route to each condition. A route planning problem is proposed to obtain the favorable common route supplying target satisfactions under various conditions. As a basic case of fuzzy numbers, trapezoidal fuzzy numbers and the order relation are introduced. From the order relation, the proposed model is transformed into an extended model of network optimization problems.

This paper proposes a new approach of constructing an appropriate membership function to integrate a specific given probability density function, particularly Gaussian function, and fuzzy Shannon entropy extending the information theory based on the human cognitive behavior and subjectivity. The proposed approach is formulated as a more general mathematical programming problem than previous approaches due to using a general Gaussian-based function and the fuzzy Shannon entropy. The optimal condition of parameters is obtained by performing deterministic equivalent transformations to the initial problem. Furthermore, in order to show the appropriate membership function using the proposed approach, some probability density functions are provided as numerical examples. © 2014 ICIC International.

This paper proposes a mathematical model of multi-period food supply chain optimization maximizing the total profit based on the data-driven approach from the information system. Our propose model is focused on accommodating surplus foods among stores in a regional area. Our proposed model is formulated as a stochastic programming problem. With respect to a previous model, the explicit optimal ordering quantity at each time slot is obtained. However,it is hard to solve the formulated problem directly. Therefore, a scenario-based approach derived from POS data using the information system and deterministic equivalent transformations are introduced to apply our proposed model.

This paper proposes a multiobjective portfolio selection problem with most probable random distribution derived from current market data and other random distributions of boom and recession under the risk-controlled parameters determined by an investor. The current market data and information include not only historical data but also interpretations of economists' oral and linguistic information, and hence, the boom and recession are often caused by these nonnumeric data. Therefore, investors need to consider several situations from most probable condition to boom and recession and to avoid the risk less than the target return in each situation. Furthermore, it is generally difficult to set random distributions of these cases exactly. Therefore, a robust-based approach for portfolio selection problems using the only mean values and variances of securities is proposed as a multi objective programming problem. In addition, an exact algorithm is developed to obtain an explicit optimal portfolio using a principle of compromise.

This paper proposes a sightseeing route planning problem with time-dependent traveling times among sightseeing sites. Since traveling times are dependent on the time of day, Time-Expanded Network (TEN), which contains a copy to the set of nodes in the underlying static network for each discrete time step, is introduced. In addition, it is hard to set satisfaction values at sightseeing sites numerically due to tourist's ambiguous sensitivity, but it is not difficult to classify sightseeing sites into several groups by the tourist. Therefore, the objective function of our proposed model is set to maximize the total visiting sightseeing sites in each group. The problem is a multiobjective programming problem, and hence, a principle of compromise is introduced to solve our proposed problem in network optimization. Furthermore, a strict algorithm is also developed to equivalently transform the main problem into the existing TEN-based problem.

This paper develops a constructing approach of a membership function to integrate the fuzzy Shannon entropy with a smoothing function into intervals set by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in decision making. Therefore, the main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the problem efficiently using previous constructing approaches. In this paper, performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each membership value is developed.

This paper considers a robust portfolio selection problem with an uncertainty set of future returns and satisfaction levels in terms of the total return and robustness parameter. Since the proposed model is formulated as an ill-defined problem due to uncertainty and is bi-objective, that is, to maximize both the abovementioned satisfaction levels, it is difficult to solve the model directly without introducing some criterion of optimality for the bi-objective functions. Therefore, by introducing fuzzy goals and an interactive fuzzy satisficing method, the proposed model is transformed into a deterministic equivalent problem. Furthermore, to obtain the exact optimal portfolio analytically, a solution method is developed by introducing the auxiliary problem and performing equivalent transformations. In order to compare the proposed model with previous useful models, numerical examples are provided, and the results show that it is important to maximize the robustness parameter and total return using the interactive process for adjusting investor's satisfaction levels.

This paper considers inventory problems for perishable or deteriorating products to maximize the total profit considering high- and low-priority customers based on the conditional Value-at-Risk (cVaR). The cVaR is a useful risk measure in economics and finance, which satisfies all requirements of ideal risk measures such as coherence and stochastic dominance. In order to apply random sampling derived from known distributions or historical data to our proposed model and to develop an analytical and efficient solution algorithm, the scenario-based solution algorithm is developed by performing equivalent transformations into a linear programming problem. Furthermore, numerical examples are provided to compare our proposed model with the previous standard model based on the expected value for the total profit. Furthermore, the results also show differences from the previous cVaR-based model with only one demand under some random distributions.

This paper deals with a minimum spanning tree problem where each edge cost includes uncertainty and importance measure. In risk management to avoid adverse impacts derived from uncertainty, a d-confidence interval for the total cost derived from robustness is introduced. Then, by maximizing the considerable region as well as minimizing the cost-importance ratio, a biobjective minimum spanning tree problem is proposed. Furthermore, in order to satisfy the objects of the decision maker and to solve the proposed model in mathematical programming, fuzzy goals for the objects are introduced as satisfaction functions, and an exact solution algorithm is developed using interactive decision making and deterministic equivalent transformations. Numerical examples are provided to compare our proposed model with some previous models. (C) 2012 Elsevier Inc. All rights reserved.

This paper proposes a model for a robust shortest path problem with random edge costs. The proposed model is formulated as a bicriteria optimization problem to minimize the total cost of the path from a start node to an end node as well as to maximize the range of the confidence interval satisfying the condition that the total cost of any path in the region is less than a target value in terms of robustness. It is not always the case that a solution that simultaneously optimizes all of the objectives exists when the objectives conflict with each other. In this paper, fuzzy goals for both objectives and the aggregation function are introduced in a solution approach that considers the decision maker's preference and the subjectivity of her or his judgment in multicriteria decision making. The fuzzy bicriteria problem is transformed into a constrained shortest path problem. Furthermore, an exact algorithm based on Dijkstra's algorithm and a heuristic algorithm based on the Lagrange relaxation-based algorithm are developed for the constrained shortest path problem. (C) 2012 Elsevier Inc. All rights reserved.

This paper considers a robust-based random fuzzy mean-variance portfolio selection problem using a fuzzy reasoning method, particularly a single input type fuzzy reasoning method. Arbitrage Pricing Theory (APT) is introduced as a future return of each security, and each factor in APT is assumed to be a random fuzzy variable whose mean is derived from a fuzzy reasoning method. Furthermore, under interval inputs of fuzzy reasoning method, a robust programming approach is introduced in order to minimize the worst case of the total variance. The proposed model is equivalently transformed into the deterministic nonlinear programming problem, and so the solution steps to obtain the exact optimal portfolio are developed. © 2013 Springer Science+Business Media Dordrecht.

This paper proposes a tour route planning problem to flexibly reschedule the initial route plan with uncertain traveling times and satisfaction values of sightseeing places dependent on sightseeing. The objective of our proposed model is to maximize the total satisfaction value in all possible conditions after visiting a sightseeing place under such time-dependent parameters. Since traveling times are dependent on the time of day, it is hard to represent our proposed model using the general static network model. In this paper, Time-Expanded Network (TEN), which contains a copy to the set of nodes in the underlying static network for each discrete time step, is introduced. Using the proposed TEN-based model, it is possible to construct various types of tour route planning problems in a single static network. Furthermore, a 0-1 mixed integer programming problem is formulated to the above-mentioned objective, and the strict algorithm is also developed to equivalently transform the main problem into the existing TEN-based problem.

This paper proposes a versatile and interactive route planning problem for sightseeing under various conditions based on constraints of required traveling times and total satisfaction of sightseeing activities, which are time-dependent. In general, traveling times among sightseeing places and the satisfactions of activities also change dependent on various conditions such as weather, climate and season. It is important to represent a satisfying route to ensure the large satisfaction even if any assumable condition happens. In order to incorporate the above-mentioned situations, a multi-objective route planning problem is formulated as a network optimization problems based on Time-Expanded Network to represent time-dependent parameters in a static network. Furthermore, an interactive approach based on the Satisficing Trade-Off Method is introduced to transform the multi-objective into the single. In addition, the proposed problem is equivalently transformed into an extended model of network optimization problems by introducing parameters, and the interactive algorithm is developed. (C) 2013 The Authors. Published by Elsevier B.V.

This paper proposes a personal tour planning problem with uncertain traveling times and satisfaction values of sightseeing places dependent on sightseeing. Since traveling times are dependent on the time of day, it is difficult to represent this uncertain model using the general static network model. In this paper, Time-Expanded Network (TEN), which contains a copy to the set of nodes in the underlying static network for each discrete time step, is introduced. Using the proposed TEN-based model, it is possible to construct various variations of traveling times and satisfactions values of sightseeing places in a single static network Furthermore, uncertain sightseeing times are represented as fuzzy variables and the proposed model is formulated as a fuzzy 0-1 mixed integer programming problem, and also equivalently transformed into several existing tour planning problems using some natural assumptions in fuzzy programming.

This paper proposes an approach to analyze the tourism information and data derived from the Web, particularly seat availability data of bullet trains in Japan, and to discover some useful knowledge for the tourism. For the fast development of information and communication technologies, the relation between the web data and tourism is inseparable. However, the Web data include various types of information such as numerical, linguistic, and graded data. Furthermore, the expert tourism planner's subjectivity is also an important factor to develop new favorable plans. A simplified fuzzy reasoning method, which is one of the useful approaches in Data mining, is introduced in order to deal with these data mathematically. The analysis of the tourism data and the knowledge discovery are performed using actual data of bullet trains in Japan.

This paper proposes an extended analytical approach to developing an equilibrium pricing vector with various types of investor's subjectivity based on extended Mean-Variance (MV) theory. Weighted fuzzy mean and variance are introduced in order to represent investor's subjectivity numerically. Similar to the traditional MV-based equilibrium approach, the equilibrium pricing vector of the proposed model is analytically obtained in mathematical programming. A macroeconomic index based on risky assets, which provides information with respect to the soundness of the capital market with subjectivity, is also constructed.

This paper considers a minimum spanning tree problem under the situation where costs for constructing edges in a network include both fuzziness and randomness. In particular, this article focuses on the case that the edge costs are expressed by random fuzzy variables. A new decision making model based on a possibility measure and a value at risk measure is proposed in order to find a solution which fully reflects random and fuzzy information. It is shown that an optimal solution of the proposed model is obtained by a polynomial-time algorithm. (C) 2012 Elsevier Ltd. All rights reserved.

This paper considers several portfolio selection problems considering Socially Responsible Investment (SRI), which is the most important measure to sustain continuous developments of companies by performing environment-friendliness and suitable social activity, and which is also essential for avoiding the latent risk. Corporate Social Responsibility (CSR) is presented as linguistic and ambiguous information including several types of subjectivities, and so effects of SRI activities for the investment based on the CSR are formulated as fuzzy numbers. Furthermore, several types of portfolio models, considering direct evaluation approach of SRI, fuzzy variance including SRI, and biased future return derived from random simulation, are proposed. In order to evaluate these portfolio performances, a practical example derived from the current market is provided.

This paper considers a DEA-based model of technical and cost efficiencies with fuzziness. Previous studies of fuzzy DEA model in terms of cost efficiency had critical shortcoming if the unit prices of the inputs are not identical across DMUs in the economy. Therefore, in this paper, a new fuzzy model is proposed by extending the revised scheme of DEA -based cost efficiency that is free from such inconsistencies. The proposed model is a fuzzy programming problem, and so introducing order relations of fur y inequalities, it is equivalently transformed into a linear programming problem. Furthermore, comparing the proposed model with the original model, a numerical example derived from hospital data is provided.

We model for 'Naiji System' which is a unique corporation technique between a manufacturer and suppliers in Japan. We propose a two stage solution procedure for a production planning problem with advance demand information, which is called 'Naiji'. Under demand uncertainty, this model is formulated as a nonlinear stochastic programming problem which minimizes the sum of production cost and inventory holding cost subject to a probabilistic constraint and some linear production constraints. By the convexity and the special structure of correlation matrix in the problem where inventory for different periods is not independent, we propose a solution procedure with two stages which are named Mass Customization Production Planning & Management System (MCPS) and Variable Mesh Neighborhood Search (VMNS) based on meta-heuristics. It is shown that the proposed solution procedure is available to get a near optimal solution efficiently and practical for making a good master production schedule in the suppliers.

This paper considers a robust-based random fuzzy mean-variance portfolio selection problem using a fuzzy reasoning method, particularly a single input type fuzzy reasoning method. Capital Asset Pricing Model is introduced as a future return of each security, and the market portfolio is assumed to be a random fuzzy variable whose mean is derived from a fuzzy reasoning method. Furthermore, under interval inputs of fuzzy reasoning method, a robust programming approach is introduced in order to minimize the worst case of the total variance. The proposed model is equivalently transformed into the deterministic nonlinear programming problem, and so the solution steps to obtain the exact optimal portfolio are developed.

This paper considers a new risk-control and management approach for a bottleneck spanning tree problem under the situation where edge costs in a given network include randomness and reliability. Particularly, this paper focuses on the case that only mean value and variance of edge costs are calculated without assuming a specific random distribution. In order to develop the risk control approach, a confidence interval-based formulation is introduced. Using this interval, as well as minimizing the maximum value of worse edge costs, maximizing the minimum value of robust parameters to edge costs is introduced as objective functions in the risk-control. Furthermore, in order to maintain the constructing spanning tree network entirely, the reliability for each edge is introduced, and maximizing the total reliability of spanning tree is assumed as the third objective function. The proposed model is a multiobjective programming problem, and hence, it is difficult to solve it directly without setting some optimal criterion. Therefore, satisfaction functions for each object and the integrated function are introduced, and the exact solution algorithm is developed by performing deterministic equivalent transformations. A numerical example is provided by comparing our proposed model with previous standard models.

This paper considers an entropy model of portfolio selection problem with fuzzy random variables to future returns. Since standard mean-variance portfolio models suffer from some shortcomings, the entropy is introduced as a risk measure instead of variances to overcome the shortcomings. Furthermore, introducing the sum of entropy to each portfolio as well as the entropy of fuzzy random variables, the previous entropy-based fuzzy random portfolio selection problem is extended, the exact optimal portfolio is explicitly obtained using nonlinear programming such as Karush-Kuhn-Tucker condition.

This paper proposes a route planning problem for sightseeing with fuzzy random variables based on constraints of required traveling times and satisfactions of the total sightseeing activity. In general, traveling times among sightseeing places and the satisfactions of activities depend on weather and climate conditions. Tourists will like to do their favorable route planning without drastically changing the tour route of usual condition such as fine even if the weather condition changes for the worse. Therefore, the fuzzy random variables for traveling times and satisfactions of activities derived from uncertainty conditions are introduced, and a new route planning problem is proposed to obtain the favorable route similar to the optimal route under the usual condition. As a basic case of fuzzy numbers, interval values and the order relation are introduced. From the order relation, the proposed model is transformed into an extended model of network optimization problems. A numerical example is provided to compare the proposed model with standard route planning problems for sightseeing.

This paper proposes a robust-based mean-variance portfolio selection problem with random fuzzy returns using a fuzzy reasoning method, particularly a standard TS fuzzy reasoning method. Arbitrage Pricing Theory (APT) is introduced as a future return of each security, and each factor in APT is assumed to be a random fuzzy variable whose mean is derived from a fuzzy reasoning method. Furthermore, under interval inputs of fuzzy reasoning method, a robust programming approach is introduced in order to minimize the worst case of the total variance. The proposed model is equivalently transformed into the deterministic nonlinear programming problem, and so the solution steps to obtain the exact optimal portfolio are developed.

This paper proposes a versatile route planning problem for sightseeing with fuzzy random variables based on constraints of required traveling times and total satisfaction of sightseeing activities. In general, traveling times among sightseeing places and the satisfactions of activities depend on weather and climate conditions. Furthermore, the satisfactions of activities are also dependent on the tourist's fatigue degree. Therefore, the fuzzy random variables for traveling times and satisfactions of activities dependent on the fatigue degree under uncertainty are introduced. Tourists will like to do their favorable route planning without drastically changing the tour route of usual condition such as fine even if the weather condition changes for the worse. A new route planning problem is proposed to obtain the favorable route similar to the optimal route under the usual condition. As a basic case of fuzzy numbers, interval values and the order relation are introduced. From the order relation, the proposed model is transformed into an extended model of network optimization problems. A numerical example is provided to compare the proposed model with standard route planning problems for sightseeing.

This paper develops a new constructing approach of an appropriate membership function to integrate a given probability density function and fuzzy Shannon entropy extending the statistical theory into the heuristic method based on the human cognitive behavior and subjectivity. The proposed approach is formulated as a more general mathematical programming problem than previous approaches due to using a general S-curve function and the fuzzy Shannon entropy. Then, performing deterministic equivalent transformations to the initial problem, the optimal condition of parameters is obtained. Furthermore, in order to show the appropriate membership function using the proposed approach, some probability density functions are provided as numerical examples.

This paper deals with a minimum spanning tree problem where each edge weight is a fuzzy random variable. In terms of risk management in order to avoid adverse impacts derived from uncertainty, conditional Value-at-Risk including a necessity measure for fuzziness is introduced as a risk measure. Furthermore, by performing the deterministic equivalent transformation, the proposed problem is transformed into an existing minimum spanning tree problem to apply polynomialtime algorithms, and a solution algorithm is developed to solve the proposed problem. © 2011 IEEE.

This paper considers a shortest path problem with interval costs for directed arcs and reliability for networks, and proposes a bi-objective interval shortest path problem. The proposed model is not well-defined due to interval costs, and so the deterministic constrained shortest path problem is obtained by introducing the order relation of interval values. In order to solve this bi-objective problem, a solution algorithm based on interactive fuzzy satsificing method in terms of multi-objective programming is developed. © 2011 IEEE.

This paper considers a robust portfolio selection problem considering a confidence interval with subjectivity to the weight for the standard deviation. Since the proposed model is formulated as an ill-defined problem due to fuzziness and bi-object derived from maximizing both robustness and investor's satisfaction level to the total profit, it is hard to solve it directly. Therefore, introducing fuzzy goals for the bi-objective functions, the proposed model is transformed into the deterministic equivalent problem. Furthermore, in order to obtain the exact optimal portfolio analytically, the solution method is developed introducing a parameter and doing the equivalent transformations.

This paper considers a fuzzy DEA-based model of technical and cost efficiencies with a ranking function. Previous studies of fuzzy DEA model in terms of cost efficiency had critical shortcoming if the unit prices of the inputs are not identical across DMUs in the economy. Therefore, in this paper, a new fuzzy model is proposed by extending the revised scheme of DEA-based technical and cost efficiencies that are free from such inconsistencies. The proposed model is a fuzzy programming problem, and so introducing a ranking function for fuzzy inequalities, it is equivalently transformed into a linear programming problem. Furthermore, comparing the proposed model with the original model, a numerical example derived from hospital data is provided. © 2011 IEEE.

This chapter considers various types of risk-management models based on the portfolio theory under some social uncertainty that received historical data includes ambiguity, and that they are assumed not to be constant. These models with uncertainty are represented many social problems such as assets allocation, logistics, scheduling, urban project problems, etc. However, since these problems with uncertainty are formulated as stochastic and fuzzy programming problems, it is difficult to solve them analytically in the sense of deterministic mathematical programming. Therefore, introducing possibility and necessity measures based on the fuzzy programming approach and considering the concept of risk-management based on the portfolio theory, main problems are transformed into the deterministic programming problems. Then, in order to solve the deterministic problems efficiently, the solution method is constructed. © 2010, IGI Global.

This paper considers the optimal production decision considering Corporate Social Responsibility (CSR) in the supply chain. CSR is currently the most important measure to sustain continuous developments of companies by performing environment-friendliness and suitable social activity, and it is also essential for avoiding the latent risk. In this paper, we consider the evaluation of environmental conservation activities and resource recycling as CSR activities, and propose a new optimal production policy based on CSR. In mathematical programming, these CSR activities are formulated as fuzzy numbers due to linguistic and ambiguous information including several types of subjectivities, and so our proposed model is formulated as an uncertainty programming problem with both randomness and fuzziness. Therefore, performing deterministic equivalent transformations and considering the application in practice, the analytical and effective solution algorithm is developed.

This paper considers a fuzzy random shortest path problem and proposes a new risk measure to synthesize both stochastic conditional Value at Risk and credibility measure for fuzziness. The proposed model defined by the hybrid conditional Value at Risk is equivalently transformed into a 0-1 mixed integer programming problem. In order to this problem analytically and efficiently, the Lagrange 0-1 relaxation problem using the property of totally unimodular and proposed the efficient solution algorithm based on the hybrid algorithm of standard Dijkstra algorithm and subgradient method. © 2010 IEEE.

This paper considers a portfolio selection problem considering an investor's subjectivity and the sensitivity analysis for the change of subjectivity. Since this proposed problem is formulated as a random fuzzy programming problem, it is not well-defined due to randomness and fuzziness. Therefore, introducing Sharpe ratio which is one of important performance measures of portfolio models, the main problem is transformed into the standard fuzzy programming problem. Furthermore, using the sensitivity analysis for fuzziness, the analytical optimal portfolio with the sensitivity factor is obtained.http://www.iaeng.org/publication/IMECS2010/IMECS2010_pp2186-2190.pdf

This paper focuses on the proposition of a portfolio selection problem considering an investor's subjectivity and the sensitivity analysis for the change of subjectivity. Since this proposed problem is formulated as a random fuzzy programming problem due to both randomness and subjectivity presented by fuzzy numbers, it is not well-defined. Therefore, introducing Sharpe ratio which is one of important performance measures of portfolio models, the main problem is transformed into the standard fuzzy programming problem. Furthermore, using the sensitivity analysis for fuzziness, the analytical optimal portfolio with the sensitivity factor is obtained.

This paper considers two-level linear programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. A new decision making model is proposed in order to maximize both of possibility and probability with respect to the objective function value. After the original random fuzzy two-level programming problem is reduced to a deterministic one through the proposed model, interactive programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented.

This chapter considers some versatile portfolio selection models with general normal mixture distributions and fuzzy or interval numbers. Then, these mathematical approaches to obtain the optimal portfolio are developed. Furthermore, in order to compare our proposed models with standard models and represent the advantage of our proposed models, a numerical example is provided. © 2010 Springer-Verlag Berlin Heidelberg.

This paper considers single-period inventory models with fuzzy shortage costs dependent on discrete and continuous random demands considering the close relation between consumer's demands and shortage costs. Since these inventory models include randomness and fuzziness, they are formulated as fuzzy random programming problems. Then, in order to deal with the uncertainty and find the optimal order quantity analytically, the solution approach is proposed using Yager's ranking method with respect to the total expected future profit, and the strict solution is obtained. Furthermore, in order to compare with previous inventory models, basic random variables and fuzzy numbers are introduced, and differences between our proposed models and previous models are discussed.

This paper considers a new equilibrium pricing vector with various types of investor's subjectivity based on the standard Mean-Variance theory. In order to present each investor's subjectivity, the fuzzy theory is introduced. In a way similar to the traditional MV-based equilibrium approach, the analytical equilibrium pricing vector is obtained using the degree of credibility considering credibility measure and fuzzy goal. Furthermore, a macroeconomic index based on risky assets, which provides information with respect to the soundness of the capital market with the subjectivity, is constructed.

This paper considers a multi-criteria mathematical decision model including fuzzy variables. As the proposed model is not well-defined due to fuzzy variables, thus to solve them directly and analytically, the possibility measure is introduced. Then, in order to aggregate the multi-criteria objective functions into the single-criterion, the fuzzy compromise programming model is proposed. Furthermore, by introducing the interval of each weight to the objective functions, the proposed model is reformulated as a robust programming problem. Since this problem is a semi-infinite programming problem, the an efficient algorithm. is developed using the linearity of the proposed model. Finally, a numerical example is provided to compare proposed models with the basic model.

This paper considers several portfolio selection problems including probabilistic future returns with ambiguous expected returns assumed as random fuzzy variables. Random fuzzy portfolio selection problems are formulated as nonlinear programming problems based on both stochastic and fuzzy programming approaches Since there is no efficient solution method to solve these problems directly, main problems are transformed into equivalent deterministic quadratic programming problems using probabilistic chance constraints, possibility measure and fuzzy goals, and their efficient solution methods to find a global optimal solution of each problem is constructed. Furthermore, numerical examples of portfolio selection problems are provided to illustrate our proposed models and solution methods compared with several previous basic models and to show that our proposed model is a versatile model to be applicable to various unexpected conditions. (C) 2008 Elsevier B.V. All rights reserved.

This paper considers several models of product-mix decision problems and production planning problems under uncertain conditions, and shows that these are extensional and versatile models for resolving previous product-mix problems. These proposed models include randomness derived from statistical analysis based on historical data, ambiguity of decision maker's intuition and the quality of received information, and flexibility in accomplishing the original plan. Furthermore, given that the upper limit values of some constraints have flexibility, and given a decision maker's level of satisfaction, we propose a flexible product mix of problems using the theory of constraints (TOC), and develop an efficient solution method. We then provide a numerical example that compares our models with some previous basic models. Efficiency of flexibility is obtained when our proposed models are applied to several conditions, such as measurable changes from the expected value Of future returns. (C) 2008 Elsevier Ltd. All rights reserved.

This paper considers safety first models with respect to portfolio selection problems, particularly using the multi-scenario for the future return of each asset including ambiguity. Then, the fuzzy extensions for safety first models are proposed. These models are generally formulated as stochastic and fuzzy programming problems. Since they are not well-defined problems due to random and fuzzy variables and it is difficult to solve them directly and analytically, introducing the probability and possibility chance constraints, they are equivalently transformed into 0-1 mixed linear programming problems and the efficient solution methods are constructed. Furthermore, a numerical example of Portfolio selection problem is provided to compare proposed models with the basic model.

This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers' predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model.

This paper considers product mix problems including randomness of future returns, ambiguity of coefficients and flexibility of upper value with respect to each constraint such as budget, human resource, time and several costs. Particularly, the flexibility is assumed to be a fuzzy goal. Then, several models based on maximizing total future profits under a level of satisfaction to each fuzzy goal are proposed. Furthermore, the model considering preference ranking to each fuzzy goal of constraints is proposed. Since these problems are basically formulated as nonlinear programming problems, the transformations into deterministic equivalent problems are introduced and the efficient solution methods are developed. A numerical example for product mix problem is given to illustrate our proposed models. (C) 2008 Elsevier Ltd. All rights reserved.

This paper considers a multi-period and multi-criteria product mix problem minimizing the total cost, maximizing the total profit and minimizing the inventory levels under various random and ambiguous conditions. The proposal model is an extended model including some standard product mix problems and the model integrating manufacturing and distribution planning decisions in supply chains, and it represents more complex situations in real world. Since this problem is not well-defined problem due to including random and fuzzy variables, it is hard to solve it directly. Therefore, introducing chance constraints, main problem is transformed into a nonlinear programming problem. Furthermore, for solving it more efficiently, the solution method using the mean absolute deviation is constructed and so it is easier to obtain an optimal solution than previous analytical solution procedures. © 2009 Taylor &amp
Francis Group, LLC.

This paper considers a general 0-1 random fuzzy programming problem based on the degree of necessity including some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not a well-defined problem due to including random fuzzy variables. Therefore, by introducing chance constraint and fuzzy goal for objective function, and considering the maximization for the degrees of necessity that the objective function value satisfies the fuzzy goal, main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed according to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed.

This paper considers an expectation optimization model using a possibility measure to the objective function in the fuzzy random programming problem, based on possibilistic programming and stochastic programming. The main fuzzy random programming problem is not a well-defined problem due to including random variables and fuzzy numbers. Therefore, in order to solve it analytically, a criterion for goal of objective function is set and the chance constraint are introduced. Then, considering decision maker's subjectivity and flexibility of the original plan, a fuzzy goal for each objective function is introduced. Furthermore, this paper considers that the occurrence probability of each scenario has ambiguity, and is represented as an interval value. Considering this interval of probability, a robust expectation optimization problem is proposed. Main problem is transformed into the deterministic equivalent linear programming problem, and so the analytical solution method extending previous solution approaches is constructed.

This paper considers robust programming problems based on the mean-variance model including uncertainty sets and fuzzy factors. Since these problems are not well-defined problems due to fuzzy factors, it is hard to solve them directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed models are transformed into the deterministic equivalent problems. Furthermore, in order to solve these equivalent problems efficiently, the solution method is constructed introducing the mean-absolute deviation and doing the equivalent transformations.

This paper considers a hi-criteria general 0-1 random fuzzy programming problem based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems The proposal problem is not well-defined due to including randomness and fuzziness Therefore, by introducing chance constraint and fuzzy goals for objectives, and considering the maximization of the aspiration level for total profit and the degree of necessity that the objective function's value satisfies the fuzzy goal, the main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed according to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed

Many researchers have proposed portfolio models based on the stochastic and fuzzy approaches until now, and there are some models considering both random and ambiguous conditions, particularly using fuzzy random or random fuzzy variables. However, few studies with multiobjective random fuzzy models for the portfolio selection problems have been performed. Therefore, a multiobjective random fuzzy portfolio selection problem based on CAPM, which is one of the most standard factor models, is proposed. In the sense of mathematical programming, our proposed problems are not well-defined problems due to randomness and fuzziness. Therefore, setting some criterions and introducing chance constrains, main problems are transformed into deterministic programming problems. Finally, we construct a solution method to obtain a global optimal solution of the problem.

This paper discusses a portfolio selection problem with type-2 fuzzy future returns involving interval numbers considering the investor's subjectivity. Since this proposed problem is not well-defined due to primary and secondary fuzziness, introducing the possibility measure that the total return is more than the target value, the main problem is transformed into the type-1 fuzzy programming problem with the interval value. Furthermore, using the hybrid solution approach based on the linearity of the deterministic equivalent problem and the interval programming problem, the efficient solution is constructed. In order to compare the proposed model with previous standard models, a numerical example derived from the current stock market is provided.

This paper considers a portfolio selection problem with type-2 fuzzy future returns involving ambiguous and subjectivity. Since this proposed problem is not well-defined due to fuzziness, introducing the fuzzy goal for the total future return and the degree of possibility, the main problem is transformed into the standard fuzzy programming problem including the secondary fuzzy numbers. Furthermore, using the hybrid solution approaches based on the linearity of the deterministic equivalent problem and the crisp possibilistic mean value, the efficient solution is constructed.

Two multiobjective random fuzzy programming problems considered based on the possibility maximization model using possibilistic and stochastic programming are not initially well defined due to the random variables and fuzzy numbers included. To solve them analytically, probability criteria are set for objective functions and chance constraints are introduced. Taking into account the decision maker's subjectivity and the original plan's flexibility, a fuzzy goal is introduced for each objective function. The original problems are then changed into deterministic equivalent problems to make the possibility fractile optimization problem equivalent to a linear programming problem. The possibility maximization problem for probability is changed into a nonlinear programming problem, and an analytical solution is constructed extending previous solution approaches.

This paper considers multi-criteria mathematical decision models with respect to portfolio selection problems, particularly multi-scenario models to the future return of each asset including ambiguity and the fuzzy extension of mean-variance model and mean-absolute deviation model. The proposed models are generally formulated as multi-criteria stochastic programming problems and fuzzy programming problems. Since they are not well-defined problems due to random and fuzzy variables and it is difficult to solve them directly and analytically, two cases with respect to proposed models are considered. Furthermore, introducing the possibility and necessity chance constraints, they am equivalently transformed into linear or quadratic programming problems and the efficient solution methods am constructed. Then, a numerical example of portfolio selection problem is given to compare proposal models with the basic model.

This paper considers a product mix problem both maximizing the total future profit and reducing excessive inventories including uncertainty with respect to future profits and customers' demands. Furthermore, since a decision maker has a goal with respect to the total future profit and each inventory of the product, in this paper, aspiration levels for them are also introduced. The proposal product mix problem is formulated as a multi-criteria programming problem considering maximizing all aspiration levels assumed to be fuzzy goals. Then, since each future return and customer's demand are assumed to be random variables, this problem including randomness is basically formulated as a multi-criteria stochastic programming problem. Since it is hard to solve it analytically, the transformations into deterministic equivalent problems are introduced and the efficient solution methods are constructed. © 2008 IEEE.

This paper considers robust mean-variance portfolio selection problems including uncertainty sets and fuzzy factors. Since these problems are not well-defined problems due to fuzzy factors, it is hard to solve them directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed models are transformed into the deterministic equivalent problems. Furthermore, since it is difficult to solve them analytically and efficiently due to nonlinear programming problems, the solution method is constructed introducing a parameter and doing the equivalent transformations.

This paper considers linear programming problems where each coefficient of the objective function is expressed by a random fuzzy variable. New decision making model am proposed based on stochastic and possibilistic programming in order to maximize both of possibility and probability with respect to the objective function value. It is shown that each of the proposed models is transformed into a deterministic equivalent one. Solution algorithms using convex programming techniques and/or the bisection method are provided for obtaining an optimal solution of each model.

This paper considers a new model of 0-1 knapsack problem including probabilistic coefficients with ambiguous expected returns assumed as random fuzzy variables. Since the random fuzzy 0-1 knapsack problem is not well-defined integer programming problem due to involve random fuzzy variables, it is hard to construct the efficient solution method to solve this problem directly. In this paper, using chance constraints, possibility measure and fuzzy goal based on both stochastic and fuzzy programming approaches, the main problem is transformed into a deterministic equivalent quadratic integer programming. Then, the efficient solution method to rind a strict optimal solution based on dynamic programming is constructed.

In this paper, we propose the solution method about the multiobjective portfolio selection problem, particularly the scenario model to include the ambiguous factors and chance constraints. Generally, mathematical programming problems with probabilities and possibilities are called to stochastic programming problem and fuzzy programming problem, and it is difficult to find its global optimal solution. In this paper, we manage to develop the efficient solution method to find its global optimal solution of such a problem introducing the some subproblems.

In this paper, two portfolio selection problems including probabilistic future returns with ambiguous expected returns are proposed. Until now, many researchers have proposed models of portfolio selection problems, and there are some models considering both random conditions and ambiguous conditions, particularly using fuzzy random variables. However, the model including the random fuzzy variables has not been proposed yet. Therefore in this paper, we propose a random fuzzy portfolio selection problem. The formulated problem is transformed into a nonlinear programming problem. Finally, we construct a solution method to find a global optimal solution of the problem.