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Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility

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FUZZY SETS AND SYSTEMS 2012年第1期188卷 45-57页

作者： Sakawa, Masatoshi Katagiri, Hideki Matsui, Takeshi Hiroshima Univ Grad Sch Engn Dept Cybernet Syst Higashihiroshima 7398527 Japan

This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods. (C) 2011 Elsevier B.V. All rights reserved.

关键词： two-level linear programming Fuzzy random variable Stackelberg solutions Possibility Necessity Probability maximization

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Interactive fuzzy stochastic two-level linear programming with simple recourse

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INFORMATION SCIENCES 2014年 278卷 67-75页

作者： Sakawa, Masatoshi Katagiri, Hideki Matsui, Takeshi Hiroshima Univ Fac Engn Dept Syst Cybernet Higashihiroshima 7398527 Japan

In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems involving random variables in constraints are considered. Using the concept of simple recourse, the formulated stochastic two-level simple recourse problems are transformed into deterministic two-level programming ones. Taking into account vagueness of judgments of the decision makers, interactive fuzzy programming is presented. In the proposed interactive method, after determining the fuzzy goals of the decision makers at both levels, a satisfactory solution is derived efficiently by updating the satisfactory degree of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. (C) 2014 Elsevier Inc. All rights reserved.

关键词： two-level linear programming Random variable Simple recourse Interactive fuzzy programming

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Stackelberg solutions for random fuzzy two-level linear programming through possibility-based probability model

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EXPERT SYSTEMS WITH APPLICATIONS 2012年第12期39卷 10898-10903页

作者： Sakawa, Masatoshi Matsui, Takeshi Hiroshima Univ Fac Engn Higashihiroshima 7398527 Japan

This paper considers computational methods for obtaining Stackelberg solutions to random fuzzy two-level linear programming problems. Assuming that the decision makers concerns about the probabilities that their own objective function values are smaller than or equal to certain target values, fuzzy goals of the decision makers for the probabilities are introduced. Using the possibility-based probability model to maximize the degrees of possibility with respect to the attained probability, the original random fuzzy two-level programming problems are reduced to deterministic ones. Extended concepts of Stackelberg solutions are introduced and computational methods are also presented. A numerical example is provided to illustrate the proposed method. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： two-level linear programming Random fuzzy variable Stackelberg solutions Possibility Probability maximization

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Fuzzy random non-cooperative two-level linear programming through fractile models with possibility and necessity

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ENGINEERING OPTIMIZATION 2013年第7期45卷 811-833页

作者： Sakawa, Masatoshi Matsui, Takeshi Hiroshima Univ Fac Engn Hiroshima 730 Japan

In this article, assuming non-cooperative behaviour of the decision makers, solution methods for decision making problems in hierarchical organizations under fuzzy random environments are presented. Taking into account hte vagueness of judgments by decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. Considering the possibility and necessity measures that each objective function fulfils the corresponding fuzzy goal, the fuzzy random two-level linear programming problems to minimize each objective function with fuzzy random variables are transformed into stochastic two-level programming problems to maximize the degree of possibility and necessity that each fuzzy goal is fulfilled. Through the fractile criterion optimization model, or Kataoka's model in stochastic programming, the transformed stochastic two-level programming problems can be reduced to deterministic two-level programming problems. For the transformed problems, extended concepts of Stackelberg solutions are introduced and computational methods are also presented. A numerical example is provided to illustrate the proposed methods.

关键词： two-level linear programming fuzzy random variables fractile criterion optimization Stackelberg solutions

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Stackelberg solutions for fuzzy random two-level linear programming through level sets and fractile criterion optimization

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2012年第1期20卷 101-117页

作者： Sakawa, Masatoshi Katagiri, Hideki Hiroshima Univ Fac Engn Higashihiroshima 7398527 Japan

This paper considers Stackelberg solutions for two-level linear programming problems under fuzzy random environments. To deal with the formulated fuzzy random two-level linear programming problem, an alpha-stochastic two-level linear programming problem is defined through the introduction of alpha-level sets of fuzzy random variables. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the alpha-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through fractile criterion optimization in stochastic programming, the transformed stochastic two-level programming problem can be reduced to a deterministic two-level programming problem. An extended concept of Stackelberg solution is introduced and a numerical example is provided to illustrate the proposed method.

关键词： two-level linear programming Fuzzy random variables Stackelberg solutions level sets Fractile criterion optimization

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Interactive fuzzy programming for two-level stochastic linear programming problems through expectation and variance models

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INTERNATIONAL JOURNAL OF KNOWLEDGE-BASED AND INTELLIGENT ENGINEERING SYSTEMS 2009年第3-4期13卷 111-118页

作者： Kato, Kosuke Sakawa, Masatoshi Katagiri, Hideki Hiroshima Inst Technol Fac Appl Informat Sci Dept Comp Sci Hiroshima Japan Hiroshima Univ Grad Sch Engn Dept Artificial Complex Syst Engn Hiroshima Japan

In this paper, we focus on two-level linear programming problems involving random variable coefficients in objective functions and constraints. According to the concept of chance constrained programming, the two-level stochastic linear programming problems are transformed into deterministic ones through the expectation optimization model and the variance minimization model. After introducing fuzzy goals for objective functions, interactive fuzzy programming to derive a satisfactory solution for decision makers is presented as a fusion of stochastic approach and fuzzy one. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.

关键词： two-level linear programming stochastic programming interactive fuzzy programming expectation optimization variance minimization

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两层线性规划问题全局解的一个平行切平面算法

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高等学校计算数学学报 2012年第4期34卷 365-374页

作者：邵建峰刘浩南京工业大学理学院

1问题介绍起源于线性静态Stackelberg问题的两层线性规划为决策理论中的一类基本问题."变量传递型"的两层线性规划其一般模型为

关键词： two-level linear programming global optimal solution duality gap cutting plane

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Optimal allocation model of construction land based on two-level system optimization theory

Optimal allocation model of construction land based on two-l...

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15th International Conference on Geoinformatics

作者： Liu, Min Liu, Yanfang Xia, Yuping Lei, Qihong Wuhan Univ Sch Resource & Environm Sci 129 Luoyu Rd Wuhan 430079 Hubei Peoples R China Wuhan Univ Key Lab Geog Informat Syst Minist Educ Wuhan 430079 Hubei Peoples R China South Digital Technol Co LTD Guangzhou 510665 Guangdong Peoples R China

ISBN: (纸本)9780819469144

The allocation of construction land is an important task in land-use planning. Whether implementation of planning decisions is a success or not, usually depends on a reasonable and scientific distribution method. Considering the constitution of land-use planning system and planning process in China, multiple levels and multiple objective decision problems is its essence. Also, planning quantity decomposition is a two-level system optimization problem and an optimal resource allocation decision problem between a decision-maker in the topper and a number of parallel decision-makers in the lower. According the characteristics of the decision-making process of two-level decision-making system, this paper develops an optimal allocation model of construction land based on two-level linear planning. In order to verify the rationality and the validity of our model, Baoan district of Shenzhen City has been taken as a test case. Under the assistance of the allocation model, construction land is allocated to ten townships of Baoan district. The result obtained from our model is compared to that of traditional method, and results show that our model is reasonable and usable. In the end, the paper points out the shortcomings of the model and further research directions.

关键词： two-level linear programming construction land allocation model

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