Stackelberg solutions for fuzzy random bilevel linear programming through level sets and probability maximization

作     者：Sakawa, Masatoshi Katagiri, Hideki Matsui, Takeshi 

作者机构：Hiroshima Univ Fac Engn Higashihiroshima 7398527 Japan 

出 版 物：《OPERATIONAL RESEARCH》 (运筹学)

年 卷 期：2012年第12卷第3期

页      面：271-286页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：Grants-in-Aid for Scientific Research [22651060  22710145  24710167] Funding Source: KAKEN 

主　　题：Bilevel linear programming Fuzzy random variables Stackelberg solutions Level sets Probability maximization 

摘      要：This paper considers Stackelberg solutions for bilevel linear programming problems under fuzzy random environments. To deal with the formulated fuzzy random bilevel linear programming problem, alpha-level sets of fuzzy random variables are introduced and an alpha-stochastic bilevel linear programming problem is defined for guaranteeing the degree of realization of the problem. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the alpha-stochastic bilevel linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through probability maximization in stochastic programming, the transformed stochastic bilevel programming problem can be reduced to a deterministic bilevel programming problem. An extended concept of Stackelberg solution is introduced and a computational method is also presented. A numerical example is provided to illustrate the proposed method.