Optimistic Stackelberg solutions to bilevel linear programming with fuzzy random variable coefficients

In this paper, we consider a kind of bilevel linear programming problem where the coefficients of both objective functions are fuzzy random variables. The purpose of this paper is to develop a computational method for obtaining optimistic Stackelberg solutions to such a problem. Based on α-level set...

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Bibliographic Details
Published in:Knowledge-based systems Vol. 67; pp. 206 - 217
Main Authors: Ren, Aihong, Wang, Yuping
Format: Journal Article
Language:English
Published: Elsevier B.V 01.09.2014
Subjects:
Bilevel linear programming
Fuzzy
Fuzzy logic
Fuzzy random variables
Fuzzy set theory
Interval number
Intervals
Level sets
Linear programming
Mathematical analysis
Mathematical models
Multiobjective
Optimistic Stackelberg solutions
Random variables
Multiobjective
Fuzzy random variables
Level sets
Bilevel linear programming
Interval number
Optimistic Stackelberg solutions
ISSN:0950-7051, 1872-7409
Online Access:Get full text
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Summary:In this paper, we consider a kind of bilevel linear programming problem where the coefficients of both objective functions are fuzzy random variables. The purpose of this paper is to develop a computational method for obtaining optimistic Stackelberg solutions to such a problem. Based on α-level sets of fuzzy random variables, we first transform the fuzzy random bilevel programming problem into an α-stochastic interval bilevel linear programming problem. To minimize the interval objective functions, the order relations which represent the decision maker’s preference are defined by the right limit and the center of random interval simultaneously. Using the order relations and expectation optimization, the α-stochastic interval bilevel linear programming problem can be converted into a deterministic multiobjective bilevel linear programming problem. According to optimistic anticipation from the upper level decision maker, the optimistic Stackelberg solution is introduced and a computational method is also presented. Finally, several numerical examples are provided to demonstrate the feasibility of the proposed approach.
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ISSN:0950-7051
1872-7409
DOI:10.1016/j.knosys.2014.05.010