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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| Published in: | Knowledge-based systems Vol. 67; pp. 206 - 217 |
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| Language: | English |
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01.09.2014
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| ISSN: | 0950-7051, 1872-7409 |
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| Abstract | 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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| AbstractList | 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. 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 alpha - alpha -level sets of fuzzy random variables, we first transform the fuzzy random bilevel programming problem into an alpha - alpha -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 alpha - alpha -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. |
| Author | Wang, Yuping Ren, Aihong |
| Author_xml | – sequence: 1 givenname: Aihong surname: Ren fullname: Ren, Aihong organization: School of Computer Science and Technology, Xidian University, Xi’an, Shaanxi 710071, China – sequence: 2 givenname: Yuping surname: Wang fullname: Wang, Yuping email: ywang@xidian.edu.cn organization: School of Computer Science and Technology, Xidian University, Xi’an, Shaanxi 710071, China |
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| Keywords | Multiobjective Fuzzy random variables Level sets Bilevel linear programming Interval number Optimistic Stackelberg solutions |
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| SubjectTerms | 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 |
| Title | Optimistic Stackelberg solutions to bilevel linear programming with fuzzy random variable coefficients |
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