Abstract
This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.
Highlights
In the past few decades, the bilevel programming problem has been researched from the theoretical and computational points of view [1,2,3,4,5,6] and has been successfully applied to a variety of fields, such as transport network design [7, 8], principal-agent problems [9], price control [10], and electricity markets [11, 12]
As a matter of fact, the fuzzy bilevel programming problem in which the coefficients either in the objective functions or in the constraints are represented by fuzzy numbers has received much attention of some researchers
Zhang and Lu [15] developed an extended Kuhn-Tucker approach based on the new definition of optimal solution to solve this problem
Summary
In the past few decades, the bilevel programming problem has been researched from the theoretical and computational points of view [1,2,3,4,5,6] and has been successfully applied to a variety of fields, such as transport network design [7, 8], principal-agent problems [9], price control [10], and electricity markets [11, 12]. In most real-world bilevel decision making problems, in logistics planning or human resource planning, it is very hard to determine the values of the coefficients because of incomplete or imprecise information when establishing these models. In this situation, it is more appropriate to apply fuzzy set theory to handle imprecise data [13]. Zhang and Lu [16] presented a fuzzy bilevel decision making model for a general logistics planning problem and developed a fuzzy number based Kth-best approach to find an optimal solution for the proposed model. Some of the studies in the direction of solving fuzzy multiobjective
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