A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem

作者：Ren Aihong^*

来源：Mathematical Problems in Engineering, 2015, 2015: 280380.

DOI：10.1155/2015/280380

We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers. This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method. To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number of alpha-level sets. By using alpha-level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bilevel linear programming problem for each alpha-level set. The main idea to solve the obtained interval bilevel linear programming problem is to convert the problem into two deterministic subproblems which correspond to the lower and upper bounds of the upper level objective function. Based on the Kth-best algorithm, the two subproblems can be solved sequentially. Based on a series of alpha-level sets, we introduce a linear piecewise trapezoidal fuzzy number to approximate the optimal value of the upper level objective function of the fully fuzzy bilevel linear programming problem. Finally, a numerical example is provided to demonstrate the feasibility of the proposed approach.

• 出版日期2015
• 单位宝鸡文理学院