Interactive programming approach for solving the fully fuzzy bilevel linear programming problem

In this paper, a fully fuzzy bilevel linear programming problem in which all the coefficients and decision variables of both objective functions and the constraints are expressed as fuzzy numbers is addressed. The purpose of this paper is to develop an interactive programming approach to obtain a balanced solution of the fully fuzzy bilevel programming problem. To this end, we first define the feasible region of the problem, and give a concept of the fuzzy optimal solution of the problem. Based on a fuzzy relationship to rank fuzzy numbers, the fully fuzzy bilevel programming problem can be converted into a deterministic one under different feasibility degrees of the constraints. Taking into account a tradeoff between better objective function values and higher feasibility degrees of the constraints, an interactive programming approach is presented to solve the fully fuzzy bilevel programming problem. Finally, several numerical examples are provided to demonstrate the feasibility of the proposed method.