Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

Abstract EN

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.