A Solution of Fuzzy Trilevel Quadratic Fractional Programming Problem through Interactive Fuzzy Goal Programming Approach

Abstract

The purpose of this paper is to study the fuzzy Trilevel Quadratic Fractional Programming Problem (TLQFPP) through Fuzzy Goal Programming procedure. A TLQFPP is a special case of multilevel quadratic fractional programming problem with three levels and fuzzy TLQFPP contains fuzzy parameters as coefficients in its cost of objective function, the resources and the technological coefficients. In this paper, we are considering those fuzzy parameters as the triangular fuzzy numbers. Firstly, we are converting this type of fuzzy TLQFPP into a deterministic tri-objective TLQFPP by using Zadeh extension principle and then interactive fuzzy goal programming procedure is used to solve this equivalent deterministic Trilevel Triobjective Quadratic Fractional Programming Problem (TLTOQFPP) by using respective membership functions. An illustrative numerical example for fuzzy trilevel quadratic fractional programming problem is provided to reveal the applicability of the proposed method.