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

Abstract

The purpose of this paper is to study the fuzzy multilevel quadratic fractional programming problem through fuzzy goal programming procedure. A fuzzy multilevel quadratic fractional programming problem is a type of hierarchical programming problem which contains fuzzy parameters as coefficients of cost in objective function, the resources and the technological coefficients. Here, we are considering those fuzzy parameters as the triangular fuzzy numbers. Firstly, we are transferring the fuzzy multilevel quadratic fractional programming problem into a deterministic multilevel multiobjective quadratic fractional programming problem by using Zadeh extension principle. Then, an interactive fuzzy goal programming procedure is used to solve this equivalent deterministic multiobjective multilevel quadratic fractional programming problem by using respective membership functions. An illustrative numerical example for fuzzy four level quadratic fractional programming problem is provided to reveal the practicability of the proposed method.