An Interactive Dynamic Fuzzy Goal Programming for Bi-level Multiobjective Linear Fractional Programming Problems.

Abstract

This paper presents an interactive dynamic fuzzy goal programming (DFGP) approach for solving bi-level multiobjective linear fractional programming (BL MOLFP) problems with the characteristics of dynamic programming (DP). In the proposed approach, the membership function of the objective goals of a problem with fuzzy aspiration levels are defined first as the membership function for vector of fuzzy goals of the decision variables controlled by first–level decision maker are developed first in the model formulation of the problem. The method of variable change, on the under and over deviational variables of the membership goals associated with the fuzzy goals of the model, is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Then, under the framework of preemptive priority based GP, a multi  stage DP model of the problem is used for achievement of the highest degree (unity) of each of the membership functions. In the decision process, the goal satisficing philosophy of GP is used recursively to arrive at the most satisfactory solution and the suggested algorithm to simplify the solution procedure by DP at each stage is proposed. This paper is considered as an extension work of Mahmoud A. Abo-Sinna and Ibrahim A. Baky (2010) by using dynamic approach. Finally, this approach is illustrated by a given numerical example.