Priority Based Fuzzy Goal Programming Approach for Fractional Multilevel Programming Problems

In this paper, a priority based fuzzy goal programming (FGP) model is presented to solve fractional multilevel programming problems in a hierarchical decision making organization. In the proposed approach, the independent best and worst solutions each each of the decision makers (DMs) located individually at each of the hierarchical decision levels are determined first. Then, the tolerance membership functions for the fuzzily described fractional objective goals are constructed for measuring the degree of achievement of the objectives of the DMs. In the FGP model formulation, a linearization approach is introduced to the defined fractional membership goals to solve the problem by using the priority based linear FGP methodology. In the solution process, achievement of the defined membership goals to the highest value (unity) to the extent possible on the basis of their priorities is taken into consideration. In the decision process, the sensitivity analysis on the solution with the variation of priority structure of the goals is performed. Then, the notion of Euclidean distance function is used to identify the proper priority structure under which the most satisfactory decision is reached. A numerical example is provided to illustrate the approach.