A genetic algorithm approach to fuzzy goal programming formulation of fractional multiobjective decision making problems

This paper presents a genetic algorithm (GA) based fuzzy goal programming (FGP) solution method to multiobjective decision making (MODM) problems with fractional criteria. In the model formulation of the problem, first fractional objectives are transformed into fuzzy goals by defining the imprecise aspiration levels to each of them by employing the proposed GA. Then, the concept of membership functions in fuzzy set theory (FST) for measuring the degree of achievement of the fuzzy goals by defining the tolerance limits of them is introduced in the decision making context. In the executable FGP model, the achievement of the highest membership values (unity) of the defined membership goals to the extent possible by minimizing the associated under-deviational variables on the basis of the priorities of achieving the goals is considered. In the solution process, the GA scheme is iteratively used to the FGP formulation by defining the fitness function and without linearizing the fractional membership goals unlike the conventional linear transformation approach to reach a satisfactory decision in the decision making environment. In the decision process, the notion of Euclidean distance function is used to perform the sensitivity analysis with the change of priorities and thereby to identify the appropriate priority structure under which the most satisfactory decision can be reached in the decision situation. Two numerical examples are solved to illustrate the approach and the model solution of a problem is compared with the linear transformation approach studied previously.