A penalty function based fuzzy goal programming procedure for solving multiobjective decision making problems

This paper presents how fuzzy penalty functions can be grafted to the fuzzy goal programming formulation of a multiobjective decision making problem for making proper decisions in uncertain environment. In the proposed approach, the fuzzily described objectives are first characterized by the associated membership functions. The membership functions are then transformed into membership goals by assigning the highest degree (unity) as the aspiration level and introducing under- and over- deviational variables to each of them. In the model formulation, the penalty functions in terms of degree of achievement of membership values in different ranges are introduced to the framework of the model for minimizing deviations from the goal levels to the extent possible for arriving at most satisfactory solution in the decision making context. In the solution process, the minsum fuzzy goal programming method is employed to achieve the solution on the basis of relative weights of importance of achieving the aspired goal levels in the decision making horizon. A numerical example is provided to illustrate the efficient use of the approach.