Comparison of defuzzification methods for fuzzy stochastic linear programming

Abstract

The present study focused on comparison of three defuzzification methods in transforming fuzzy two-stage stochastic linear programming problem into a crisp problem. The fuzzy transformation techniques that utilized in this study were Yager’s robust ranking method, generalized mean integration representation (GMIR) method, and centroid defuzzification method (CDM). Besides that, an assumption that the probability distribution obtained via expert was fuzzy and consisted only partial information was made. Five problems which modified based on Dakota’s Furniture Company were presented to give an illustration on how the fuzzy transformations using the three mentioned techniques were carried out. The defuzzified two-stage stochastic linear programming problems from each of the techniques were solved using a modelling system of GAMS, which implemented using a solver called DECIS. The difference between first problem and the rest of the problems was demand levels in first problem were symmetric triangular fuzzy numbers. Transformation of first problem using three different techniques resulted in getting the same model formulation, and hence the result obtained from GAMS/DECIS obviously was similar. The results of Problem 2 and Problem 3 obtained from the GAMS/DECIS showed a slight difference in resource quantities, production quantities, and the total profit, and CDM method showed the best optimum solutions. Meanwhile, GMIR method showed better optimum solutions in Problem 4 and 5. Hence, it can be concluded that CDM and GMIR are best methods of defuzzification for non-symmetric triangular fuzzy numbers problems comparing to Yager’s robust ranking method.