(The) goal dividing concept and fuzzy linear goal programming

Abstract

In this study, the fuzzy (goal) programming is extended to handle various types of membership functions by transformation of the complicated (goal) programming problems into the equivalent crisp linear programming problems with single objective. It is well-known that fuzzy programming problem with linear membership functions (ramp type) can be easily transformed into a linear programming problem by introducing one dummy variable in order to minimize the worst unwanted deviation. However, even though many research paid their lot of attentions to the fuzzy (goal) progamming area. They did not extend their studies into various complicated (generalized) linear membership functions, which might be more realistic than ramp or triangular type functions. In this research, we accomplished to transform fuzzy (goal) programming problems with these membership functions into linear programming problems easily by using the goal dividing concept, which is based on the fuzzy set operation (i.e., intersection and union operations). The resultant linear programming problem has a simple form. In addition, since the membership function is continuous and monotonely increasing, any nonlinear membership function is also able to be considered with the aid of the piecewise approximation technique.