Fuzzy linear programming with grade of satisfaction in each constraint

Abstract

The authors introduce and modify a method for fuzzy linear programming (FLP) in which each constraint has a different grade of satisfaction. The FLP problem dealt with in the paper has fuzzy coefficients in its constraints. The fuzzy constraints can be expressed by four feasibility indices introduced by Dubois (1987) derived from four ranking indices of fuzzy numbers. A decision maker (DM) can assign the grades to the constraints by giving /spl alpha/ different values. The authors propose a modified method in which the grade is given as a fuzzy set on the unit closed interval [0, 1] reflecting human imprecision. In the authors' method, several optimal solutions are calculated, for a DM to choose from.<>