Linear Programming with fuzzy joint parameters: A Cumulative Membership Function approach

Abstract

This paper shows an alternative methodology to find optimal solutions of a linear programming problem defined in a fuzzy environment. The classical fuzzy linear programming (FLP) problem is treated by using fuzzy restrictions in the form Ax les bbreve where indicates a type-1 fuzzy set (Tl FS). The proposed approach uses joint Abreve and bbreve fuzzy parameters to solve a linear programming model under uncertainty conditions. Triangular fuzzy sets are used to reduce the computational complexity of the model, however other types of fuzzy sets can be used. A cumulative membership function (CMF) approach is defined, some optimality conditions are discussed and a new theorem is proved. Finally a small example is provided.