An Efficient Piecewise Linearization Method in Fuzzy Multi-objective Programs

Fuzzy set theory was first introduced by Zadeh in 1965 to manipulate data and information processing uncertainties which statistics is not proper for use. It was particularly designed to mathematically represent uncertainty as well as vagueness and to offer formalized tools for handling the imprecision intrinsic to many domains. In 1978 Zimmermann presented the linear programming and multiobjective programs into fuzzy set theory. Since then many methods using linear programming have been developed to solve fuzzy multi-objective programming problems (FMOP). For the nonlinear membership functions, how to solve FMOP to obtain the global optimum has been discussed extensively by many researchers. One of the promising methods of linearizing nonlinear membership functions is the piecewise linearization. In this study an efficient piecewise linearization method for solving FMOP is proposed.