On the Application of a Lexicographic Method to Fuzzy Linear Programming Problems

Abstract

The literature on fuzzy variable linear programming (FVLP) and fuzzy number linear programming (FNLP) is prolific in terms of the number of available solution methods. In FVLP problems, only the decision variables and right-hand side values of the constraints are fuzzy numbers. In FNLP problems, except for the decision variables, all parameters are fuzzy numbers. A widespread approach for solving problems in FVLP and FNLP is to use linear ranking functions in order to transform the fuzzy problems into conventional ones. Previous studies have shown that linear ranking functions do not guarantee uniqueness of the optimal fuzzy objective values. In this paper, we use a lexicographic method to find unique optimal fuzzy objective values of such problems and compare the results with those obtained via linear ranking function approaches. The paper also discusses applications of the lexicographic method in diet and time–cost trade-off problems in fuzzy environments.