A New Approximate Algorithm for Solving Multiple Objective Linear Programming with Fuzzy Parameters

Many business decisions can be modeled as multiple objective linear programming (MOLP) problems. When formulating a MOLP problem, objective functions and constraints involve many parameters which possible values are assigned by the experts who are often imprecisely or ambiguously known. So, it would be certainly more appropriate to interpret the experts’ understanding of the parameters as fuzzy numerical data which can be represented by fuzzy numbers. This paper focuses on fuzzy multiple objective linear programming (FMOLP) problems with fuzzy parameters in any form of membership function in both objective functions and constraints. Based on the related results of fuzzy linear programming (FLP) and linear programming problems with fuzzy equality and inequality constraints proposed by Zhang et al, this paper firstly proposes related definitions and concepts about FMOLP problems with fuzzy parameters. It then proposes a new approximate algorithm developed for solving the corresponding MOLP problems and the FMOLP problems. Finally, the use of related concepts, theorems, and the proposed approximate algorithm is illustrated by an example involving different cases which include setting various iterate steps, tolerances, weights, and satisfaction levels.