On fuzzy multiple objective linear programming problems

Abstract

In recent years, multiple objective decision making (MODM) has become more and more important, and multiple objective linear programming (MOLP) approaches have been widely used for solving MODM problems. Three popular fuzzy mathematical programming approaches, including maxmin, arithmetical average, and two-phase methods, are often employed to solve MOLP problems. However, maxmin and two-phase methods cannot obtain an efficient solution. Ideal and anti-ideal solutions are required in all traditional methods. Such solutions cannot easily be established as a model for a knowledge-based system or expert system. In order to enrich the body of knowledge related to the field of MOLP, a new multi-choice goal programming (MCGP) model is proposed to solve fuzzy MOLP (FMOLP) problems in which the ideal and anti-ideal solutions are no longer required. This reduces the complexity of the solution process for solving MODM. The original feasible region can be expended to a potential feasible region to determine the appropriate aspiration level for decision makers. The proposed methods can systematically solve MODM problem to obtain satisfactory solutions in one step. Thus, a model-based can easily be established for expert systems, knowledge-based system, and artificial intelligence systems. In addition, a revised utility function (UF) is derived to solve qualitative and quantitative MODM problems. Based on illustrative examples, the five methods (maxmin, arithmetical average, two-phase, goal programming (GP), and proposed models) are compared to reveal managerial implications. On the basis of these comparisons, DMs can easily determine the best suited solution for their specific MODM problems. Finally, a realistic example is provided to demonstrate the usefulness of the proposed methods.