Multiple objective decision making in a fuzzy environment

Abstract

Multiobjective linear fractional programming (MOLEP) is encountered in various decision-making environments where several ratios are to be optimized simultaneously. However, the scope of most studies in MOLEP has been so limited to the oversimplified deterministic models that the decisions made are frequently for from the real situations. The primary objective of this study is to enhance the practicality of MOLEP by incorporating fuzziness that is associated with the imprecision in decision-making process. For this aim, three major issues relevant to the fuzzified version of MOLEP (FMOLEP) are considered as follows. First, based on the observation that an FMOLFP can be reduced to a sequence of linear inequality problems(LIPs), we develop a basic solution procedure for obtaining the best compromise solution of the FMOLEP which alternates between Khachiyan``s ellipsoid method for an LIP, and an ascent method for updating the objective value. The efficiency of the proposed algorithm as well as the practicality of FMOLEP is demonstrated with an example of financial planning. Depending on 1)how to solve an LIP, and 2)how to modify the parameter, two variants of the basic solution procedure are also suggested later. Second, the duality and sensitivity analysis in FMOLFP are considered to investigate the relations between the change in the overall satisfaction and those in various parameters associated with fuzzy sets. Based on the dual problem satisfying the strong duality an complementary slackness, the relations are expressed using the optimal dual variables in analytic form. The special structure of dual FMOLFP is exploited to develop one variant of the basic solution procedure, called parallel algorithm, by which the convergence rate can be considerably sped up without significant increase in computational effort. finally, as a realistic application of FMOLEP, we consider the problem of designing a parallel processors system, for which three level of decision are...