Reduction method based on fuzzy principal component analysis in multi-objective possibilistic programming

Abstract

Most of real problems are modeling as multi-objective problems (MOPs) with imprecise coefficients. Coefficients or parameters are commonly imprecise because information is incomplete or unavailable. One category of these problems is multi-objective possibilistic problem (MOPP). Possibility theory is favorable for modeling incomplete information expressed by fuzzy propositions. On the other hand, MOPPs are a class of MOPs with imprecise parameters. Solving of MOPPs is usually difficult. Therefore, we should design approaches or extend exciting algorithms for solving them. This paper is a pre-processing stage for solving MOPPs. In other words, it discusses simple and useful integrated approach for reducing the number of objectives in multi-objective possibilistic problems. For this purpose, fuzzy principal component analysis (FPCA) can be used. The approach consists of a two-stage algorithm that in the first stage, we use FPCA for reducing objectives. In the second stage, we use results of previous stage for solving reduced problem. The new objective functions cover maximum variances of primal functions. We show that the proposed approach can generate efficient solutions without added extra constraints and variables than the general problems found in the literatures. An example illustrates steps of the procedure.