Fuzzy preference modeling and its application to multiobjective decision making

  • Authors:

  • P. Ya. Ekel;M. R. Silva;F. Schuffner Neto;R. M. Palhares

  • Affiliations:

  • Graduate Program in Electrical Engineering Pontifical Catholic University of Minas Gerais Av. Dom Jose Gaspar, 500 30535-610, Belo Horizonte, MG, Brazil;Graduate Program in Electrical Engineering Pontifical Catholic University of Minas Gerais Av. Dom Jose Gaspar, 500 30535-610, Belo Horizonte, MG, Brazil;Department of Electronics Engineering and Telecommunications Pontifical Catholic University of Minas Gerais Av. Dom Jose Gaspar, 500 30535-610, Belo Horizonte, MG, Brazil;Department of Electronics Engineering Federal University of Minas Gerais Av. Antonio Carlos, 6627 31270-010, Belo Horizonte, MG, Brazil

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2006

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Abstract

This paper reflects results of research into the construction and analysis of models within the framework of a general approach to solving optimization problems with fuzzy coefficients. This approach involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually interrelated models. The use of the approach allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty region is based on reducing the problem to models of multiobjective choosing alternatives in a fuzzy environment with the use of fuzzy preference relation techniques for analyzing these models. Three techniques for fuzzy preference modeling are discussed in the paper. The first technique is based on the construction of membership functions of subsets of nondominated alternatives with simultaneous considering of all criteria (fuzzy preference relations). The second technique is of a lexicographic character and consists of step-by-step introducing of fuzzy preference relations. The third technique is based on aggregating membership functions of subsets of nondominated alternatives corresponding to each preference relation. These techniques have served for developing a corresponding system for multiobjective decision making (MDMS). C++ windows of the MDMS are presented for input, output, and some intermediate procedures. The results of the paper are of a universal character and are already being used to solve power engineering, naval engineering, and management problems.