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Multicriteria optimization in a fuzzy environment: The fuzzy analytic hierarchy process

In the paper the fuzzy extension of the Analytic Hierarchy Process (AHP) based on fuzzy numbers, and its application in solving a practical problem, are considered. The paper advocates the use of contradictory test to check the fuzzy user preferences during fuzzy AHP decision-making process. We also propose consistency check and deriving priorities from inconsistent fuzzy judgment matrices to be included in the process, in order to check if the fuzzy approach can be applied in the AHP for the problem considered. | Yugoslav Journal of Operations Research Volume 20 (2010), Number 1, 71-85 10.2298/YJOR1001071G MULTICRITERIA OPTIMIZATION IN A FUZZY ENVIRONMENT: THE FUZZY ANALYTIC HIERARCHY PROCESS1 Milanka GARDAŠEVIĆ-FILIPOVIĆ Faculty of Mathematics, University of Belgrade, milanka@arh.bg.ac.rs Dragan Z. ŠALETIĆ University ‘’Union’’, School of Computing, Belgrade, dsaletic@raf.edu.rs Received: March 2008 / Accepted: April 2010 Abstract: In the paper the fuzzy extension of the Analytic Hierarchy Process (AHP) based on fuzzy numbers, and its application in solving a practical problem, are considered. The paper advocates the use of contradictory test to check the fuzzy user preferences during fuzzy AHP decision-making process. We also propose consistency check and deriving priorities from inconsistent fuzzy judgment matrices to be included in the process, in order to check if the fuzzy approach can be applied in the AHP for the problem considered. An aggregation of local priorities obtained at different levels into composite global priorities for the alternatives based on weighted-sum method is also discussed. The contradictory fuzzy judgment matrix is analyzed. Our theoretical consideration has been verified by an application of commercially available Super Decisions program (developed for solving multi-criteria optimization problems using AHP approach) on the problem previously treated in the literature. The obtained results are compared with those from the literature. The conclusions are given and the possibilities for further work in the field are pointed out. Keywords: Fuzzy decision-making, fuzzy AHP, consistency check, military application. 1 The authors are grateful to the referees for their valuable remarks and comments. 72 M., Gardašević Filipović, D., Šaletić / Multicriteria Optimization in a Fuzzy Environment 1. INTRODUCTION Establishing criteria for decision-making is a difficult and responsible task. Today we almost always deal with multi-criteria optimisation,