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2598. A Simulation Analysis of Inconsistency Indices Values for Transitive Pairwise Comparison Matrices

Invited abstract in session TD-44: Pairwise comparisons and preference relations 2, stream Multiple Criteria Decision Analysis.

Tuesday, 14:30-16:00
Room: 20 (building: 324)

Authors (first author is the speaker)

1. Tomasz Starczewski
Department of Mathemtics, Czestochowa Uniwersity of Technology
2. Pawel Tadeusz KAZIBUDZKI
Department of Corporate Management, e-Business and Electronic Economy, Opole University of Technology

Abstract

In the Analytic Hierarchy Process (AHP), a Consistency Index (CI) is used for detecting inconformity of a Pairwise Comparison Matrix (PCM). An original idea of T. Saaty is to compare value of CI with an average value of CI obtained for a large amount (e.g. 100,000) of random PCMs. The inventor of AHP idea has specified percentage thresholds for CI values, which should not be exceeded. However, as A.Z. Grzybowski has shown, very small number of random PCMs is even close to consistent in Saaty's sense (https://doi.org/10.1016/j.eswa.2012.04.051). Furthermore, according to Grzybowski’s research, for PCMs of the size larger than 5, the probability of gaining PCM, that satisfies Saaty's consistency condition is close to 0. Hence, evaluation of the relationship between random PCMs and consistent PCMs is rather pointless. However, much higher percentage of randomly matrices are consistent, when transitive PCMs are taken into account. Moreover, PCMs given by real decision makers usually are transitive (despite of their inconsistency). Therefore, it was decided to investigate mostly that kind of PCMs. Thus, Monte Carlo simulations for various CIs have been designed. The intent is to discuss the result of that examination, in particular certain characteristics of CIs distribution obtained for transitive PCMs. It is believed that, on the bases of these results, one can more credibly classify PCM as enough or not enough consistent.

Keywords

Status: accepted

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