Title: An automatic method to reach consensus in a local context for AHP group decision making

Authors: Yucheng Dong; Weijun Xu; Weidong Xu

Addresses: Business School, Sichuan University, Chengdou 610065, China ' School of Business Administration, South China University of Technology, Guangzhou 510640, China ' Management School, Zhejiang University, Hangzhou 310058, China

Abstract: In the analytic hierarchy process (AHP), Saaty's consistency index is performed to ensure that the preference information, provided in an individual judgement matrix, is neither random nor illogical. Based on the extension of Saaty's consistency index, this paper proposes a consensus index to measure the difference between the individual preference values and the collective preference value in AHP group decision making. Furthermore, based on the consensus index, we propose a consensus prioritisation method to obtain the collective priority vector for AHP group decision making, and develop a non-linear programme model to automatically reach acceptable consensus in a local context (a unique criterion). The consensus model in this paper can optimally preserve original preference information in reaching acceptable consensus (in some sense). A genetic algorithm also is designed to solve this non-linear programme model. [Received 25 June 2011; Revised 25 August 2011; Revised 7 November 2011; Accepted 2 December 2011]

Keywords: decision analysis; group decision making; analytical hierarchy process; AHP; consensus index; individual preference values; collective preference value; consensus prioritisation; nonlinear programming; modelling; local context; genetic algorithms; GAs.

DOI: 10.1504/EJIE.2013.055018

European Journal of Industrial Engineering, 2013 Vol.7 No.4, pp.456 - 474

Published online: 25 Jun 2013 *

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