Guaranteed-consensus posterior-aggregation fuzzy analytic hierarchy process method
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ORIGINAL ARTICLE
Guaranteed-consensus posterior-aggregation fuzzy analytic hierarchy process method Tin-Chih Toly Chen1 Received: 14 December 2018 / Accepted: 11 April 2019 Ó Springer-Verlag London Ltd., part of Springer Nature 2019
Abstract Current group decision-making fuzzy analytic hierarchy processes (FAHPs) have two major problems. First, inconsistent fuzzy pairwise comparison results, rather than compromised fuzzy weights, are aggregated. Second, a consensus among decision makers (DMs) cannot be guaranteed. To address these problems, in this study, the guaranteed-consensus posterioraggregation FAHP (GCPA-FAHP) method was proposed. In the proposed methodology, the membership functions of the linguistic terms for performing fuzzy pairwise comparisons were designed to guarantee a consensus among the DMs and can be modified afterward to enhance the estimation precision. In addition, fuzzy intersection and center of gravity were used to aggregate and defuzzify the estimated fuzzy weights. The GCPA-FAHP method was applied to a real case to evaluate its effectiveness. The experimental results revealed that the GCPA-FAHP method guaranteed consensus among the DMs and improved the precision of estimating fuzzy weights. Keywords Fuzzy analytic hierarchy process Decision maker Consensus Posterior aggregation
1 Introduction Fuzzy analytic hierarchy process (FAHP) has been widely used in various fields [17, 19, 33]. In FAHP, decision makers (DMs) express their belief on the relative importance of a criterion over another [19, 28, 35]. However, the belief of a single DM can be subjective. To address this problem, many studies have solicited opinions of a group of DMs to make a compromised decision [1, 13, 18, 20]. For example, the DM groups in Lima Junior et al. [22] and Gu¨ran et al. [15] contained three members each. Zheng et al. [39] and Sirisawat and Kiatcharoenpol [33] used a group of ten DMs. Gnanavelbabu and Arunagiri [14] formed a DM group of 30 members. A group decisionmaking FAHP method presents four challenges: (1) the uncertainty of a pairwise comparison result; (2) the inconsistency among pairwise comparison results; (3) the approximation for simplifying the required computation; & Tin-Chih Toly Chen [email protected] 1
Department of Industrial Engineering and Management, National Chiao Tung University, 1001, University Road, Hsinchu, Taiwan
and (4) the lack of consensus among the DMs, as illustrated in Fig. 1. These four challenges cause difficulties in deriving the exact values of the weights/priorities of factors/attributes/criteria. Nevertheless, these issues may compensate for each other: (1)
(2)
After the uncertainty of each pairwise comparison was evaluated, the results indicate that inconsistency among them may be negligible. For example, without considering uncertainty, assuming that the relationships among the weights of three factors are w1 =w2 ¼ 2, w2 =w3 ¼ 2, and w1 =w3 ¼ 2, an inconsistency is observed because from the first two relati
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