An eigenvector method based consistency improving procedure for fuzzy and multiplicative preference relations

Article type: Research Article

Authors: Xu, Yejun^a | Wang, Huimin^{a; b; *}

Affiliations: [a] Business School, Hohai University, Jiangning, Nanjing, Jiangsu, P.R. China | [b] State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, P.R. China

Correspondence: [*] Corresponding author. Huimin Wang. Tel.: +86 25 68514611; E-mail: hmwang@hhu.edu.cn.

Abstract: This paper proposes a consistency improving procedure for fuzzy preference relations. Fuzzy consistency index (FCI) and fuzzy consistency ratio (FCR) are developed to measure the consistency level for complete (or incomplete) fuzzy reciprocal preference relations (FPRs). The principal eigenvector is used for priorities deriving from a complete (or incomplete) FPR. Two criteria are proposed to identify and locate the most inconsistency judgments. A practical iterative algorithm is developed to improve the consistency for FPRs based on the eigenvector method. Based on the transformation between the FPR and the multiplicative preference relation (MPR), the proposed method also can be used to improve the consistency of complete and incomplete MPRs. The improved FPRs or MPRs are the nearest preference relations to the original ones, which aims to retain the original judgements as much as possible. Finally, examples are illustrated and comparative analysis demonstrates the effectiveness of the proposed method.

Keywords: Fuzzy preference relation, consistency improving, eigenvector, fuzzy consistency index (FCI), fuzzy consistency ratio (FCR)

DOI: 10.3233/JIFS-161239

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 3, pp. 1491-1503, 2017