Consensus models based on distance for interval fuzzy and multiplicative preference relations

Article type: Research Article

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

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

Correspondence: [*] Corresponding author. Yejun Xu. Tel.: +86 25 68514612; E-mail: [email protected].

Abstract: This paper presents consensus models based on distance for group decision making problems under interval fuzzy and multiplicative preference relations. First, some quadratic programming models based upon the idea of minimizing the sum of squared distances between all pairs of weighted interval fuzzy or multiplicative preference judgments are developed to obtain the weights of experts. Then, two indices, an individual to group consensus index (ICI) and a group consensus index (GCI) are defined. Furthermore, iterative consensus algorithms are proposed and the processes stop until both the ICI and GCI are less than predefined thresholds or reaching the maximum number of iteration. Finally, two illustrative examples are given to demonstrate the feasibility and effectiveness of the proposed methods.

Keywords: Group decision making, interval fuzzy preference relation, interval multiplicative preference relation, consensus, iterative algorithms

DOI: 10.3233/IFS-162163

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 1, pp. 503-518, 2016