Algorithms for improving consistency or consensus of reciprocal [0,1]-valued preference relations

Authors:
Meimei Xia;Zeshui Xu;Jian Chen
Affiliations:
School of Economics and Management, Tsinghua University, Beijing 100084, China;Institute of Sciences, PLA University of Science and Technology, Nanjing 210007, China;School of Economics and Management, Tsinghua University, Beijing 100084, China
Venue:
Fuzzy Sets and Systems
Year:
2013

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Abstract

We investigate the consistency and consensus of reciprocal [0,1]-valued preference relations (also called fuzzy preference relations by many authors) based on the multiplicative consistency property, which is an important issue in fuzzy set theory. An algorithm is first developed to improve the consistency level of a reciprocal [0,1]-valued preference relation, and the corresponding algorithm for the incomplete reciprocal [0,1]-valued preference relation is also developed. We further propose the consensus improving algorithms for individual reciprocal [0,1]-valued preference relations or incomplete ones. The convergence and robustness of the algorithms are proven and some important conclusions are obtained. In addition, the proposed algorithms can improve the consistency or consensus of reciprocal [0,1]-valued preference relations with less interactions with the decision makers, which can save a lot of time and obtain the results quickly.