A method for repairing the inconsistency of fuzzy preference relations

  • Authors:

  • Jian Ma;Zhi-Ping Fan;Yan-Ping Jiang;Ji-Ye Mao;Louis Ma

  • Affiliations:

  • Department of Information Systems, City University of Hong Kong, Kowloon, Hong Kong, China;Department of Management Science and Engineering, School of Business Administration, Northeastern University, Shenyang, 110004, China;Department of Management Science and Engineering, School of Business Administration, Northeastern University, Shenyang, 110004, China;School of Business, Renmin University of China, Beijing 100872, China;Department of Information Systems, City University of Hong Kong, Kowloon, Hong Kong, China

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2006

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Abstract

This paper investigates the inconsistency problems of preference information about alternatives expressed as a fuzzy preference relation by a decision maker. An analysis method is presented to identify the inconsistency and weak transitivity of a fuzzy preference relation and to repair its inconsistency to reach weak transitivity. First, several definitions are given on additive consistency, inconsistency and weak transitivity of a fuzzy preference relation. Next, two methods derived from graph theory are presented to judge whether a fuzzy preference relation has weak transitivity or not. Then, an algorithm is developed to repair an inconsistent fuzzy preference relation and to make it become one with weak transitivity, via a synthesis matrix which reflects the relationship between the fuzzy preference relation with additive consistency and the initial one given by a decision maker. A convergence theorem is also given for the algorithm. Lastly, two numerical examples are shown to illustrate the proposed method.