Journal
FUZZY SETS AND SYSTEMS
Volume 157, Issue 1, Pages 20-33Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.fss.2005.05.046
Keywords
fuzzy preference relations; additive consistency; weak transitivity; inconsistency
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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. (C) 2005 Elsevier B.V All rights reserved.
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