Journal
APPLIED MATHEMATICAL MODELLING
Volume 37, Issue 7, Pages 5171-5183Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2012.10.008
Keywords
Incomplete fuzzy preference relation; Eigenvector method; Multiplicative consistency; Consistency test; Inconsistency repairing
Funding
- National Natural Science Foundation of China (NSFC) [71101043, 50979024, 90924027]
- College Philosophy and Social Science Research Project of Jiangsu Province [2011SJD630007]
- International Academic Cooperation Team Development Foundation of Business School, Hohai University [UAH-2011-181]
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In this paper, we extend the eigenvector method (EM) to priority for an incomplete fuzzy preference relation. We give a reasonable definition of multiplicative consistency for an incomplete fuzzy preference relation. We also give an approach to judge whether an incomplete fuzzy relation is acceptable or not. We develop the acceptable consistency ratio for an incomplete multiplicative fuzzy preference relation, which is simple and similar to Saaty's consistency ratio (CR) for the multiplicative preference relation. If the incomplete fuzzy preference relation is not of acceptable consistency, we define a criterion to find the unusual and false element (UFE) in the preference relation, and present an algorithm to repair an inconsistent fuzzy preference relation until its consistency is satisfied with the consistency ratio. As a result, our improvement method cannot only satisfy the consistency requirement, but also preserve the initial preference information as much as possible. Finally, an example is illustrated to show that our method is simple, efficiency, and can be performed on computer easily. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.
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