Journal
SOFT COMPUTING
Volume 22, Issue 14, Pages 4833-4849Publisher
SPRINGER
DOI: 10.1007/s00500-017-2671-y
Keywords
Ordinal consistency; Additive consistency; Linguistic preference relation; Distance; Nonlinear programming
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Funding
- Key Project of National Natural Science Foundation of China [71433003]
- National Natural Science Foundation of China (NSFC) [71471056]
- Fundamental Research Funds for the Central Universities [2015B23014]
- Excellent Innovative Talent Program of Hohai University - Qing Lan Project of Jiangsu Province
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This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definition of adjacency matrix of a linguistic preference relation, the necessary and sufficient conditions of a linguistic preference relation being ordinally consistent are given. Then, a distance-based nonlinear programming method is developed to identify and adjust the ordinal and additive inconsistencies for linguistic preference relations. The proposed methods can not only solve the ordinal inconsistency, additive inconsistency problems, respectively, but also solve the ordinal and additive inconsistency problems simultaneously. Finally, numerical examples and comparative analysis are provided to show the effectiveness and advantages of the proposed methods.
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