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On consistency measures of linguistic preference relations. (English) Zbl 1149.90349
Summary: Inspired by the concept of deviation measure between two linguistic preference relations, this paper further defines the deviation measure of a linguistic preference relation to the set of consistent linguistic preference relations. Based on this, we present a consistency index of linguistic preference relations and develop a consistency measure method for linguistic preference relations. This method is performed to ensure that the decision maker is being neither random nor illogical in his or her pairwise comparisons using the linguistic label set. Using this consistency measure, we discuss how to deal with inconsistency in linguistic preference relations, and also investigate the consistency properties of collective linguistic preference relations. These results are of vital importance for group decision making with linguistic preference relations.

MSC:
90B50 Management decision making, including multiple objectives
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[1] Chiclana, F.; Herrera, F.; Herrera-Viedma, E., Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations, Fuzzy sets and systems, 97, 33-48, (1998) · Zbl 0932.91012
[2] Chiclana, F.; Herrera, F.; Herrera-Viedma, E., Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations, Fuzzy sets and systems, 122, 277-291, (2001) · Zbl 1098.90523
[3] Chiclana, F.; Herrera, F.; Herrera-Viedma, E.; Martínez, L., A note on the reciprocity in the aggregation of fuzzy preference relations using OWA operators, Fuzzy sets and systems, 137, 71-83, (2003) · Zbl 1056.91016
[4] Delgado, M.; Verdegay, J.L.; Vila, M.A., On aggregation operations of linguistic labels, International journal of intelligent systems, 8, 351-370, (1993) · Zbl 0794.68154
[5] Delgado, M.; Herrera, F.; Herrera-Viedma, E.; Martínez, L., Combining numerical and linguistic information in group decision making, Journal of information science, 107, 177-194, (1998)
[6] Fan, Z.P.; Jiang, Y.P., A judgment method for the satisfying consistency of linguistic judgment matrix, Control and decision, 19, 903-906, (2004)
[7] Fan, Z.P.; Chen, X., Consensus measures and adjusting inconsistency of linguistic preference relations in group decision making, (), 130-139
[8] Herrera, F., A sequential selection process in group decision making with linguistic assessment, Information sciences, 85, 223-239, (1995) · Zbl 0871.90002
[9] Herrera, F.; Herrera-Viedma, E.; Verdegay, J.L., A model of consensus in group decision making under linguistic assessments, Fuzzy sets and systems, 78, 73-87, (1996) · Zbl 0870.90007
[10] Herrera, F.; Herrera-Viedma, E.; Verdegay, J.L., Direct approach processes in group decision making using linguistic OWA operators, Fuzzy sets and systems, 79, 175-190, (1996) · Zbl 0870.90007
[11] Herrera, F.; Herrera-Viedma, E., Linguistic decision analysis: steps for solving decision problems under linguistic information, Fuzzy sets and systems, 115, 67-82, (2000) · Zbl 1073.91528
[12] Herrera, F.; Martinez, L., A 2-tuple fuzzy linguistic representation model for computing with words, IEEE transactions on fuzzy systems, 8, 746-752, (2000)
[13] Herrera-Viedma, E.; Herrera, F.; Chiclana, F., A consensus model for multiperson decision making with different preference structures, IEEE transactions on systems, man and cybernetics, 32, 394-402, (2002) · Zbl 1027.91014
[14] Herrera-Viedma, E.; Herrera, F.; Chiclana, F.; Luque, M., Some issues on consistency of fuzzy preference relations, European journal of operational research, 154, 98-109, (2004) · Zbl 1099.91508
[15] Jong, P., A statistical approach to saaty’s scaling method for priorities, Journal of mathematical psychology, 28, 467-478, (1984) · Zbl 0564.62089
[16] Ma, W.Y., A practical approach to modifying pair wise comparison matrices and two criteria of modificatory effectiveness, System science & systems engineering, 3, 4, 334-338, (1994)
[17] Ma, J.; Fan, Z.P.; Jiang, Y.P.; Mao, J.Y.; Ma, L., A method for repairing the inconsistency of fuzzy preference relations, Fuzzy sets and systems, 157, 20-33, (2006) · Zbl 1117.91330
[18] Orlorski, S.A., Decision-making with a fuzzy preference relation, Fuzzy sets and systems, 3, 155-167, (1978) · Zbl 0396.90004
[19] Peláez, J.I.; Lamata, M.T., A new measure method of consistency for positive reciprocal matrices, Computers and mathematics with applications, 46, 1839-1845, (2003) · Zbl 1121.91334
[20] Saaty, T.L., The analytic hierarchy process, (1980), McGraw-Hill New York · Zbl 1176.90315
[21] Tanino, T., Fuzzy preference orderings in group decision making, Fuzzy sets and systems, 12, 117-131, (1984) · Zbl 0567.90002
[22] Xu, Z.S.; Wei, C.P., A consistency improving method in analytic hierarchy process, European journal of operational research, 116, 443-449, (1999) · Zbl 1009.90513
[23] Xu, Z.S., Uncertain attribute decision making: method and applications, (2004), Tsinghua University Press Beijing
[24] Xu, Z.S., A method based on linguistic aggregation operators for group decision making with linguistic preference relations, Information sciences, 166, 19-30, (2004) · Zbl 1101.68849
[25] Xu, Z.S., Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment, Information sciences, 168, 171-184, (2004) · Zbl 1170.91328
[26] Xu, Z.S., EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations, International journal of uncertainty, fuzziness and knowledge-based systems, 12, 6, 791-810, (2004) · Zbl 1076.91508
[27] Xu, Z.S., Deviation measures of linguistic preference relations in group decision making, Omega, 33, 249-254, (2005)
[28] Xu, Z.S., An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations, Decision support systems, 41, 488-499, (2006)
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