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Mathematical Problems in Engineering
Volume 2015, Article ID 680635, 12 pages
Research Article

The Likelihood Ranking Methods for Interval Type-2 Fuzzy Sets Considering Risk Preferences

1School of Business Administration, Northeastern University, Shenyang 110819, China
2Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

Received 7 April 2015; Revised 10 August 2015; Accepted 19 August 2015

Academic Editor: Dan Simon

Copyright © 2015 Meng Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a ranking method that considers the risk preferences of decision makers for multiple-attribute decision-making problems in a multiple-interval type-2 trapezoidal fuzzy set environment. First, decision makers are classified according to the risk preferences and a measurement method of risk preferences is proposed. Second, a risk preference decision matrix is obtained and a new calculation formula of likelihood is defined. Finally, we obtain the ranking results of alternatives by calculating the signed distance. Our example analysis shows that the proposed method is scientific and reasonable, and different risk preferences influence the results of decision making. Comparison with previous methods shows that the proposed algorithm is more feasible; it is applicable for decision making on both risk preferences and risk conservation.