A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations
To express uncertain information in decision making, triangular fuzzy reciprocal preference relations (TFRPRs) might be adopted by decision makers. Considering consistency of this type of preference relations, this paper defines a new additive consistency concept, which can be seen as an extension of that for reciprocal preference relations. Then, a simple method to calculate the triangular fuzzy priority weight vector is introduced. When TFRPRs are inconsistent, a linear goal programming framework to derive the completely additive consistent TFRPRs is provided. Meanwhile, an improved linear goal programming model is constructed to estimate the missing values in an incomplete TFRPR that can address the situation where ignored objects exist. After that, an algorithm for decision making with TFRPRs is presented. Finally, numerical examples and comparison analysis are offered.
KeywordsDecision making Triangular fuzzy reciprocal preference relation Additive consistency Goal programming model
The authors first gratefully thank the Associate Editor and the anonymous referees for their valuable and constructive comments which have much improved the paper. This work was supported by the State Key Program of National Natural Science of China (No. 71431006), the Projects of Major International Cooperation NSFC (No. 71210003), the National Natural Science Foundation of China (Nos. 71571192, 71501189, 71201089, 71271217, and 51204100), the Hunan Province Foundation for Distinguished Young Scholars of China (2016JJ1024), and the Postdoctoral Science Special Foundation of China (2015T80901), the Innovation-Driven Planning Foundation of Central South University (No. 2016CXS027).
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