An approach to decision-making with triangular fuzzy reciprocal preference relations and its application

ABSTRACT

Triangular fuzzy reciprocal preference relations (TFRPRs) are powerful tools to denoting decision-makers’ fuzzy judgments, which permit the decision-makers to apply triangular fuzzy ratio rather than real numbers to express their judgements. Consistency analysis is one of the most crucial issues in preference relations that can guarantee the reasonable ranking order. However, all previous consistency concepts cannot well address this type of preference relations. Based on the operational laws on triangular fuzzy numbers, this paper introduces an additive consistency concept for TFRPRs by using quasi TFRPRs, which can be seen as a natural extension of the crisp case. Using this consistency concept, models to judging the additive consistency of TFRPRs and to estimating missing values in complete TFRPRs are constructed. Then, an algorithm to decision-making with TFRPRs is developed. Finally, two numerical examples are offered to illustrate the application of the proposed procedure, and comparison analysis is performed.

KEYWORDS:

• Decision-making
• triangular fuzzy reciprocal preference relation
• additive consistency
• programming model

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 71571192], [grant number 71671188], and [grant number 71501189], the Innovation-Driven Planning Foundation of Central South University [grant number 2016CXS027], the State Key Program of National Natural Science of China [grant number 71431006], the Projects of Major International Cooperation NSFC [grant number 71210003], the Hunan Province Foundation for Distinguished Young Scholars of China [grant number 2016JJ1024], and the China Postdoctoral Science Foundation [grant number 2016M602170].

Notes on contributors

Fanyong Meng

Fan-yong Meng received his Ph.D. degree in management and economics from Beijing Institute of Technology, Beijing, China, in 2011. Currently, he is a professor at School of Business, Central South University. His research interests include decision-making, fuzzy mathematics and games theory. His research results have been published in the Omega, Fuzzy Sets and Systems, Information Sciences, Applied Mathematical Modelling, IEEE Transactions on Systems, Man, and Cybernetics Systems, Group Decision and Negotiation, Fuzzy Optimisation and Decision Making, Applied Soft Computing, Knowledge-Based Systems, Applied Mathematics and Computation, Information Fusion, Journal of the Operational Research Society, and Computers and Industrial Engineering, among others.