International Journal of Fuzzy Systems

, Volume 19, Issue 5, pp 1317–1332 | Cite as

A Consistency-Based Method to Decision Making with Triangular Fuzzy Multiplicative Preference Relations

  • Jie Tang
  • Fanyong Meng


Triangular fuzzy multiplicative preference relations (TFMPRs) enable decision makers to apply triangular fuzzy numbers to denote their preferences, which can express their vagueness and fuzziness. Consistency analysis is an important research topic that can guarantee logical ranking order. Considering previous research regarding the consistency of TFMPRs, several issues and limitations exist with these relations. The researches cannot cope well with certain situations, such as unacceptably consistent TFMPRs and incomplete TFMPRs. In this paper, a new consistency definition for TFMPRs is defined that can overcome the issues in the previous concepts. Next, several desirable properties of the definition are discussed, and the relationship between the new definition and two existing ones is presented. A linear goal programming model is also built to judge the consistency of TFMPRs, and a method is introduced to obtain an acceptably consistent TFMPR from an inconsistent one. Furthermore, several goal programming models are constructed to estimate missing values in an incomplete TFMPR. Finally, a decision-making method with TFMPRs is developed. Illustrative examples are offered to demonstrate the concrete application of the developed procedure, and a comparison analysis is also made.


Decision making Triangular fuzzy multiplicative preference relation Consistency analysis Programming model 



This work was supported by the National Natural Science Foundation of China (Nos. 71571192, 71671188, and 71501189), the Innovation-Driven Planning Foundation of Central South University (No. 2016CXS027), the State Key Program of National Natural Science of China (No. 71431006), the Projects of Major International Cooperation NSFC (No. 71210003), the Hunan Province Foundation for Distinguished Young Scholars of China (No. 2016JJ1024) and the China Postdoctoral Science Foundation (No. 2016M602170).


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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Business SchoolCentral South UniversityChangshaChina
  2. 2.School of International AuditNanjing Audit UniversityNanjingChina

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