An approach to decision-making with triangular fuzzy reciprocal preference relations and its application. (English) Zbl 1385.93050
Summary: 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 judge the additive consistency of TFRPRs and to estimate 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 a comparison analysis is performed.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |
Keywords:
decision-making; triangular fuzzy reciprocal preference relation; additive consistency; programming modelReferences:
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