Consistency test and weight generation for additive interval fuzzy preference relations. (English) Zbl 1406.91093
Summary: Some simple yet pragmatic methods of consistency test are developed to check whether an interval fuzzy preference relation is consistent. Based on the definition of additive consistent fuzzy preference relations proposed by T. Tanino [Fuzzy Sets Syst. 12, 117–131 (1984; Zbl 0567.90002)], a study is carried out to examine the correspondence between the element and weight vector of a fuzzy preference relation. Then, a revised approach is proposed to obtain priority weights from a fuzzy preference relation. A revised definition is put forward for additive consistent interval fuzzy preference relations. Subsequently, linear programming models are established to generate interval priority weights for additive interval fuzzy preference relations. A practical procedure is proposed to solve group decision problems with additive interval fuzzy preference relations. Theoretic analysis and numerical examples demonstrate that the proposed methods are more accurate than those in [Z. Xu and J. Chen, Eur. J. Oper. Res. 184, No. 1, 266–280 (2008; Zbl 1152.91416)].
MSC:
| 91B06 | Decision theory |
| 90B50 | Management decision making, including multiple objectives |
| 91B08 | Individual preferences |
| 90C05 | Linear programming |
| 03E72 | Theory of fuzzy sets, etc. |
Keywords:
multiple criteria decision analysis; interval fuzzy preference relation; consistency test; weight generation; additive consistent; linear programmingReferences:
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