Consistency analysis and priority derivation of triangular fuzzy preference relations based on modal value and geometric mean

摘要: Existing consistency notions of triangular fuzzy preference relations (TFPRs) are illustrated to be non-robust.New and acceptable definitions put forward for TFPRs.We propose a notion normalized multiplicative weights (NTFMWs).Transformation formulae provided convert NTFMWs into consistent TFPRs.A logarithmic least square model is developed derive NTFMW vector from TFPR. Triangular relation (TFPR) an effective framework pairwise estimations with imprecision vagueness. In order obtain reliable rational decision result, it important investigate priority derivation TFPRs. The paper analyzes existing properties TFPRs, illustrates that they have no invariance respect permutations alternatives. A new arithmetic based transitivity equation introduced define reflects modal values geometric means estimations. Some presented Geometric mean uncertainty ratio transformation devised further established deriving weight TFPR consistency. method compare rank weights. Three numerical examples including group making problem examined demonstrate validity advantages the proposed models.