A Monotonous Intuitionistic Fuzzy TOPSIS Method Under General Linear Orders via Admissible Distance Measures

All intuitionistic fuzzy TOPSIS methods contain two key elements: (1) the order structure, which can affect choices of positive and negative ideal-points, construction admissible distance/similarity measures; (2) measure, is closely related to values relative closeness degrees determines accuracy rationality decision-making. For many efforts are devoted constructing some score functions, strictly distinguish different (IFVs) preserve natural partial for IFVs. This paper proves that such a function does not exist. distance or similarity examples given show classical measures based on Euclidean Minkowski do meet axiomatic definition IF measures. Moreover, illustrative ensure monotonicity with linear orders, may yield counter-intuitive results. To overcome limitation non-monotonicity, we propose novel method, using three new distances orders measured by degree/similarity degree, aggregation prove proposed method monotonous under these orders. first result strict mathematical proof method. Finally, practical illustrate efficiency developed TOPSIS.