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Power of Continuous Triangular Norms with Application to Intuitionistic Fuzzy Information Aggregation

Xinxing WuDan HuangHarish GargGuanrong ChenMicha{\l} Baczy\'nskiPeide Liu
Dec 2022
摘要
The paper aims to investigate the power operation of continuous triangularnorms (t-norms) and develop some intuitionistic fuzzy information aggregationmethods. It is proved that a continuous t-norm is power stable if and only ifevery point is a power stable point, and if and only if it is the minimumt-norm, or it is strict, or it is an ordinal sum of strict t-norms. Moreover,the representation theorem of continuous t-norms is used to obtain thecomputational formula for the power of continuous t-norms. Based on the poweroperation of t-norms, four fundamental operations induced by a continuoust-norm for the intuitionistic fuzzy (IF) sets are introduced. Furthermore,various aggregation operators, namely the IF weighted average (IFWA), IFweighted geometric (IFWG), and IF mean weighted average and geometric (IFMWAG)operators, are defined, and their properties are analyzed. Finally, a newdecision-making algorithm is designed based on the IFMWAG operator, which canremove the hindrance of indiscernibility on the boundaries of some classicalaggregation operators. The practical applicability, comparative analysis, andadvantages of the study with other decision-making methods are furnished toascertain the efficacy of the designed method.
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