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Heronian aggregation operators of intuitionistic fuzzy numbers based on the Archimedean t-norm and t-conorm

The aggregation operators based on the Archimedean t-norm and t-conorm provide general operational rules for intuitionistic fuzzy numbers (IFNs), where they can generalize most of the existing aggregation operators. The Heronian mean (HM) considers interrelationships among attributes. Therefore, it is very necessary to extend the HM to IFNs for developing intuitionistic fuzzy HM operators based on the Archimedean t-norm and t-conorm. In this paper, we firstly discuss intuitionistic fuzzy operational rules based on the Archimedean t-norm and t-conorm. Then, we propose the intuitionistic fuzzy Archimedean Heronian aggregation (IFAHA) operator and the intuitionistic fuzzy weight Archimedean Heronian aggregation (IFWAHA) operator of IFNs. We also discuss some properties and some special cases of the proposed operators. The proposed IFAHA operator and the proposed IFWAHA operator of IFNs can be used for group decision making in intuitionistic fuzzy environments.