In multicriteria decision‐making (MCDM), the existing aggregation operators are mostly based on algebraic t‐conorm and t‐norm. But, Archimedean t‐conorms and t‐norms are the generalized forms of t‐conorms and t‐norms which include algebraic, Einstein, Hamacher, Frank, and other types of t‐conorms and t‐norms. From that view point, in this paper the concepts of Archimedean t‐conorm and t‐norm are introduced to aggregate Pythagorean hesitant fuzzy information. Some new operational laws for Pythagorean hesitant fuzzy numbers based on Archimedean t‐conorm and t‐norm have been proposed. Using those operational laws, Archimedean t‐conorm and t‐norm‐based Pythagorean hesitant fuzzy weighted averaging operator and weighted geometric operator are developed. Some of their desirable properties have also been investigated. Afterwards, these operators are applied to solve MCDM problems in Pythagorean hesitant fuzzy environment. The developed Archimedean aggregation operators are also applicable in Pythagorean fuzzy contexts also. To demonstrate the validity, practicality, and effectiveness of the proposed method, a practical problem is considered, solved, and compared with other existing method.

In this paper, Bonferroni mean (BM) and Dombi t-conorms and t-norms (Dt-CN&t-Ns) are combined under dual hesitant q-rung orthopair fuzzy (DHq-ROF) environment to produce DHq-ROF-Dombi BM, weighted Dombi BM, Dombi geometric BM, and Dombi weighted geometric BM aggregation operators (AOs). Using these operators, the decision making processes would become more flexible and also would possess the capabilities of capturing interrelationships among input arguments under imprecise decision making environments. Apart from those, a large number of AOs either already developed or not yet developed may also be derived from the proposed AOs. In the process of developing the AOs, some operational laws of DHq-ROF numbers based on Dt-CN&t-Ns are defined first. Several important properties of the developed operators are discussed. The proposed AOs are used to frame a new methodology to solve multicriteria group decision making problems under DHq-ROF contexts. Several illustrative examples are solved to demonstrate effectiveness and benefits of the developed method. Sensitivity analysis is performed to show the variations of ranking values with the change of different parameters in the decision making contexts. Finally, the introduced method is compared with several existing techniques to establish superiority and effectiveness of the proposed method.

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In this article, Archimedean t‐norm and t‐conorm (At‐N&t‐CN)‐based aggregation operators are developed for aggregating the interval‐valued dual hesitant fuzzy (IVDHF) elements (IVDHFEs), which can cover a wide variety of existing aggregation operators. After introducing the concept of IVDHF set, several related terms, viz., score function, accuracy function, and degree of hesitancy are defined. Using At‐N&t‐CN, different operations for IVDHFEs are presented. Conversion processes from the developed operators to other forms of operators in several variants of fuzzy environments are discussed. An approach to solve multicriteria decision making problem in IVDHF context is presented using the developed concepts. To demonstrate proficiency of the developed method, an illustrative example is presented. Furthermore, several numerical examples, studied previously, are also solved, and achieved solutions are compared with the existing ones to establish the robustness of the proposed operator.

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