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Aggregation of q-rung orthopair fuzzy information serves as an important branch of the q-rung orthopair fuzzy set theory, where operations on q-rung orthopair fuzzy values (q-ROFVs) play a crucial role. Recently, aggregation operators on q-ROFVs were established by employing the Einstein operations rather than the algebraic operations. In this paper, we give a further investigation on operations and aggregation operators for q-ROFVs based on the Einstein operational laws. We present the operational principles of Einstein operations over q-ROFVs and compare them with those built on the algebraic operations. The properties of the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator and q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator are investigated in detail, such as idempotency, monotonicity, boundedness, shift-invariance and homogeneity. Then, the developed operators are applied to multiattribute decision making problems under the q-rung orthopair fuzzy environment. Finally, an example for selecting the design scheme for a blockchain-based agricultural product traceability system is presented to illustrate the feasibility and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Dombi operations which include the Dombi product and Dombi sum are special cases of t-norms and t-conorms besides the algebraic operations. Recently, operations and aggregation operators for q-rung orthopair fuzzy values (q-ROFVs) based on Dombi operations were proposed. In this paper, we further discuss some additional issues relating to Dombi operations and Dombi aggregation operators of q-ROFVs. First, we give a reasonable explanation for the definition of the Dombi scalar multiplication and Dombi exponentiation which are constructed respectively by the Dombi sum and Dombi product over q-ROFVs, and then investigate the fundamental properties of these operations. Subsequently, the shift-invariance and homogeneity properties of the q-rung orthopair fuzzy Dombi weighted averaging/geometric operators are analyzed. And the boundedness of aforementioned aggregation operators are precisely characterized with respect to the parameter in Dombi operations. Finally, a method for multiattribute decision making is proposed by utilizing the developed operators under the q-rung orthopair fuzzy environment and an example of the selection of investment companies is given to illustrate the detailed decision making process. [ABSTRACT FROM AUTHOR]

Weighted power means with weights and exponents serving as their parameters are generalizations of arithmetic means. Taking into account decision makers' flexibility in decision making, each attribute value is usually expressed by a q‐rung orthopair fuzzy value (q‐ROFV, q≥1), where the former indicates the support for membership, the latter support against membership, and the sum of their qth powers is bounded by one. In this paper, we propose the weighted power means of q‐rung orthopair fuzzy values to enrich and flourish aggregations on q‐ROFVs. First, the q‐rung orthopair fuzzy weighted power mean operator is presented, and its boundedness is precisely characterized in terms of the power exponent. Then, the q‐rung orthopair fuzzy ordered weighted power mean operator is introduced, and some of its fundamental properties are investigated in detail. Finally, a novel multiattribute decision making method is explored based on developed operators under the q‐rung orthopair fuzzy environment. A numerical example is given to illustrate the feasibility and validity of the proposed approach, and it is shown that the power exponent is an index suggesting the degree of the optimism of decision makers. [ABSTRACT FROM AUTHOR]