The generalized Heronian mean and geometric Heronian mean operators provide two aggregation operators that consider the interdependent phenomena among the aggregated arguments. In this paper, the generalized Heronian mean operator and geometric Heronian mean operator under the q‐rung orthopair fuzzy sets is studied. First, the q‐rung orthopair fuzzy generalized Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy geometric Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy generalized weighted Heronian mean (q‐ROFGWHM) operator, and q‐rung orthopair fuzzy weighted geometric Heronian mean (q‐ROFWGHM) operator are proposed, and some of their desirable properties are investigated in detail. Furthermore, we extend these operators to q‐rung orthopair 2‐tuple linguistic sets (q‐RO2TLSs). Then, an approach to multiple attribute decision making based on q‐ROFGWHM (q‐ROFWGHM) operator is proposed. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we presented 10 similarity measures between Pythagorean fuzzy sets (PFSs) based on the cosine function by considering the degree of membership, degree of nonmembership and degree of hesitation in PFSs. Then, we applied these similarity measures and weighted similarity measures between PFSs to pattern recognition and medical diagnosis. Finally, two illustrative examples are given to demonstrate the efficiency of the similarity measures for pattern recognition and medical diagnosis.

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Highlights EMV-ID tracker is used to measure the infectious disease pandemic. GARCH-MIDAS is adopted to model the impacts of EMV-ID on stock market volatility. Lagged realized volatility and economic policy uncertainty are used as controlling variables. Infectious disease pandemic imposes significant positive impact on stock market volatility. Infectious disease pandemic has the smallest impact on permanent volatility of china's stock market.

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The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multi‐input arguments. In this paper, we extend the MSM operator and dual MSM operator to q‐rung orthopair fuzzy sets to propose the q‐rung orthopair fuzzy MSM operator, q‐rung orthopair fuzzy dual MSM operator, q‐rung orthopair fuzzy weighted MSM operator, and q‐rung orthopair fuzzy weighted dual MSM operator. Then, some desirable properties and special cases of these operators are discussed in detail. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver the sensitivity analysis and comparative analysis.

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