Power Muirhead mean in spherical normal fuzzy environment and its applications to multi-attribute decision-making: Spherical normal fuzzy power Muirhead mean.

This study aims to propose the power Muirhead mean (PMM) operator in the spherical normal fuzzy sets (SNoFS) environment to solve multiple attribute decision-making problems. Spherical normal fuzzy sets better characterize real-world problems. On the other hand, the Muirhead mean (MM) considers the relationship between any number of criteria of the operator. Power aggregation (PA) reduces the negative impact of excessively high or excessively low values on aggregation results. This article proposes two new aggregation methods: spherical normal fuzzy power Muirhead mean (SNoFPMM) and spherical normal fuzzy weighted power Muirhead mean (SNoFWPMM). Also, these operators produce effective results in terms of their suitability to real-world problems and the relationship between their criteria. The proposed operators are applied to solve the problems in choosing the ideal mask for the COVID-19 outbreak and investment company selection. However, uncertainty about the effects of COVID-19 complicates the decision-making process. Spherical normal fuzzy sets can handle both real-world problems and situations involving uncertainty. Our approach has been compared with other methods in the literature. The superior aspects and applicability of our strategy are also mentioned.