Abstract
The aim of this paper is to introduce the notion of m-polar spherical fuzzy set (mPSFS) as a hybrid model of spherical fuzzy set (SFS) and m-polar fuzzy set (mPFS). The proposed model named as mPSFS is an efficient model to address multi-polarity in a spherical fuzzy environment. That is, an mPSFS assigns [Formula: see text] number of ordered triple of three independent grades (membership degree, neutral-membership degree and non-membership degree) against each alternative in the universe of discourse. The existing models, namely, mPFS and SFS, are the special cases of suggested hybrid mPSFS. In order to ensure the novelty of this robust extension, various operations on the m-polar spherical fuzzy sets (mPSFSs) are introduced with some brief illustrations to understand these concepts. A robust multi-criteria decision-making (MCDM) method is established by using new score function and accuracy function for m-polar spherical fuzzy numbers (mPSFNS). Additionally, the extensions of technique of order preference by similarity to ideal solution (TOPSIS) and gray relationship analysis (GRA) towards m-polar spherical fuzzy environment are proposed. Moreover, an application to nephrotic syndrome which may lead to kidney damage is analyzed by extensions TOPSIS and GRA. The proposed techniques and their algorithms provide a fruitful diagnosis procedure in the treatment of nephrotic syndrome. Lastly, we give a comparison analysis of the suggested models with some existing models as well.