Soft rough Pythagoreanm-polar fuzzy sets and Pythagorean m-polar fuzzy soft rough sets with application to decision-making

The aim of this paper is to present the notions of soft rough Pythagorean m-polar fuzzy sets (SRPMPFSs) and Pythagorean m-polar fuzzy soft rough sets (PMPFSRSs), by combining the prevailing ideas of soft sets, rough sets, Pythagorean sets and m-polar fuzzy sets. The suggested models of SRPMPFSs and PMPFSRSs are more efficient to discuss the roughness of the input data by means of crisp soft and Pythagorean m-polar fuzzy soft approximation spaces. We present some fundamental properties of Pythagorean m-polar fuzzy soft approximation spaces and their related examples. We discuss a case study of image denoising method in the field of image processing with the help of proposed models. We develop two novel algorithms for the selection of best image denoising method under crisp soft and Pythagorean m-polar fuzzy soft approximation spaces. We also demonstrate the feasibility and flexibility of the proposed models for solving multi-criteria decision-making problems involving parameterizations, Pythagorean grades and multi-polar information.