The aim of this paper is to establish some common fixed point theorems under occasionally weakly compatible maps using implicit functions.

The fundamental goal of this research is to develop a MAGDM (Multi-Attribute Group Decision Making) problem of Medical Consumption Products. We propose TODIM–VIKOR approach in this paper, which combines the TODIM (an acronym in Portuguese for Interactive and Multi-criteria Decision-Making) and VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) procedures under Fermatean fuzzy information. A new Fermatean fuzzy scoring function is presented for dealing with comparison problems. In addition, we introduce a novel entropy measure for assessing the degree of fuzziness associated with an FFS. We also offer a Jensen–Shannon divergence measure for the Fermatean Fuzzy set that can be used to compare the discrimination information of two FFSs. This suggested measure meets all mathematical standards for being considered a measure. We introduced entropy and divergence measures to determine the objective weight in the TODIM–VIKOR approach. Meanwhile, to deal with multiple attribute group decision-making, a new decision procedure based on the suggested Entropy and Jensen–Shannon divergence measure was proposed in a Fermatean Fuzzy environment. In this article, TODIM has in view to find out the overall dominance degree, and VIKOR is to determine the compromise solution. Finally, we manage a supplier selection problem to verify the performance of the suggested Fermatean fuzzy TODIM–VIKOR method by comparing the ranking solution to the rankings of existing methodologies. We investigate the reliability and effectiveness of our proposed methodology.

In present paper, we proposed a Gini Simpson index for picture fuzzy set with their application in MADM and discuss it’s properties which are investigated in a mathematical framework. We developed an algorithm based on TODIM(An acronym in Portuguess for interactive multi-attribute decision making) which we applied ton the proposed entropy to solve the MADM problems under the picture fuzzy environment when the criteria weights are completely known. With took a numerical example on Muthoot Finance Limited to demonstrate the applicability and feasibility of the proposed approach.

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