Eigen spherical fuzzy set and its application to decision-making problem

Eigen fuzzy set of a fuzzy relation often occurs to be invariant under different computational aspects. The present communication introduces the novel concept of eigen spherical fuzzy set of spherical fuzzy relation along with various composition operators for the first time. We have proposed two algorithms to determine the greatest eigen spherical fuzzy sets and least eigen spherical fuzzy sets using the $max-min$ and $min-max$ composition operators respectively and illustrated the steps with the help of flow charts. Further, two numerical examples related to different fields of decision-making problems have been taken into account for illustrating the proposed methodology. The scope of future work in the field of image information retrieval, genetic algorithm for image reconstruction and notion of eigen spherical fuzzy soft sets/matrices has been duly outlined. The comparative remarks and advantages of the proposed eigen spherical fuzzy sets have also been included for a better readability.