ABSTRACT
This study mainly aims to develop two effective and practical multi-criteria group decision-making approaches by taking advantage of the ground-breaking theory of PROMETHEE family of outranking methods. The presented variants of Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method are acknowledged to address the complex decision-making problems carrying the ambiguous information, expressible in terms of yes, no, abstinence and refusal, owing to the preeminent condition and wider structure of spherical fuzzy sets. Both of the proposed approaches seek help from the Shannon's entropy formula to evaluate the object weights of the decision criteria. The proposed techniques operate by taking into account the deviation between each pair of potential alternatives in accordance to different types of preference functions to determine the preference indices. The proposed technique of spherical fuzzy PROMETHEE I method carefully compares the positive and negative outranking flows of the alternative to get partial rankings. In contrast, the spherical fuzzy PROMETHEE II method has the edge to eliminate the incomparable pair by employing the net outranking flow to derive the final ranking. The application of proposed approaches is explained via a case study in the field of medical concerning the selection of appropriate site to establish Fangcang shelter hospital in Wuhan to treat COVID-19 patients. The convincing comparisons of the proposed methodologies with q-rung orthopair fuzzy PROMETHEE and spherical fuzzy TOPSIS methods are also included to verify the aptitude of the proposed methodology.