Picture fuzzy set-based decision-making approach using Dempster-Shafer theory of evidence and grey relation analysis and its application in COVID-19 medicine selection

To offer better treatment for a COVID-19 patient, preferable medicine selection has become a challenging task for most of the medical practitioners as there is no such proven information regarding it. This article proposes a decision-making approach for preferable medicine selection using picture fuzzy set (PFS), Dempster-Shafer (D-S) theory of evidence and grey relational analysis (GRA). PFS is an extended version of the intuitionistic fuzzy set, where in addition to membership and non-membership grade, neutral and refusal membership grades are used to solve uncertain real-life problems more efficiently. Hence, we attempt to use it in this article to solve the mentioned problem. Previously, researchers considered the neutral membership grade of the PFS similar to the other two membership values (positive and negative) as applied to the decision-making method. In this study, we explore that neutral membership grade can be associated with probabilistic uncertainty which is measured using D-S theory of evidence and FUSH operation is applied for the aggregation purpose. Then GRA is used to measure the performance among the set of parameters which are in conflict and contradiction with each other. In this process, we propose an alternative group decision-making approach by the evidence of the neutral membership grade which is measured by the D-S theory and the conflict and contradiction among the criteria are managed by GRA. Finally, the proposed approach is demonstrated to solve the COVID-19 medicine selection problem.