Retraction Note: 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.

[This retracts the article DOI: 10.1007/s00500-021-05909-9.].

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.

Preferred hospitalization of COVID-19 patients using intuitionistic fuzzy set-based matching approach

Preferable hospitalization of COVID-19 patients has become an urgent and challenging task to save lives amidst the unexpected rising of the 3rd wave, where fuzzy set and matching techniques are considered due to their inherent capability to deal with uncertain suitable pair selection. The matching technique has been widely used to solve decision-making problems due to its capability to determine the suitable pair between the objects of two disjoint sets, whereas fuzzy set is well known to manage uncertain situations. This paper extends the matching technique using fuzzy set and proposes a novel fuzzy matching approach to solve uncertain decision-making problems. We also extend the fuzzy matching approach in the framework of an intuitionistic fuzzy set. A relation between the matching technique and fuzzy set theory is established by developing the preference sequence of the elements. The fuzzy entropy is used to measure the closeness among the elements between two distinct sets. Applicability of the proposed approach is measured by providing an illustrative case study concerned with the preferred hospitalization of the COVID-19 patients. Finally, a comparative study is given to analyze the effectiveness of the proposed approach, where the intuitionistic fuzzy set-based matching approach shows better performance compared to fuzzy and conventional matching based approach. For experimentation purpose, this study uses 9424 patients and 234 hospitals with a total available capacity of 18,024 beds.