A bipolar fuzzy [formula omitted]-competition graph based ARAS technique for prioritizing COVID-19 vaccines

Abstract

A bipolar fuzzy competition graph helps to examine the competition between two vertices when they have a common out-neighbourhood. With this idea, the bipolar fuzzy p-competition graph (BFpCG) can be defined when two vertices have p common out-neighbourhood. In this study, the above-said concepts are defined along with certain characteristics such as low, high, semi-perfect and perfect competitive competition graphs based on the number of components, and certain important results are derived. Moreover, the extensions of BFpCG are discussed by considering various situations and illustrated by a food web problem of 13 species. Besides, an application is taken to find the competition among the COVID-19 vaccines against five mutations: Alpha, Beta, Gamma, Delta and Omicron. Multi-criteria decision-making (MCDM) techniques utilize to access the prioritization problems. The additive ratio assessment (ARAS) is a robust MCDM technique and it simplifies complex decision-making problems through the utility degree. An efficient outcome can be attained by this technique when it works with positive and negative perceptions. Therefore, this study constructs a novel bipolar fuzzy ARAS system based on the BFpCG. To demonstrate the applicability of the proposed system, an application is taken in prioritizing COVID-19 vaccines, where Moderna and CoronaVac resulted in first and last rank, respectively. For this purpose, the efficacy rate of the vaccines against severe disease is considered. Finally, the outcomes are validated through sensitivity and comparative analyses. Then, the managerial implications, future works and limitations of the study are provided to explore the proposed research.