A study on coopetition using bipolar fuzzy bunch graphs

Several methodologies have been proposed in the literature of graph theory for depicting collaboration among entities. However, in these studies, the measure of collaboration is taken based on the crisp graphical properties and discusses only its positive effects. In this manuscript, we discuss the simultaneous collaboration and competition that are observed among individuals, organizations, countries, communities and many others. The notion of bipolar fuzzy bunch graph (BFBG) is introduced in this study to effectively capture the positive and negative effects of both the terms collaboration and competition, which is jointly called coopetition. The goal of this paper is to introduce an improved representation and analytical measure for coopetition. To further enrich the literature on competition graphs, the notion of survival and winning competition among species has been introduced and also provides its bipolar fuzzy competition degrees. We also introduce two types of coopetition measures to understand the ranking structure of entities (i.e. which node batter collaborates and competes with other nodes) in the network: a) bipolar fuzzy coopetition degree and b) bipolar fuzzy coopatition index. In the form of a bipolar fuzzy coopetition graph, we find evidence to validate our framework and computations. We gathered research articles on COVID-19 and their citations over a specific time period from a specific journal. To demonstrate our approach, we displayed bipolar fuzzy collaboration and competition of various countries on COVID-19 and classified their rankings based on their positive and negative coopetition indices.