Some New Concepts of Interval-Valued Picture Fuzzy Graphs and Their Application Toward the Selection Criteria

Abstract

Interval-valued picture fuzzy sets (IVPFSs) being the most advanced form of fuzzy sets (FSs) has more capacity to analyze the network state more intelligently. It is proven that IVPFS is most useful to solve many real life problems having uncertainties. In comparison with the other generalizations of fuzzy graphs (FGs), IVPFG is proven more beneficial in solving complicated problems containing uncertainties. In this study, we propose some new concepts of covering and matching in IVPFGs based on strong arcs. We begin our study by introducing the concepts of covering in IVPFGs which includes strong node covering (SNC), strong arc covering (SAC), strong arc covering number (SAC number), and strong independent set (SIS). Based on these terms, we provide several characterizations of different types of IVPFGs like complete IVPFGs and complete bipartite IVPFGs. Afterward, we introduce the terms matching, strong matching etc for IVPFGs. We also present some useful results related to some special IVPFGs with respect to these terms. Finally, we provide the utilization of strong arcs and SIS in order to arrange the meeting of the members of social network comprising players engaged in diverse games.