Connectivity Concepts in Intuitionistic Fuzzy Incidence Graphs with Application

Abstract

In this research article, we presented the idea of intuitionistic fuzzy incidence graphs (IFIGs) along with connectivity concepts. IFIGs are the generalization of fuzzy incidence graphs (FIGs). Specific ideas analogous to intuitionistic fuzzy cut-vertices and intuitionistic fuzzy bridges in intuitionistic fuzzy graphs, intuitionistic incidence cut-vertices, and intuitionistic incidence bridges are explored. The notion of intuitionistic incidence gain and intuitionistic incidence loss for intuitionistic incidence paths and pairs of vertices is also initiated. In the case of FIGs, we have only membership value, and we do not have non-membership value (NMSV). Therefore, we use IFIGs because they are more reliable, valuable, and helpful than FIGs. Also, we can not apply graphs, fuzzy graphs, and FIGs to the application provided in Sect. 3 due to the non-availability of NMSV. An application in selecting the best paint company for investment among different companies by using IFIG is also obtained.

Complex t-Intuitionistic Fuzzy Graph with Applications of Rubber Industrial Water Wastes

“…Even though CIFS and CFS work together concept-wise in the field of cylindrical extensions, followed by projections and distant measurements, the individuality differs in the part of introducing a group of phase words, as CFS will always have one more additional term. The concept of IFG and its extensive application and evidence have been cited [32][33][34][35]. The recent research work by Asima Razzaque [36] in the area of TIFGs reveals solutions to complicated problems with the support of multiple factors considering the physical situations.…”

Connectivity Status of Intuitionistic Fuzzy Graph and Its Application to Merging of Banks

“…Naeem et al [21] introduced the connectivity index (CI), and average connectivity index (ACI) on intuitionistic fuzzy graphs. Nazeeret al [22] proposed the notion of intuitionistic fuzzy incidence graphs (IFIGs) with connectivity ideas. Alzoubi et al [23] introduced some concepts of connectivity in an intuitionistic fuzzy graph and connectivity in complete intuitionistic fuzzy graphs.…”

Some Connectivity Parameters of Interval-Valued Intuitionistic Fuzzy Graphs with Applications

“…The extension of IFG, named intuitionistic fuzzy competition graphs [20], intuitionistic fuzzy tolerance graphs [21], etc., have also been discussed in the literature. Similarly, the concepts of connectivity in intuitionistic fuzzy incidence graphs and their applications were explored in [22]. The term internally stable set in IFGs was explained in [23].…”