Analysis of double domination by using the concept of spherical fuzzy information with application

Abstract

The concept of fuzzy graph (FG) and its generalized forms have been developed to cope with several real-life problems having some sort of imprecision like networking problems, decision making, shortest path problems etc. This paper is based on some developments in generalization of FG theory to deal with situations where imprecision is characterized by four types of membership grades. A novel concept of the domination of T-spherical fuzzy graph (TSFG) is proposed as a common generalization of the domination of FG, intuitionistic fuzzy graph (IFG) and picture fuzzy graph (PFG) based on a recently introduced concept of T-spherical fuzzy set (TSFS). This paper aims to bring into focus the proposal of the graph of T-Spherical fuzzy sets. Moreover, this research analyzes the concepts of domination and double domination theory in T-spherical fuzzy environment. More precisely, the framework of T-spherical fuzzy graphs is introduced, and their related theory is provided with the help of illustrative examples. Further, the domination theory that attached to T-spherical fuzzy graphs is developed. Some cardinality, order, strength and completeness on domination, neighbors in a TSFG bipartite TSFG and double domination set and some results are also studied in the environment of T-spherical fuzzy graphs. As an application, a political campaign is modeled using the proposed work, and explored that how the double domination could deal with political campaign. Finally, a comparison amongst the proposed and the existing studies is developed and advantages of the work in the environment of T-spherical fuzzy graph are discussed.