Strong pair domination number in intuitionistic fuzzy influence graphs with application for the selection of hospital having the optimal medical facilities

Abstract

A fuzzy influence graph is a well-organized, practical, and applicable tool to manage the uncertainty involved in all real-life challenges where uncertain facts, figures, and findings are present. A fuzzy influence graph gives knowledge about the effect of a node on any edge of the graph. This article presents the notion of domination for intuitionistic fuzzy influence graph (IFIG). Some results regarding the domination in fuzzy graphs are also extended in IFIGs. Some basic concepts in IFIGs such as walk, path, strength of influence pair, strong influence pair, strongest influence pair, weak influence pair, influence cut node, influence bridge, influence cut pair, complete IFIG, order of IFIG, size of IFIG, strong fuzzy influence pair domination number and minimum strong fuzzy influence pair domination number are being defined. Finally, an application is explored in which minimum strong fuzzy influence pair domination number is obtained by using minimal strong fuzzy influence pair dominating set, which indicates the hospital has the optimal medical facilities. To improve the analysis of our suggested model, the TOPSIS and VIKOR methods are presented together with various entropies.