Abstract

In this manuscript, we first initiate several types of effective arcs of intuitionistic fuzzy directed graphs, followed by discussions on different types of dominations in intuitionistic fuzzy directed graphs and their application in decision-making. The notion of dominations in fuzzy graphs, fuzzy directed graphs, intuitionistic fuzzy graphs and picture fuzzy graphs have been extensively discussed in the literature. Thus, the work presented in our study is two-fold: on one side, it extends the notion of domination in fuzzy directed graphs, while on the other side, it fills the gap existing in the literature. Initially, we introduce several types of effective arcs like semi-λ effective arc, semi-ν effective arcs in intuitionistic fuzzy directed graphs. Subsequently, we initiate the notions of dominations and domination numbers for several types of intuitionistic fuzzy directed graphs based on these effective arcs. We present numerous significant characterizations of dominations in intuitionistic fuzzy directed graphs by utilizing minimal dominating sets. Furthermore, we investigate the minimal dominating sets and domination numbers of intuitionistic fuzzy-dipaths and dicycles, and provide various fascinating results. Finally, by utilizing the concepts presented in this study, we provide the algorithm for the solution of the problem related to decision-making regarding the opening of restaurants in various areas of the different cities.