Fuzzy Directed Graphs and its Real-time Applications

Abstract

Fuzzy directed graphs are a generalization of directed graphs, where the degree to which a vertex dominates another vertex is not binary, but rather can be any value in the interval [0, 1]. This allows for a more nuanced representation of domination, as the degree of domination can be used to represent the strength or confidence of the domination relationship. Fuzzy directed graphs can be used to model a variety of real-world problems, such as power grid management, air traffic control, and transportation planning. Fuzzy directed graph algorithms can be used to solve problems such as finding a fuzzy dominating set, finding a fuzzy spanning tree, and finding a fuzzy Eulerian path. This paper presents a review of the literature on fuzzy directed graphs and their real-time applications. The paper discusses the theoretical aspects of fuzzy directed graphs, as well as their applications to real-world problems. The paper also discusses the challenges and opportunities for future research in this area.