Intuitionistic fuzzy threshold graphs

In this study, we provide a generalization of fuzzy threshold graphs, and introduce three notions, which are intuitionistic fuzzy threshold graphs, intuitionistic fuzzy alternating 4-cycle, and threshold dimension of intuitionistic fuzzy graphs. Then we discuss some properties about intuitionistic fuzzy graphs, and obtain two main results. The first one is that under some conditions, an intuitionistic fuzzy graph is equivalent to an intuitionistic fuzzy threshold graph. The second one is that the underlying graph of an intuitionistic fuzzy threshold graph is a split graph, and conversely, a given split graph can be used to construct an intuitionistic fuzzy threshold graph. Finally, we give two applications of intuitionistic fuzzy threshold graphs, which are used to control water resource and power resources, respectively. Through the two applications, we know that intuitionistic fuzzy threshold graphs are more appropriate than fuzzy threshold graphs in controlling water resource and power resource, because intuitionistic fuzzy sets are more suitable and powerful to deal with uncertainty and vagueness compared to fuzzy sets.