Fuzzy k-competition graphs

Fuzzy competition graph as the generalization of competition graph is introduced here. A generalization of fuzzy competition graph known as fuzzy k-competition graph is also defined. These graphs are related to fuzzy digraphs. Fuzzy neighbourhood graphs, which are related to fuzzy graphs are defined here. Some relations between fuzzy competition graphs and fuzzy neighbourhood graphs have been established. Also several results to find strong edges of the stated graphs are obtained.