Connection Properties in FN-Spaces

In this paper we have studied the connection properties in fuzzy nearness spaces. We have defined the fuzzy uniform local uniform connectedness and fuzzy uniform local connectedness of fuzzy nearness spaces. We have shown that a fuzzy nearness space is fuzzy uniformly locally uniformly connected iff its completion is. Also every topological fuzzy locally connected fuzzy nearness space is fuzzy uniformly locally uniformly connected. We also establish the result for a fuzzy topological space X that X has a fuzzy locally connected regular T1- extension iff X is the underlying fuzzy topological space of a fuzzy nearness space Y which is concrete, regular and fuzzy uniformly locally uniformly connected. Lastly we achieve the equivalence of the concepts of fuzzy uniform local uniform connectedness, fuzzy uniform local connectedness and fuzzy local connectedness.