In this paper, edge dominating set, fuzzy edge independent set of a fuzzy graph and relation between them are discussed. The edge domination number  of the fuzzy graph G is the minimum cardinality taken over all edge dominating sets of G. The fuzzy edge independence number  is the maximum cardinality taken over all fuzzy edge independent sets of G. We also prove some results on

edgedominatingset, edgedominationnumber,fuzzyedge independent set, fuzzy edge independence number.