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A dominating set in a fuzzy graph is said to be a g-eccentric dominating set if for every vertex in at least one g-eccentric vertex of in . If contains g-eccentric dominating set ′ of a fuzzy graph then is called as an inverse g-eccentric dominating set with respect to . The lowest cardinality taken over all the inverse g-eccentric dominating sets of is called the inverse g-eccentric domination number. In this article, an inverse g-eccentric point set, the inverse g-eccentric dominating set and their numbers in fuzzy graphs are introduced. Bounds for some standard fuzzy graphs are obtained.