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Intervals and convexity play crucial roles in the applications of graph theory such as town planning and design of graphics. In this article, the concept of geodetic interval in graphs is extended to fuzzy graphs. Intervals are useful in the study of properties of fuzzy graphs which depend on the geodetic distance between vertices. The axiomatic definition of intervals in fuzzy graphs are used to define intervals in different fuzzy graph structures like fuzzy trees and complete fuzzy graphs. Finally a set theoretic operations of intervals like union, intersection are also discussed and some results are obtained.