Abstract
UML is a standard for object-oriented modeling. Since the majority of real world information is uncertain and vague, fuzzy UML has been presented. Analogous to UML, fuzzy UML is semi-formed. In order to solve this problem, this paper attempts to formalize fuzzy UML class diagrams with fuzzy description logics, mainly with focus on formalization of elements in fuzzy UML class diagram and applying this approach to fuzzy UML models for verifying its availability.