Abstract: Data dependencies are the formal representation for the mutual constraints condition between the values of attributes,and functional dependencies are some of important influence data dependencies for the schema design and query in the database．In the uncertain relation,there are several possible values for every attribute in a tuple,so the mutual constraints for the values of attributes are more complicated than in the certain relation．We proposed a formal definition for uncertain relation and three kind of uncertain function dependencies,and then proved their inference rules．We would illustrate that above uncertain function dependences have important meaning in the guidance of normal form design in the uncertain relation．

Key words: Uncertain relation,Uncertain function dependence,Standardized design,Inference rules