Zadeh, Mamdani and TSK are proposed different fuzzy conditional inferences for "if ... then ... ". These Zadeh and Mamdani fuzzy conditional inference are required prior information for both precedent and consequent part. Zadeh defined fuzzy set with single membership function. Fuzzy set with two membership function will give more evidence than single membership function. In this paper, fuzzy conditional inference is studied for "if ... then ..." when prior information is not available for consequent part. Generalized fuzzy certainty factor is proposed for fuzzy set with two membership function. Fuzzy medial expert system is given as an application.