Zadeh defined fuzzy sets for incomplete information with single fuzzy membership. REN Ping has defined Generalized fuzzy set with two fold membership functions “True” and “False”. In this paper Zadeh fuzzy logic is extended to REN Ping generalize fuzzy logic for incomplete information. Generalized fuzzy logic, fuzzy inference and fuzzy reasoning are discussed using Feneralized fuzzy sets. Generalized Fuzzy Certainty Factor(GFCF) is studied as the difference of “True “ and “False” fuzzy membership functions to eliminate the conflict of evidence in Incomplete Information. The fuzzy truth variables are also discussed for Generalised fuzzy sets