Sometimes Artificial Intelligence (AI) has to deal with undecided problems. An undecided problem has no computer solution. The non-monotonic problem is undecided. Fuzzy logic will make undecided into decided. Fuzzy logic with twofold fuzzy set will give conclusion for non-monotonic reasoning. In this paper, Fuzzy non-monotonic reasoning is studied with twofold fold fuzzy membership functions belief and disbelief twofold to made undecided problem in to decidable. Fuzzy certainty factor (FCF) is defined to eliminate conflict between belief and disbelief. Fuzzy truth maintenance system (FTMS) is studied for computation of fuzzy non-monotonic reasoning to make monotonic. Some examples are given for fuzzy non-monotonic reasoning.