Fuzzy logic based on Belief and Disbelief membership functions

Many theories are developed based on probability to deal with incomplete information. The fuzzy logic deals with belief rather than likelihood (probability). Zadeh first defined fuzzy set as a single membership function. The two fold fuzzy sets with two membership functions will give more evidence than a single membership one. Therefore there is need of fuzzy logic with two membership functions. In this paper, The fuzzy set is defined with two membership functions “Belief” and “Disbelief”. The fuzzy inference and fuzzy reasoning are studied for “a two fold fuzzy set”. The fuzzy certainty factor (FCF) is defined as a single membership function by taking difference between “ Belief” and “ Disbelief ”. The quantification of fuzzy truth variables are studied for “a two fold fuzzy set”. The medical expert system shell EMYCIN is given as an application of “a two fold fuzzy set”.