Generalized Fuzzy Theory with Two Fuzzy Membership Functions and Application to Medical Expert Systems

Zadeh defined fuzzy set with membership function A=μA(x ) for the proposition of the type “x is A”. Fuzzy set with single membership function is not sufficient to deal with uncertain information. The fuzzy set with two fuzzy membership functions will give more evidence to deal with uncertainty. In this paper, fuzzy set is defined by generalized fuzzy set A={μABelief(x), μDisbelief(x)} with the two fuzzy membership functions based on Belief and Disbelief. The fuzzy inference and the fuzzy reasoning are studied with generalized fuzzy set. The fuzzy conditional inference for "if … then …" and "if … then …  else" are discussed with two fuzzy membership functions, also Fuzzy Certainty Factor is defined with difference between "Belief" and "Disbelief" membership functions to made as single fuzzy membership function. An Medical Expert System is discussed as one of the applications of Generalized fuzzy set. In EMYCIN, Belief anf Disbelief are defined with Probability. In this paper, generalized fuzzy sets are discussed for EMYCIN.