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In many medical applications, we diagnose a disease and/or apply a certain remedy if, e.g., two out of five conditions are satisfied. In the fuzzy case, i.e., when we only have certain degrees of confidence that each of n statement is satisfied, how do we estimate the degree of confidence that k out of n conditions are satisfied? In principle, we can get this estimate if we use the usual methodology of applying fuzzy techniques: we represent the desired statement in terms of “and” and “or”, and use fuzzy analogues of these logical operations. The problem with this approach is that for large n, it requires too many computations. In this paper, we derive the fastest-to-compute alternative formula. In this derivation, we use the ideas from neural networks. 1 Formulation of the Problem Need for fuzzy logic in medical applications. To diagnose a patient, to come up with appropriate cure, it is often important to perform many tests. Each tests results in numerous numerical values that describe the state of the patient: even a routine blood test returns several pages of numbers. These numbers are important and need to be taken into account, but, of course, medical doctors do not just operate based on these numbers, they also use their experience and intuition – if they operated by numbers only, it would have been easy

How to Describe Conditions Like 2-out-of-5 in Fuzzy Logic: A Neural Approach