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

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<p>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.</p>

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