Implications of the frequentist interpretation of fuzzy logic
D.G. Joder · 2005
A generalization of Kronecker's delta symbol is introduced to emphasize a frequency-ratio interpretation of fuzzy truth valuations. Methods of inferring such valuations for compound expressions are then considered, and some problems with several of the currently accepted formulas for fuzzy conjunction are exhibited. The universal validity, in this context, of the stochastic (probabilistic) version of fuzzy logic is demonstrated, and a conjecture is advanced that for expressions involving large numbers of base predicates, only the stochastic formulation reliably satisfies the constraints of the frequentist interpretation.