Application of conditional and relational event algebra to the defining of fuzzy logic concepts

Beginning with work in the mid 1970's and early 1980's, it was discovered that fundamental homomorphic-like relations exist between many first order fuzzy logic concepts and naturally corresponding probability ones via the one-point coverage events for appropriately chosen random subsets of the domains of the fuzzy sets considered. This paper first extends and modifies the above-mentioned homomorphic-like relations previously established. It also introduces a number of new homomorphic-like relations between fuzzy logic concepts and probability, utilizing two recently derived subfields of probability theory: conditional and relational event algebra. In addition, a newly invigorated branch of probability theory dealing with second order probabilities (or "probabilities of probabilities") is shown to be applicable to treating certain deduction problems involving conditioning of populations.