27 July 1999 Application of conditional and relational event algebra to the defining of fuzzy logic concepts
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Abstract
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.
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I. R. Goodman, H. T. Nguyen, "Application of conditional and relational event algebra to the defining of fuzzy logic concepts", Proc. SPIE 3720, Signal Processing, Sensor Fusion, and Target Recognition VIII, (27 July 1999); doi: 10.1117/12.357169; https://doi.org/10.1117/12.357169
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