Conditional Randomized Divergence Degree of Theories in the Fuzzy Propositional Logic System BL*
DOI:
https://doi.org/10.15377/2409-5761.2026.13.1Keywords:
Fuzzy logic, Conditional randomized truth degree, Conditional randomized divergence degree, Conditional randomized logical metric space.Abstract
Using the concept of conditional probability and the randomization method of valuation sets, the conditional randomized truth degree of formulas is proposed in the fuzzy propositional logic system BL* with valuation domain [0,1]. The MP rule and HS rule for conditional randomized truth degrees are proven based on the semantics of BR0 algebra. At the same time, the concepts of conditional randomized similarity and conditional randomized pseudo-metric between formulas are introduced. It established a conditional randomized logic metric space. Within this conditional randomized logic metric space, the conditional randomized divergence of theories and its equivalent forms are proposed. Along with three different types of approximate reasoning modes, the relationships among them are discussed.
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