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By means of randomization, the concept of randomized truth degree and randomized logic pseudo-metric of formulas in R0-logic with six-valued nonlinear valuation set are introduced. The concept of randomized logic metric space based on R0-logic with six-valued nonlinear valuation set is also introduced and it is proved that the new built randomized concepts are extensions of the corresponding concepts...
By means of the probability measure theory of MV-algebras we introduce the concepts of probability truth degrees of the elements of MV-algebra and probability similarity degrees between elements, and then define therefrom three probability metric spaces on MV-algebra, and get some good results.
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