Abstract
In order to study the logic foundation of fuzzy reasoning and the construction of the sets D(Γ) , this paper first put forth a definition of generalized root of theoretic in Łukasiewicz propositional fuzzy logic system, \(G\ddot{o}del\) propositional fuzzy logic system, product propositional fuzzy logic system,and the R 0-propositional fuzzy logic system. Then it goes on to prove that D(Γ) is completely determined by its generalized root whenever theory Γ has a generalized root, thereafter it puts forward the construction of D(Γ). Finally, it argues that every finite theory Γ has a generalized root, which can be expressed in some specific form, and that there does exist certain relationship between different theory Γ.
Published Version
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