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A New Model of Fuzzy Logic: Monadic Monoidal T-Norm Based Logic
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Abstract
In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators. After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras. By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras and characterize simple and subdirectly irreducible monadic MTL-algebras. Moreover, present monadic monoidal t-norm based logic (MMT L), a system of many valued logic capturing the tautologies of monadic MTL-algebras and prove a completeness theorem.AMS Classification: 08A72, 03G25, 03B50, 03C05.
Title: A New Model of Fuzzy Logic: Monadic Monoidal T-Norm Based Logic
Description:
Abstract
In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators.
After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras.
By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras and characterize simple and subdirectly irreducible monadic MTL-algebras.
Moreover, present monadic monoidal t-norm based logic (MMT L), a system of many valued logic capturing the tautologies of monadic MTL-algebras and prove a completeness theorem.
AMS Classification: 08A72, 03G25, 03B50, 03C05.
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