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.
2018 ◽
2011 ◽
Vol 10
(02)
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pp. 231-243
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2014 ◽
Vol 24
(03)
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pp. 375-411
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2010 ◽
Vol 5
(5)
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pp. 642
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