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Soft Computing

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01.04.2010 | Original Paper

State BL-algebras

verfasst von: Lavinia Corina Ciungu, Anatolij Dvurečenskij, Marek Hyčko

Erschienen in: Soft Computing | Ausgabe 4/2010

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Abstract

The concept of a state MV-algebra was firstly introduced by Flaminio and Montagna (An algebraic approach to states on MV-algebras. In: Novák V (ed) Fuzzy logic 2, proceedings of the 5th EUSFLAT conference, September 11–14, Ostrava, vol II, pp 201–206, 2007; Int J Approx Reason 50:138–152, 2009) as an MV-algebra with internal state as a unary operation. Di Nola and Dvurečenskij (Ann Pure Appl Logic 161:161–173, 2009a; Math Slovaca 59:517–534, 2009b) gave a stronger version of a state MV-algebra. In the present paper, we introduce the notion of a state BL-algebra, or more precisely, a BL-algebra with internal state. We present different types of state BL-algebras, like strong state BL-algebras and state-morphism BL-algebras, and we study some classes of state BL-algebras. In addition, we give a sample of important examples of state BL-algebras and present some open problems.

Nächster Artikel Commutative bounded integral residuated orthomodular lattices are Boolean algebras

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Titel: State BL-algebras
verfasst von: Lavinia Corina Ciungu
Anatolij Dvurečenskij
Marek Hyčko
Publikationsdatum: 01.04.2010
Verlag: Springer-Verlag
Erschienen in: Soft Computing / Ausgabe 4/2010
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-010-0571-5

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