Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T15:16:56.386Z Has data issue: false hasContentIssue false
  • English
  • Français

Some classes of pseudo-BL algebras

Part of: Ordered structures Algebraic structures

Published online by Cambridge University Press:  09 April 2009

George Georgescu  and
Laurenţiu Leuştean
George Georgescu
Affiliation:
Faculty of Mathematics, University of Bucharest, 14 Academiei Street, 70109 Bucharest, Romania e-mail: [email protected]
Laurenţiu Leuştean
Affiliation:
National Institute for Research, and Development in Informatics8–10 Averescu Avenue, 71316 Bucharest, Romania e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Pseudo-BL algebras are noncommutative generalizations of BL-algebras and they include pseudo-MV algebras, a class of structures that are categorically equivalent to l-groups with strong unit. In this paper we characterize directly indecomposable pseudo-BL algebras and we define and study different classes of these structures: local, good, perfect, peculiar, and (strongly) bipartite pseudo-BL algebras.

MSC classification

Secondary: 06F99: None of the above, but in this section 08A72: Fuzzy algebraic structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 1 , August 2002 , pp. 127 - 154
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Ambrosio, R. and Lettieri, A., ‘A classification of bipartite MV-algebras’, Math. Japon. 38 (1993), 111–117.Google Scholar
[2]Belluce, L. P., Di Nola, A. and Lettieri, A., ‘Local MV-algebras’, Rend. Circ. Mat. Palermo (2) 42 (1993), 347–361 (1994).Google Scholar
[3]Cignoli, R., D'Ottaviano, I. M. L. and Mundici, D., Algebraic foundations of many-valued reasoning (Kluwer Acad. Publ., Dordrecht, 1998).Google Scholar
[4]Di Nola, A., Georgescu, G. and Iorgulescu, A., ‘Pseudo-BL algebras: Part I’, Mult.-Valued Log., to appear.Google Scholar
[5]Nola, A. Di, Georgescu, G. and Iorgulescu, A., ‘Pseudo-BL algebras: Part II’, Mult.-Valued Log., to appear.Google Scholar
[6]Di Nola, A. and Lettieri, A., ‘Perfect MV-algebras are categorically equivalent to abelian l-groups’, Studia Logica 53 (1994), 417–432.CrossRefGoogle Scholar
[7]Di Nola, A., Liguori, F. and Sessa, S., ‘Using maximal ideals in the classification of MV-algebras’, Portugal. Math. 50 (1993), 87–102.Google Scholar
[8]Di Nola, A., Sessa, S., Esteva, F., Godo, L. and Garcia, P., ‘The variety generated from perfect BL-algebras: an algebraic approach in fuzzy logic setting’, preprint, 2000.Google Scholar
[9]Dvurecenskij, A., ‘Pseudo MV-algebras are intervals in ℓ-groups’, J. Aust. Math. Soc. 72 (2002), 427–445.Google Scholar
[10]Flondor, P., Georgescu, G. and Iorgulescu, A., ‘Pseudo-t-norms and pseudo-BL algebras’, Soft Computing 5 (2001), 355–371.Google Scholar
[11]Georgescu, G. and Iorgulescu, A., ‘Pseudo-MV algebras: a noncommutative extension of MV-algebras’, in: Information technology (Bucharest, 1999) (Inforec, Bucharest, 1999) pp. 961–968.Google Scholar
[12]Georgescu, G. and Iorgulescu, A., ‘Pseudo-MV algebras’, Mult.-Valued Log. 6 (2001), 95–135.Google Scholar
[13]Georgescu, G. and Iorgulescu, A., ‘Pseudo-BL algebras: a noncommutative extension of BL-algebras (Abstract)’, in: The Fifth International Conference FSTA 2000 on Fuzzy Sets Theory and its Application, February 2000, pp. 90–92.Google Scholar
[14]Hájek, P., Metamathematics of fuzzy logic (Kluwer Acad. Publ., Dordrecht, 1998).Google Scholar
[15]Leuştean, I., ‘Local pseudo MV-algebras’, Soft Computing 5 (2001), 386–395.Google Scholar
[16]Mundici, D., ‘Interpretation of A F C*-algebras in Lukasiewicz sentential calculus’, J. Funct. Anal. 65 (1986), 15–63.CrossRefGoogle Scholar
[17]Turunen, E., ‘Boolean deductive systems of BL-algebras’, Arch. Math. Logic 40 (2001), 467–473.CrossRefGoogle Scholar
[18]Turunen, E., Mathematics behind fuzzy logic (Physica-Verlag, Heidelberg, 1999).Google Scholar
[19]Turunen, E. and Sessa, S., ‘Local BL-algebras’, Mult.-Valued Log. 6 (2001), 1–21.Google Scholar