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The class of bipartite pseudo-BL algebras (denoted by BP) and the class of strongly bipartite pseudo-BL algebras (denoted by BP0) are investigated. We prove that the class BP0 is a variety and show that BP is closed under subalgebras and arbitrary direct products but it is not a variety. We also study connections between bipartite pseudo-BL algebras and other classes of pseudo-BL algebras.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
487--496
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
autor
- Warsaw School of Information Technology Newelska 6 Pl-01447 Warszawa, Poland, walent@interia.pl
Bibliografia
- [1] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467–490.
- [2] A. Di Nola, G. Georgescu, A. Iorgulescu, Pseudo-BL algebras: Part I , Multiple-Valued Logic 8 (2002), 673–714.
- [3] A. Di Nola, G. Georgescu, A. Iorgulescu, Pseudo-BL algebras: Part II , Multiple-Valued Logic 8 (2002), 717-750.
- [4] A. Di Nola, F. Liguori, S. Sessa, Using maximal ideals in the classification of MV algebras, Portugal. Math. 50 (1993), 87–102.
- [5] G. Dymek, Bipartite pseudo-MV algebras, Discuss. Math., General Algebra and Ap-plications 26 (2006), 183–197.
- [6] G. Georgescu, A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV algebras, The Proceedings of the Fourth International Symposium on Economic Informatics, Bucharest, Romania, May 1999, 961-968.
- [7] G. Georgescu, A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras, Abstracts of the Fifth International Conference FSTA 2000, Slovakia 2000, 90–92.
- [8] G. Georgescu, L. Leustean, Some classes of pseudo-BL algebras, J. Austral. Math. Soc. 73 (2002), 127–153.
- [9] P. Hájek, Metamathematics of Fuzzy Logic, Kluwer, Amsterdam, 1998.
- [10] P. Hájek, Fuzzy logics with noncommutative conjuctions, J. Logic Comput. 13 (2003), 469–479.
- [11] P. Hájek, Observations on non-commutative fuzzy logic, Soft Computing 8 (2003), 38–43.
- [12] J. Rachůnek, A non-commutative generalizations of MV algebras, Math. Slovaca 52 (2002), 255–273.
- [13] A. Walendziak, M. Wojciechowska, Semisimple and semilocal pseudo-BL algebras, Demonstratio Math. 42 (2009), 453-466.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0032-0013