Some characterizations of pseudo-BL-chains

• Autorzy: Walendziak, A. , Wojciechowska-Rysiawa, M.
• Języki publikacji: EN

Abstrakty

EN

Pseudo-BL-chains are linearly ordered pseudo-BL-algebras. Characterizations of them in terms of concepts of lattice theory are given.

Słowa kluczowe

EN

pseudo-BL algebra; lattice; join irreducible element; stone lattice

• Czasopismo: Commentationes Mathematicae
• Rocznik: 2011
• Tom: Vol. 51, [Z] 2
• Strony: 121-124
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Walendziak, A.

autor

Wojciechowska-Rysiawa, M.

• Warsaw Scholl of InformationTechnology, Newelska 6, Pl-01447 Warszawa, Poland,

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 and A. Iorgulescu, Pseudo-BL algebras: Part I, Multiple-Valued Logic 8 (2002), 673-714.
• [3] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: Part II, Multiple-Valued Logic 8 (2002), 717-750.
• [4] A. Dvurecenskij, Every linear pseudo BL-algebra admits a state, Soft Comput. 11 (2007), 495-501.
• [5] G. Georgescu and 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.
• [6] G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras, Abstracts of the Fifth International Conference FSTA 2000, Slovakia 2000, 90-92.
• [7] G. Georgescu and L. Leus,tean, Some classes of pseudo-BL algebras, J. Austral. Math. Soc. 73 (2002), 127-153.
• [8] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer, Amsterdam, 1998.
• [9] P. Hajek, Fuzzy logics with noncommutative conjuctions, Journal of Logic and Computation 13 (2003), 469-479.
• [10] P. Hajek, Observations on non-commutative fuzzy logic, Soft Computing 8 (2003), 38-43.
• [11] J. Kiihr, Prime ideals and polars in DRi-monoids and pseudo BL-algebras, Math. Slovaca 53 (2003), 233-246.
• [12] J. Rachunek, A non-commutative generalizations of MV algebras, Math. Slovaca 52 (2002), 255-273.
• [13] J. Rachunek and D. Salounova, Fuzzy filters and fuzzy prime filters of bounded Ri-monoids and pseudo BL-algebras, Information Sciences 178 (2008), 3474-3481.
• [14] M. Wojciechowska-Rysiawa, Anti fuzzy filters of pseudo-BL-algebras, submitted