Semisimple and semilocal pseudo BL-algebras

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

Abstrakty

EN

The concepts of semisimple and semilocal pseudo BL-algebras are investigated. Many facts corresponding with them are considerated. Moreover, we give a negative answer to the question from [Di Nola, Georgescu and lorgulescu (Multiplae Valued Logic 8: 715-750, 2002), Problem 1.33].

Słowa kluczowe

EN

pseudoalgebra; algebraic analysis

PL

pseudoalgebra; analiza algebraiczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 3
• Strony: 453--466
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Walendziak A.

autor

Wojciechowska M.

• Warsaw Information Technology ul. Newelska 6 01-447 Warszawa, Poland,

Bibliografia

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• [3] A. Di Nola, G. Georgescu, A. Iorgulescu, Pseudo-BL algebras II, Multiple-Valued Logic 8 (2002), 715-750.
• [4] A. Dvurečenskij, J. Rachůnek, Probabilistic averaging in bounded Rℓ-monoids, Semigroup Forum 72 (2006), 190-206.
• [5] A. Dvurečenskij, Every linear pseudo BL-algebra admits a state, Soft Computing 11 (2007), 495-501.
• [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, A. Iorgulescu, Pseudo BCK-algebras: an extension of BCK-algebras. Proceedings of DMTCS’01: Combinatorics, Computability and Logic, Springer, London 2001, 97-114.
• [9] G. Georgescu, L. L. Leustean, Some classes of pseudo-BL algebras. J. Austral. Math. Soc. 73 (2002), 127-153.
• [10] P. Hájek, Metamathematics of Fuzzy Logic, Kluwer, Amsterdam, 1998.
• [11] P. Hájek, Fuzzy logics with noncommutative conjuctions, J. Logic Comput. 13 (2003), 469-479.
• [12] P. Hájek, Observations on non-commutative fuzzy logic, Soft Computing 8 (2003), 38-43.
• [13] A. Iorgulescu, Pseudo Iséki algebras. Connections with pseudo BL-algebras, Journal of Multiple-Valued Logic and Soft Computing 11 (2005), 263-308.
• [14] J. Kühr, Pseudo BL-algebras and DRℓ-monoids, Math. Bohem. 128 (2003), 199-208.
• [15] J. Rachůnek, A non-commutative generalizations of MV-algebras, Math. Slovaca 52 (2002), 255-273.
• [16] A. Walendziak, M. Wojciechowska, Another axiomatization of pseudo BL-algebras, to appear.