Geodesic
IF-filters of pseudo-BL-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 2, pp. 177-193.

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Characterizations of IF-filters of a pseudo-BL-algebra are established. Some related properties are investigated. The notation of prime IF- filters and a characterization of a pseudo-BL-chain are given. Homomorphisms of IF-filters and direct product of IF-filters are studied.
Keywords: pseudo-BL-algebra, filter, IF-filter, prime IF-filters, pseudo-BL-chain, homomorphism, direct product 
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Wojciechowska-Rysiawa, Magdalena. IF-filters of pseudo-BL-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 2, pp. 177-193. http://geodesic.mathdoc.fr/item/DMGAA_2015_35_2_a4/

[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96. doi: 10.1016/s0165-0114(86)80034-3

[2] C.C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490. doi: 10.1090/S0002-9947-1958-0094302-9

[3] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo-BL algebras I, Multiple-Valued Logic 8 (2002), 673-714.

[4] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo-BL algebras II, Multiple-Valued Logic 8 (2002), 717-750.

[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.L. Leuştean, Some classes of pseudo-BL algebras, J. Austral. Math. Soc. 73 (2002), 127-153. doi: 10.1017/s144678870000851x

[8] P. Hájek, Metamathematics of fuzzy logic, Inst. of Comp. Science, Academy of Science of Czech Rep. Technical report 682 (1996).

[9] P. Hájek, Metamathematics of Fuzzy Logic (Kluwer Acad. Publ., Dordrecht, 1998). doi: 10.1007/978-94-011-5300-3

[10] J. Rachůnek, A non-commutative generalization of MV algebras, Czechoslovak Math. J. 52 (2002), 255-273.

[11] J. Rachůnek and D. Šalounová, Fuzzy filters and fuzzy prime filters of bounded Rl-monoids and pseudo-BLalgebras, Information Sciences 178 (2008), 3474-3481. doi: 10.1016/j.ins.2008.05.005

[12] G. Takeuti and S. Titants, Intuitionistic fuzzy logic and Intuitionistic fuzzy sets theory, Journal of Symbolic Logic 49 (1984), 851-866.

[13] M. Wojciechowska-Rysiawa, Anti fuzzy filters of pseudo-BL algebras, Comment. Math. 51 (2011), 155-167.

[14] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X