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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1242, author = {Magdalena Wojciechowska-Rysiawa}, title = {IF-filters of pseudo-BL-algebras}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {35}, year = {2015}, pages = {177-193}, zbl = {1244.03172}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1242} }
Magdalena Wojciechowska-Rysiawa. IF-filters of pseudo-BL-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 35 (2015) pp. 177-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1242/
[000] [1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96. doi: 10.1016/s0165-0114(86)80034-3 | Zbl 0631.03040
[001] [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 | Zbl 0084.00704
[002] [3] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo-BL algebras I, Multiple-Valued Logic 8 (2002), 673-714. | Zbl 1028.06007
[003] [4] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo-BL algebras II, Multiple-Valued Logic 8 (2002), 717-750. | Zbl 1028.06008
[004] [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. | Zbl 0985.06007
[005] [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.
[006] [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 | Zbl 1016.03069
[007] [8] P. Hájek, Metamathematics of fuzzy logic, Inst. of Comp. Science, Academy of Science of Czech Rep. Technical report 682 (1996).
[008] [9] P. Hájek, Metamathematics of Fuzzy Logic (Kluwer Acad. Publ., Dordrecht, 1998). doi: 10.1007/978-94-011-5300-3 | Zbl 0937.03030
[009] [10] J. Rachůnek, A non-commutative generalization of MV algebras, Czechoslovak Math. J. 52 (2002), 255-273. | Zbl 1012.06012
[010] [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 | Zbl 1156.06009
[011] [12] G. Takeuti and S. Titants, Intuitionistic fuzzy logic and Intuitionistic fuzzy sets theory, Journal of Symbolic Logic 49 (1984), 851-866. | Zbl 0575.03015
[012] [13] M. Wojciechowska-Rysiawa, Anti fuzzy filters of pseudo-BL algebras, Comment. Math. 51 (2011), 155-167. | Zbl 1294.03044
[013] [14] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X | Zbl 0139.24606