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bi-BL-algebra

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Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce the notion of a bi-BL-algebra, bi-filter, bi-deductive system and bi-Boolean elements of a bi-BL-algebra and deal with bi-filters in bi-BL-algebra. We study this structure and construct the quotient of bi-BL-algebra. Also present a classification for examples of proper bi-BL-algebras.
Twórcy
  • Department of Mathematics, Science and Research Branch, Islamic Azad University, Kerman, Iran
  • Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Bibliografia
  • [1] A. Borumand Saeid, A. Ahadpanah and L. Torkzadeh, Smarandache BL-algebra, J. Applied Logic 8 (2010), 253-261. doi: 10.1016/j.jal.2010.06.001
  • [2] A. Borumand Saeid and S. Motamed, Normal filters in BL-algebras, World Applied Sci. J. 7 (Special Issue Appl. Math.), (2009), 70-76.
  • [3] A. Borumand Saeid and S. Motamed, Some Results in BL-algebras, Math. Logic Quat 55 (6) (2009), 649-658. doi: 10.1002/malq.200910025
  • [4] D. Busneag and D. Piciu, On the lattice of deductive systems of a BL-algebra, Central Eur. J Math. 1 (2) (2003), 221-238. doi: 10.2478/BF02476010
  • [5] R. Cingnoli, I.M.L. D'Ottaviano and D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer Academic publ., Dordrecht, 2000. doi: 10.1007/978-94-015-9480-6
  • [6] R. Cignoli, F. Esteva, L. Godo and A. Torrens, Basic fuzzy logic is the logic of continuous t-norm and their residua, Soft Comput 4 (2000), 106-112. doi: 10.1007/s005000000044
  • [7] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo BL-algebra: Part I, Mult val logic 8 (5-6) (2002), 673-714.
  • [8] A. Di Nola and L. Leustean, Compact representations of BL-algebras, Arch-Math. Logic 42 (2003), 737-761. doi: 10.1007/s00153-003-0178-y
  • [9] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998. http://dx.doi.org/10.1007/978-94-011-5300-3
  • [10] M. Haveshki, A. Borumand Saeid and E. Eslami, Some types of filters in BL-algebras, Soft Computing 10 (2006), 657-664. doi: 10.1007/s00500-005-0534-4
  • [11] A. Iorgulescu, Algebras of Logic as BCK-algebras, Academy of Economic Studies, Bucharest, Editura 2008.
  • [12] A. Iorgulescu, Classes of BCK-algebra-part III, Preprint series of the Institute of Mathematics of the Romanian Academy, preprint nr, 3/2004 (2004), 1-37.
  • [13] M. Kondo and W.A. Dudck, Filter theory of BL-algebras, Soft Computing 12 (2007), 419-423.
  • [14] R. Padilla, Smarandache algebraic structures, Bull. Pure Appl. Sci., Delhi 17 (1) (1998), 119-121.
  • [15] D. Piciu, Algebras of Fuzzy Logic, Ed. Universitaria Craiova, 2007.
  • [16] E. Turunen, BL-algebras of basic fuzzy logic, Mathware and soft computing 6 (1999), 49-61.
  • [17] E. Turunen, Boolean deductive systems of BL-algebras, Arch Math. Logic 40 (2001), 467-473. doi: 10.1007/s001530100088
  • [18] E. Turunen, Mathematics behind fuzzy logic, Physica-Verlag, 1999.
  • [19] W.B. Vasantha Kandasamy, Bialgebraic structures and Smaranche bialgebraic structures, American Research Press, 2003.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1185
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