bi-BL-algebra
Mahdeieh Abbasloo; Arsham Borumand Saeid
Discussiones Mathematicae - General Algebra and Applications (2011)
- Volume: 31, Issue: 2, page 231-260
- ISSN: 1509-9415
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topMahdeieh Abbasloo, and Arsham Borumand Saeid. "bi-BL-algebra." Discussiones Mathematicae - General Algebra and Applications 31.2 (2011): 231-260. <http://eudml.org/doc/276682>.
@article{MahdeiehAbbasloo2011,
abstract = {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.},
author = {Mahdeieh Abbasloo, Arsham Borumand Saeid},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {bi-BL-algebra; bi-filter; bi-deductive system; bi-Boolean elements of a bi-BL-algebra},
language = {eng},
number = {2},
pages = {231-260},
title = {bi-BL-algebra},
url = {http://eudml.org/doc/276682},
volume = {31},
year = {2011},
}
TY - JOUR
AU - Mahdeieh Abbasloo
AU - Arsham Borumand Saeid
TI - bi-BL-algebra
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2011
VL - 31
IS - 2
SP - 231
EP - 260
AB - 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.
LA - eng
KW - bi-BL-algebra; bi-filter; bi-deductive system; bi-Boolean elements of a bi-BL-algebra
UR - http://eudml.org/doc/276682
ER -
References
top- [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. Zbl1188.03047
- [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 Zbl1188.03047
- [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 Zbl1040.03047
- [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. Zbl1028.06007
- [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 Zbl1040.03048
- [9] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998. http://dx.doi.org/10.1007/978-94-011-5300-3 Zbl0937.03030
- [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 Zbl1103.03062
- [11] A. Iorgulescu, Algebras of Logic as BCK-algebras, Academy of Economic Studies, Bucharest, Editura 2008. Zbl1172.03038
- [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. Zbl0914.08003
- [15] D. Piciu, Algebras of Fuzzy Logic, Ed. Universitaria Craiova, 2007. Zbl1153.06005
- [16] E. Turunen, BL-algebras of basic fuzzy logic, Mathware and soft computing 6 (1999), 49-61. Zbl0962.03020
- [17] E. Turunen, Boolean deductive systems of BL-algebras, Arch Math. Logic 40 (2001), 467-473. doi: 10.1007/s001530100088 Zbl1030.03048
- [18] E. Turunen, Mathematics behind fuzzy logic, Physica-Verlag, 1999. Zbl0940.03029
- [19] W.B. Vasantha Kandasamy, Bialgebraic structures and Smaranche bialgebraic structures, American Research Press, 2003. Zbl1054.20054
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