Relation between (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras
Discussiones Mathematicae General Algebra and Applications (2016)
- Volume: 36, Issue: 1, page 45-58
- ISSN: 1509-9415
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topAkbar Paad. "Relation between (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras." Discussiones Mathematicae General Algebra and Applications 36.1 (2016): 45-58. <http://eudml.org/doc/286950>.
@article{AkbarPaad2016,
abstract = {In this paper, we study relationships between among (fuzzy) Boolean ideals, (fuzzy) Gödel ideals, (fuzzy) implicative filters and (fuzzy) Boolean filters in BL-algebras. In [9], there is an example which shows that a Gödel ideal may not be a Boolean ideal, we show this example is not true and in the following we prove that the notions of (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras coincide.},
author = {Akbar Paad},
journal = {Discussiones Mathematicae General Algebra and Applications},
keywords = {BL-algebra; (fuzzy) filter; (fuzzy) Boolean ideal; (fuzzy) Gödel ideal; fuzzy -fold integral ideal; fuzzy -fold Boolean ideal},
language = {eng},
number = {1},
pages = {45-58},
title = {Relation between (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras},
url = {http://eudml.org/doc/286950},
volume = {36},
year = {2016},
}
TY - JOUR
AU - Akbar Paad
TI - Relation between (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras
JO - Discussiones Mathematicae General Algebra and Applications
PY - 2016
VL - 36
IS - 1
SP - 45
EP - 58
AB - In this paper, we study relationships between among (fuzzy) Boolean ideals, (fuzzy) Gödel ideals, (fuzzy) implicative filters and (fuzzy) Boolean filters in BL-algebras. In [9], there is an example which shows that a Gödel ideal may not be a Boolean ideal, we show this example is not true and in the following we prove that the notions of (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras coincide.
LA - eng
KW - BL-algebra; (fuzzy) filter; (fuzzy) Boolean ideal; (fuzzy) Gödel ideal; fuzzy -fold integral ideal; fuzzy -fold Boolean ideal
UR - http://eudml.org/doc/286950
ER -
References
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- [8] L. Liu and K. Li, Fuzzy Boolean and positive implicative filter of BL-algebras, Fuzzy Sets and Systems 152 (2005), 141-154.
- [9] B.L. Meng and X.L. Xin, On Fuzzy ideals of BL-algebras, The Scientific World Journal 2014 Article ID 757382 (2014), 12 pages.
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