Relation between (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 36 (2016) no. 1, pp. 45-58.

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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.
Keywords: BL-algebra, (fuzzy) filter, (fuzzy) Boolean ideal, (fuzzy) Gödel ideal
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Paad, Akbar. Relation between (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 36 (2016) no. 1, pp. 45-58. http://geodesic.mathdoc.fr/item/DMGAA_2016_36_1_a3/

[1] R.A. Borzooei and A. Paad, Some new types of satbilizers in BL-algebras and their applications, Indian Journal of Science and Technology 5 (1) (2012), 1910-1915.

[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, Pseduo BL-algebras, Part I, Mult Val Logic 8 (5-6) (2002), 673-714.

[4] A. Di Nola and L. Leustean, Compact representations of BL-algebras, Department of Computer Science, University Aarhus. BRICS Report series (2002).

[5] M. Haveshki, A. Borumand Saeid and E. Eslami, Some types of filters in BL-algebras, Soft Comput. 10 (2006), 657-664. doi: 10.1007/s00500-005-0534-4

[6] C. Lele and J.B. Nganou, MV-algebras derived from ideals in BL-algebras, Fuzzy Sets and Systems 218 (2013), 103-113. doi: 10.1016/j.fss.2012.09.014

[7] C. Lele and J. B. Nganou, Pseudo-addition and fuzzy ideals in BL-algebras, Annals of Fuzzy Mathematics and Informations 8 (2) (2014), 193-207.

[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.

[10] P. Hájek, Metamathematics of fuzzy logic, Trends in Logic, vol. 4, Kluwer Academic Publishers, (1998), ISBN:9781402003707. doi: 10.1007/978-94-011-5300-3

[11] X.H. Zhang, Y.B. Jun and M.I. Doh, On fuzzy filters and fuzzy ideals of BL-algebras, Fuzzy Systems and Mathematics 20 (3) (2006), 1604-1616.