Geodesic
Fuzzy n-fold integral filters in BL-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 1, pp. 57-71.

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In this paper, we introduce the notion of fuzzy n-fold integral filter in BL-algebras and we state and prove several properties of fuzzy n-fold integral filters. Using a level subset of a fuzzy set in a BL-algebra, we give a characterization of fuzzy n-fold integral filters. Also, we prove that the homomorphic image and preimage of fuzzy n-fold integral filters are also fuzzy n-fold integral filters. Finally, we study the relationship among fuzzy n-fold obstinate filters, fuzzy n-fold integral filters and fuzzy n-fold fantastic filters
Keywords: BL-algebra, fuzzy n-fold obstinate filter, n-fold obstinate BL-algebra, n-fold integral BL-algebra and fuzzy n-fold integra filter 
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Borzooei, Rajab; Paad, Akbar. Fuzzy n-fold integral filters in BL-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 1, pp. 57-71. http://geodesic.mathdoc.fr/item/DMGAA_2013_33_1_a3/

[1] R.A. Borzooei and A. Paad, Integral filters and Integral BL-algebras, Italian J. Pure and Appl. Math., to appear.

[2] R.A. Borzooei and A. Paad, n-fold integral and n-fold obstinate BL-algebras, submitted.

[3] 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

[4] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo BL-algebra. Part I, Int. J. Mult. Val. Logic 8 (5-6) (2002) 673-714.

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

[6] 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

[7] M. Haveshki and E. Eslami, n-Fold filters in BL-algebras, Math. Log. Quart 54 (2) (2008) 176-186. doi: 10.1002/malq.200710029

[8] S. Motamed and A. Borumand Saeid, n-fold obstinate filters in BL-algebras, Neural Comput. and Applic. 20 (2011) 461-472. doi: 10.1007/s00521-011-0548-z

[9] C. Lele, Folding theory of positive implicative/fuzzy positive implicative in BL-algebras, Journal of Fuzzy Mathematics 17 (3) (2009), Los Angeles.

[10] C. Lele, Fuzzy n-fold obstinate filters in BL-algebras, Afrika Mathematika (2011) (On line).

[11] C. Lele and M. Hyland, Folding theory for fantastic filters in BL-algebra, International Journal of Artificial Life Research 2 (4) (2011) 32-42. doi: 10.4018/IJALR.2011100104

[12] L. Liu and K. Li, Fuzzy filters of BL-algebras, Information Sciences 173 (2005) 141-154. doi: 10.1016/j.ins.2004.07.009

[13] L. Lianzhen and L. Kaitai, Fuzzy Boolean and positive implicative filters of BL-algebras, Fuzzy Sets and Systems 152 (2005) 333-348. doi: 10.1016/j.fss.2004.10.005

[14] 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

[15] E. Turunen, BL-algebras of basic fuzzy logic, Mathware Soft. Comput. 6 (1999) 49-61.

[16] E. Turunen, Mathematics Behind Fuzzy Logic (Physica Verlag, 1999).