Geodesic
New Kinds of Prefilters in EQ-Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 31-49.

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In this paper, the notions of n-fold positive implicative prefilter and n-fold implicative prefilter in EQ-algebras are introduced and several properties, characterizations and equivalent conditions are provided. It is proved that the quotient EQ-algebra induced by an n-fold positive implicative prefilter is n-idempotent. Also, it is proved that in an n-idempotent EQ-algebra, any filter is an n-fold positive implicative filter. In the sequel, we investigate the relationships between these two types of prefilters. Finally, some characterizations of n-fold implicative prefilters in bounded EQ-algebras are given.
Keywords: (n-idempotent) EQ-algebra, n-fold positive implicative prefilter, n-fold implicative prefilter 
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Paad, Akbar; Bakhshi, Mahmood; Jafari, Azam; Rahimi, Maryam. New Kinds of Prefilters in EQ-Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 31-49. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_1_a2/

[1] C.C. Chang, Algebraic Analysis of Many-Valued Logic, Trans. Amer. Math. Soc. 88 (1958) 467–490. https://doi.org/10.2307/1993227

[2] M. El-Zekey, V. Novàk and R. Mesiar, On good EQ-algebras, Fuzzy Sets and Systems 178 (2011) 1–23. https://doi.org/10.1016/j.fss.2011.05.011

[3] M. El-Zekey, Representable good EQ-algebras, Soft Computing 14 (2010) 1011–1023. https://doi.org/10.1007/s00500-009-0491-4

[4] F. Esteva and L. Godo, Monoidal t-norm based logic: Towards a logic of left-continuous t-norms, Fuzzy Sets and Systems 124 (2001) 271–288. https://doi.org/10.1016/S0165-0114(01)00098-7

[5] M. Haveshki and E. Eslami, n-fold filters in BL-algebras, Math. Logic Quart. 54 (2008) 176–186. https://doi.org/10.1002/malq.200710029

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

[7] P. Hájek, Metamathematics of Fuzzy Logic (Kluwer Academic Publishers, Dordrecht, 1998).

[8] L. Liu and X. Zhang, Implicative and positive implicative prefilters of EQ-algebras, J. Intelligent and Fuzzy Systems 26 (2014) 2087–2097. https://doi.org/10.3233/IFS-130884

[9] V. Novák and B. De Baets, EQ-algebras, Fuzzy Sets and Systems 160 (2009) 2956–2978. https://doi.org/10.1016/j.fss.2009.04.010

[10] G.J. Wang, Non-Classical Mathematical Logic and Approximate Reasoning (Science Press, Beijing, 2000).

[11] M. Ward and R.P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1939) 335–354. https://doi.org/10.1090/S0002-9947-1939-1501995-3

[12] O. Zahiri and H. Farahani, n-fold filters in MTL-algebras, Afr. Mat. 25 (4) (2014) 1165–1178. https://doi.org/10.1007/s13370-013-0184-0

[13] Z. Zarrin and S. Rasouli, Some types of n-fold filters in residuated lattices, 6th Iranian Joint Congress on Fuzzy and Intelligent Systems (Shahid Bahonar University of Kerman, Kerman, 2018) 108–110.