1. bookVolume 42 (2022): Issue 1 (March 2022)
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
access type Open Access

New Kinds of Prefilters in EQ-Algebras

Published Online: 05 Apr 2022
Volume & Issue: Volume 42 (2022) - Issue 1 (March 2022)
Page range: 31 - 49
Received: 07 Jun 2020
Accepted: 29 Nov 2020
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
Abstract

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

MSC 2010

[1] C.C. Chang, Algebraic Analysis of Many-Valued Logic, Trans. Amer. Math. Soc. 88 (1958) 467–490. https://doi.org/10.2307/199322710.2307/1993227 Search in Google Scholar

[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.2011.05.01110.1016/j.fss.2011.05.011 Search in Google Scholar

[3] M. El-Zekey, Representable good EQ-algebras, Soft Computing 14 (2010) 1011–1023. https://doi.org/10.1007/s00500-009-0491-410.1007/s00500-009-0491-4 Search in Google Scholar

[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)00098-710.1016/S0165-0114(01)00098-7 Search in Google Scholar

[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.20071002910.1002/malq.200710029 Search in Google Scholar

[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/s00500-005-0534-410.1007/s00500-005-0534-4 Search in Google Scholar

[7] P. Hájek, Metamathematics of Fuzzy Logic (Kluwer Academic Publishers, Dordrecht, 1998).10.1007/978-94-011-5300-3 Search in Google Scholar

[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-13088410.3233/IFS-130884 Search in Google Scholar

[9] V. Novák and B. De Baets, EQ-algebras, Fuzzy Sets and Systems 160 (2009) 2956–2978. https://doi.org/10.1016/j.fss.2009.04.01010.1016/j.fss.2009.04.010 Search in Google Scholar

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

[11] M. Ward and R.P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1939) 335–354. https://doi.org/10.1090/S0002-9947-1939-1501995-310.1090/S0002-9947-1939-1501995-3 Search in Google Scholar

[12] O. Zahiri and H. Farahani, n-fold filters in MTL-algebras, Afr. Mat. 25 (4) (2014) 1165–1178. https://doi.org/10.1007/s13370-013-0184-010.1007/s13370-013-0184-0 Search in Google Scholar

[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) 108–110.10.1109/CFIS.2018.8336645 Search in Google Scholar

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