In this paper, by considering the notion of pseudo-hoops, which introduced by Georgescu [10], we presented the concepts of n-fold filters in pseudo-hoop. Concerning ideas, we gave some related results. Also, we extended our definition to n-fold (positive) implicative and n-fold fantastic filters and investigated their properties and the relation among these n-fold filters. In particular, we proved that every n-fold fantastic and positive implicative filter is an n-fold implicative filter. Finally, we studied the quotient of these filters.
Get full access to this article
View all access options for this article.
References
1.
Aaly KologaniM. and BorzooeiR.A., On ideal theory of hoops, Mathematica Bohemica (2019), DOI: 10.21136/MB.2019.0140-17.
2.
Aaly KologaniM., Mohseni TakalloM. and KimH.S., Fuzzy filters of hoops based on fuzzy points, Mathematics (2019), 1-11.
3.
BosbachB., Komplementäre Halbgruppen, Axiomatik und Arithmetik, Fundamenta Mathematicae64(3) (1969), 257–287.
4.
BosbachB., Komplementäre Halbgruppen, Kongruenzen und Quotienten, Fundamenta Mathematicae69(1) (1970), 1–14.
5.
BorzooeiR.A. and Aaly KologaniM., Local and perfect semihoops, Journal of Intelligent and Fuzzy Systems29(1) (2015), 223–234.
FlautC., Hoskova-MayerovaS., Borumand SaeidA. and VasileR., Wajsberg algebras of order n(n ≤ 9), Neural Computing and Applications (2019), doi.org/10.1007/s00521-019-04676-x.
8.
Di NolaA., GeorgescuG. and IorgulescuA., Pseudo-BL algebras: Part I, Multiple Valued Logic8 (5-6) (2002), 673–716.
9.
Di NolaA., GeorgescuG. and IorgulescuA., Pseudo-BL algebras: Part II, Multiple Valued Logic8 (5-6) (2002), 717–750.
10.
GeorgescuG. and IorgulescuA., Pseudo MV-algebras, Multiple Valued Logic6 (2001), 95–135.
11.
GeorgescuG., LeusteanL. and PreoteasaV., Pseudo-hoops, Journal of Multiple Valued Logic and Soft Computing11 (1-2) (2005), 153–184.
12.
HájekP., Metamathematics of fuzzy logic, Springer Science and Business Media, 4 (1998).
13.
HaveshkiM. and EslamiE., n-fold filters in BL-algebras, Mathematical Logic Quarterly54 (2) (2008), 176–186.
14.
MotamedS. and Borumand SaeidA., n-fold obstinate filters in BL-Algebras, Neural Computing and Applications20 (4) (2011), 461–472.
15.
NamdarA. and BorzooeiR.A., Nodal filter in hoop algebras, Soft Computing22(4) (2017), DOI: 10.1007/s00500-017-2986-8.
16.
NamdarA., BorzooeiR.A., Borumand SaeidA. and Aaly KologaniM., Some results in hoop algebras, Journal of Intelligent and Fuzzy Systems32 (2017), 1805–1813.
17.
OnasanyaB.O. and Hoskova-MayerovaS., Some Topological and Algebraic Properties of α-level Subsets’ Topology of a Fuzzy Subset, Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica26(3) (2018), 213–227.
18.
OnasanyaB.O. and Hoskova-MayerovaS., Multi-fuzzy group induced by multisets, Italian Journal of Pure and applied Mathematics41 (2019), 597–604.
19.
TurunenE., TchikapaN. and LeleC., A new characterization for n-fold positive implicative BL-logics, Advances on Computational Intelligence, Springer VerlagBerlin Heidelberg, (2012), 552–560.
