Folding theory applied to pseudo-hoops

Article type: Research Article

Authors: Borzooei, R. A.^a | Alavi, S. Z.^b | Kologani, M. Aaly^c | Ahn, Sun Shin^{d; *; 1}

Affiliations: [a] Department of Mathematics, Shahid Beheshti University, Tehran, Iran | [b] Bandargaz Branch, Islamic Azad University, Bandargaz, Iran | [c] Hatef Higher Education Institute, Zahedan, Iran | [d] Department of Mathematics Education, Dongguk University, Seoul, Korea

Correspondence: [*] Corresponding author. Sun Shin Ahn, Department of Mathematics Education, Dongguk University, Seoul, 04620, Korea. Tel.: +82 2 2260 3410; E-mail: sunshine@dongguk.edu.

Note: [1] This work was supported by the research programm of Dongguk University, 2020.

Abstract: 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.

Keywords: n-fold pseudo-hoop, n-fold (positive) implicative filter, n-fold fantastic filter

DOI: 10.3233/JIFS-200179

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 1, pp. 1381-1390, 2020