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Article type: Research Article
Authors: Bakhshi, Mahmooda | Ahn, Sun Shinb | Jun, Young Baec | Borzooei, Rajab Alid; e
Affiliations: [a] Department of Mathematics, University of Bojnord, Bojnord, Iran | [b] Department of Mathematics Education, Dongguk University, Seoul, Korea | [c] Department of Mathematics Education, Gyeongsang National University, Jinju, Korea | [d] Department of Mathematics, Shahid Beheshti University of Tehran, Tehran, Iran | [e] Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkiye
Correspondence: [*] Corresponding author. Sunshine Ahn, Department of Mathematics Education, Dongguk University, Seoul 04620, Korea. E-mail: [email protected].
Abstract: Some kinds of pseudo valuations such as positive implicative pseudo valuation, (weak) implicative pseudo valuation, and commutative pseudo valuation of various types are introduced. Several examples, properties and characterizations of them are given as well. The relationships between them and the substructures of hyper BCK -algebras are investigated, too. Finally, by giving various examples and theorems, the relationships among the proposed pseudo valuations are investigated and characterized, especially in hyper BCK -algebras with three elements.
Keywords: Hyper BCK -algebra, pseudo valuation, positive implicative pseudo valuation, implicative pseudo valuation, commutative pseudo valuation
DOI: 10.3233/JIFS-233898
Journal: Journal of Intelligent & Fuzzy Systems, vol. Pre-press, no. Pre-press, pp. 1-15, 2024
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