\((\bar{\varepsilon},\overline{\varepsilon\wedge q_k})\)-fuzzy Subalgebras in BCK/BCI-algebras

Volume 2, Issue 1, pp 130--140 http://dx.doi.org/10.22436/jmcs.002.01.14

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Authors

Reza Ameri - School of Mathematics, Statics and Computer Sciences, University of Tehran, P. O. Box 14155-6415, Tehran, Iran Hossein Hedayati - Department of Mathematics, Faculty of Basic Science, Babol University of Technology, Babol, Iran Morteza Norouzi - Department of Mathematics, University of Mazandaran, Babolsar, Iran

Abstract

In this paper, the notion of not quasi-coincidence \(\bar{q}\) of a fuzzy point with a fuzzy set is considered. We introduce the notion of \((\bar{\varepsilon},\overline{\varepsilon\wedge q_k})\)-fuzzy \((\bar{\varepsilon},\overline{ q_k})\)-fuzzy subalgebra in a BCK/BCI-algebra X and several properties are investigated. Specially, we show that under certain conditions an \((\bar{\varepsilon},\overline{\varepsilon\wedge q_k})\) -fuzzy subalgebra can be expressed such that consist of a union of two proper non-equivalent \((\bar{\varepsilon},\overline{\varepsilon\wedge q_k})\) - fuzzy subalgebras.

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Keywords

• BCK/BCI-algebra
• \((\bar{\varepsilon}،\bar{ q_k})\)-fuzzy subalgebra
• \((\bar{\varepsilon}،\overline{\varepsilon\wedge q_k})\)-fuzzy subalgebra
• \((\overline{\varepsilon\wedge q_k})\)-level subalgebra.

MSC

•  06F35
•  54A40
•  03E72
•  03G25
•  03B52

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