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Al-Masarwah, Anas; Ahmad, Abd Ghafur

On (complete) normality of \(m\)-pF subalgebras in BCK/BCI-algebras. (English) Zbl 1484.06070

AIMS Math. 4, No. 3, 740-750 (2019).
Summary: In this paper, we introduce the concepts of normal \(m\)-polar fuzzy subalgebras, maximal \(m\)-polar fuzzy subalgebras and completely normal \(m\)-polar fuzzy subalgebras in BCK/BCI-algebras. We discuss some properties of normal (resp., maximal, completely normal) \(m\)-polar fuzzy subalgebras. We prove that any non-constant normal \(m\)-polar fuzzy subalgebra which is a maximal element of \((\mathcal{NO}(X), \subseteq)\) takes only the values \(\widehat{0} = (0, 0, \dots, 0)\) and \(\widehat{1} = (1, 1, \dots, 1),\) and every maximal \(m\)-polar fuzzy subalgebra is completely normal. Moreover, we state an \(m\)-polar fuzzy characteristic subalgebra in BCK/BCI-algebras.

Cited in 3 Documents

MSC:

06F35 BCK-algebras, BCI-algebras

Keywords:

BCK/BCI-algebras; \(m\)-polar fuzzy sets; \(m\)-polar fuzzy subalgebras; normal \(m\)-polar fuzzy subalgebras; completely normal \(m\)-polar fuzzy subalgebras; maximal \(m\)-polar fuzzy subalgebras
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References:

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