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AIMS Mathematics

2019, Volume 4, Issue 3: 740-750. doi: 10.3934/math.2019.3.740
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Research article

On (complete) normality of m-pF subalgebras in BCK/BCI-algebras

  • School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia
  • Received: 19 March 2019 Accepted: 05 June 2019 Published: 26 June 2019

  • MSC : 03G25, 06F35, 08A72

  • 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 $\widehat{0} = (0, 0, ..., 0)$ and $\widehat{1} = (1, 1, ..., 1), $ and every maximal $m$-polar fuzzy subalgebra is completely normal. Moreover, we state an $m$-polar fuzzy characteristic subalgebra in $BCK/BCI$-algebras.

    Citation: Anas Al-Masarwah, Abd Ghafur Ahmad. On (complete) normality of m-pF subalgebras in BCK/BCI-algebras[J]. AIMS Mathematics, 2019, 4(3): 740-750. doi: 10.3934/math.2019.3.740

    Related Papers:

  • 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 $\widehat{0} = (0, 0, ..., 0)$ and $\widehat{1} = (1, 1, ..., 1), $ and every maximal $m$-polar fuzzy subalgebra is completely normal. Moreover, we state an $m$-polar fuzzy characteristic subalgebra in $BCK/BCI$-algebras.


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