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AIMS Mathematics

2020, Volume 5, Issue 2: 1035-1049. doi: 10.3934/math.2020072
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Research article

Subalgebras of type (α, β) based on m-polar fuzzy points in BCK/BCI-algebras

  • School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia
  • Received: 27 September 2019 Accepted: 05 December 2019 Published: 09 January 2020

  • MSC : 03G25, 06F35, 08A72

  • In this article, we present the idea of quasi-coincidence of an $m$-polar fuzzy point with an $m$-polar fuzzy subset. By utilizing this new idea, we further introduce the notion of $m$-polar $(\alpha, \beta)$-fuzzy subalgebras in $BCK/BCI$-algebras which is a generalization of the idea of $(\alpha, \beta)$-bipolar fuzzy subalgebras in $BCK/BCI$-algebras. Some interesting results of the $BCK/BCI$-algebras in terms of $m$-polar $(\alpha, \beta)$-fuzzy subalgebras are given. By using $m$-polar $(\in, \in \vee q)$-fuzzy subalgebras, some interesting results are obtained. Conditions for an $m$-polar fuzzy set to be an $m$-polar $(q, \in \vee q)$-fuzzy subalgebra and an $m$-polar $(\in, \in \vee q)$-fuzzy subalgebra are provided. Characterizations of $m$-polar $(\in, \in \vee q)$-fuzzy subalgebras in $BCK/BCI$-algebras by using level cut subsets are explored.

    Citation: Anas Al-Masarwah, Abd Ghafur Ahmad. Subalgebras of type (α, β) based on m-polar fuzzy points in BCK/BCI-algebras[J]. AIMS Mathematics, 2020, 5(2): 1035-1049. doi: 10.3934/math.2020072

    Related Papers:

  • In this article, we present the idea of quasi-coincidence of an $m$-polar fuzzy point with an $m$-polar fuzzy subset. By utilizing this new idea, we further introduce the notion of $m$-polar $(\alpha, \beta)$-fuzzy subalgebras in $BCK/BCI$-algebras which is a generalization of the idea of $(\alpha, \beta)$-bipolar fuzzy subalgebras in $BCK/BCI$-algebras. Some interesting results of the $BCK/BCI$-algebras in terms of $m$-polar $(\alpha, \beta)$-fuzzy subalgebras are given. By using $m$-polar $(\in, \in \vee q)$-fuzzy subalgebras, some interesting results are obtained. Conditions for an $m$-polar fuzzy set to be an $m$-polar $(q, \in \vee q)$-fuzzy subalgebra and an $m$-polar $(\in, \in \vee q)$-fuzzy subalgebra are provided. Characterizations of $m$-polar $(\in, \in \vee q)$-fuzzy subalgebras in $BCK/BCI$-algebras by using level cut subsets are explored.


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