On (complete) normality of &lt;em&gt;m&lt;/em&gt;-pF subalgebras in &lt;em&gt;BCK/BCI&lt;/em&gt;-algebras

Al-Masarwah, Anas; Ahmad, Abd Ghafur

doi:10.3934/math.2019.3.740

Cited by 13 publications

(8 citation statements)

References 11 publications

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“…Ahmad et al [17], initiated the m-Polar fuzzy ideals of BCK/BCI-algebras. Masarwah et al [18], reviewed the complete normality of m-pF subalgebras in BCK/BCI-algebras. Ahmad et al [19], evaluated the some properties of doubt bipolar fuzzy H-ideals in BCK/BCI-algebras.…”

Section: Fundamental Definitions and Resultsmentioning

confidence: 99%

Anti fuzzy bi-ideals on ordered AG-groupoids

Kausar

Munir

Gulzar

et al. 2020

JIMS

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Section: Fundamental Definitions and Resultsmentioning

confidence: 99%

Anti fuzzy bi-ideals on ordered AG-groupoids

Kausar

Munir

Gulzar

et al. 2020

JIMS

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“…Recently, Al-Masarwah and Ahmad introduced the notion of m-polar fuzzy (commutative) ideals [34] and m-polar ( , )-fuzzy ideals [35] in BCK∕BCI-algebras. As a continues work they introduced a new form of generalized m-polar fuzzy ideals in [36] and studied normalization of m-polar fuzzy subalgebras in [37]. A new advanced extensions are formed by merging two fuzzy information in one set as neutrosophic bipolar fuzzy sets, bipolar valued hesitant fuzzy sets and interval-valued m-polar fuzzy sets (IVmPF).…”

Section: Introductionmentioning

confidence: 99%

Interval Valued m-polar Fuzzy BCK/BCI-Algebras

Muhiuddin¹,

Al-Kadi²

2021

IJCIS

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The notion of interval-valued m-polar fuzzy sets (abbreviated IVmPF) is much wider than the notion of m-polar fuzzy sets. In this paper, we apply the theory of IVmPF on BCK/BCI-algebras. We introduce the concepts of IVmPF subalgebras, IVmPF ideals and IVmPF commutative ideals and some essential properties are discussed. We characterize IVmPF subalgebras in terms of fuzzy subalgebras and subalgebras of BCK/BCI-algebras. We show that in BCK-algebra, IVmPF ideals are IVmPF subalgebras and that the converse is not valid. We provide a condition under which an IVmPF subalgebra becomes an IVmPF ideal. Further, we characterize IVmPF ideals in terms of fuzzy ideals and ideals of BCK/BCI-algebras. Moreover, we prove that in any BCKalgebra, an IVmPF commutative ideal is an IVmPF fuzzy ideal but not the converse. Also, we provide conditions under which an IVmPF ideal becomes an IVmPF commutative ideal.

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“…In addition, various applications of m-pF sets and other hybrid models of fuzzy sets in pure and applied mathematics are studied in [24][25][26][27][28][29][30][31][32]. Recently, m-pF set theory has been applied to various algebraic structures on different aspects, namely, Farooq et al applied m-pF set theory to groups [33], Akram and Farooq applied m-pF set theory to Lie algebras [34,35], and the authors applied m-pF set theory to BCK/BCI-algebras (see [36][37][38][39][40]. Motivated by a lot of work on m-pF sets, we present m-polar fuzzy positive implicative (m-pFPI) ideals in BCK-algebras and discuss some related results.…”

Section: Introductionmentioning

confidence: 99%

Generalized m-Polar Fuzzy Positive Implicative Ideals of BCK-Algebras

Al-Masarwah

Ahmad

Muhiuddin

et al. 2021

Journal of Mathematics

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This study focuses on combining the theories of m -polar fuzzy sets over BCK -algebras and establishing a new framework of m -polar fuzzy BCK -algebras. In this paper, we define the idea of m -polar fuzzy positive implicative ideals in BCK -algebras and investigate some related properties. Then, we introduce the concepts of m -polar ∈ , ∈ ∨ q -fuzzy positive implicative ideals and m -polar ∈ ¯ , ∈ ¯ ∨ q ¯ -fuzzy positive implicative ideals in BCK -algebras as a generalization of m -polar fuzzy positive implicative ideals. Several properties, examples, and characterization theorems of these concepts are considered.

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

Cited by 13 publications

References 11 publications

Anti fuzzy bi-ideals on ordered AG-groupoids

Anti fuzzy bi-ideals on ordered AG-groupoids

Interval Valued m-polar Fuzzy BCK/BCI-Algebras

Generalized m-Polar Fuzzy Positive Implicative Ideals of BCK-Algebras

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