Algebraic Perspective of Cubic Multi-Polar Structures on BCK/BCI-Algebras

Al-Masarwah, Anas; Alshehri, Halimah

doi:10.3390/math10091475

Cited by 3 publications

(1 citation statement)

References 39 publications

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“…Borzooei et al [3] focused on multipolar intuitionistic fuzzy B-algebras. A new perception of cubic multi-polar structures on BCK/BCI-algebras was approached by Al-Masarwah et al [1]. In [10], the authors invented a mathematical model for nonlinear optimization which attempts membership functions to address the uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Interval Valued Intuitionistic Fuzzy β-Filters on β-Algebras

Palanivel¹,

Muralikrishna²,

Hemavathi³

et al. 2022

Int. J. Anal. Appl.

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This study establishes the concept of interval valued intuitionistic fuzzy (InVInF) β-filters on β-algebras and a few of its related properties are investigated. Some compelling results of interval valued fuzzy β-filters have been examined. Further, the notions of products and strong β-filters are also introduced. In addition that, the level set and homomorphism of interval valued intuitionistic fuzzy β-filters are too discussed. Furthermore, we enacted that the intersection between two interval valued intuitionistic fuzzy β−filters is again an interval valued intuitionistic fuzzy β-filter.

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Section: Introductionmentioning

confidence: 99%

Interval Valued Intuitionistic Fuzzy β-Filters on β-Algebras

Palanivel¹,

Muralikrishna²,

Hemavathi³

et al. 2022

Int. J. Anal. Appl.

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Groups and Structures of Commutative Semigroups in the Context of Cubic Multi-Polar Structures

2022

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In recent years, the m-polar fuzziness structure and the cubic structure have piqued the interest of researchers and have been commonly implemented in algebraic structures like groupoids, semigroups, groups, rings and lattices. The cubic m-polar (CmP) structure is a generalization of m-polar fuzziness and cubic structures. The intent of this research is to extend the CmP structures to the theory of groups and semigroups. In the present research, we preface the concept of the CmP groups and probe many of its characteristics. This concept allows the membership grade and non-membership grade sequence to have a set of m-tuple interval-valued real values and a set of m-tuple real values between zero and one. This new notation of group (semigroup) serves as a bridge among CmP structure, classical set and group (semigroup) theory and also shows the effect of the CmP structure on a group (semigroup) structure. Moreover, we derive some fundamental properties of CmP groups and support them by illustrative examples. Lastly, we vividly construct semigroup and groupoid structures by providing binary operations for the CmP structure and provide some dominant properties of these structures.

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Operational algebraic properties and subsemigroups of semigroups in view of $ k $-folded $ \mathcal{N} $-structures

Al-Masarwah

Alqahtani

2023

MATH

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<abstract><p>The concept of $ k $-folded $ \mathcal{N} $-structures ($ k $-F$ \mathcal{N} $Ss) is an essential concept to be considered for tackling intricate and tricky data. In this study, we want to broaden the notion of $ k $-F$ \mathcal{N} $S by providing a general algebraic structure for tackling $ k $-folded $ \mathcal{N} $-data by fusing the conception of semigroup and $ k $-F$ \mathcal{N} $S. First, we introduce and study some algebraic properties of $ k $-F$ \mathcal{N} $Ss, for instance, subset, characteristic function, union, intersection, complement and product of $ k $-F$ \mathcal{N} $Ss, and support them by illustrative examples. We also propose $ k $-folded $ \mathcal{N} $-subsemigroups ($ k $-F$ \mathcal{N} $SBs) and $ \widetilde{\zeta} $-$ k $-folded $ \mathcal{N} $-subsemigroups ($ \widetilde{\zeta} $-$ k $-F$ \mathcal{N} $SBs) in the structure of semigroups and explore some attributes of these concepts. Characterizations of subsemigroups are considered based on these concepts. Using the notion of $ k $-folded $ \mathcal{N} $-product, characterizations of $ k $-F$ \mathcal{N} $SBs are also discussed. Further, we obtain a necessary condition of a $ k $-F$ \mathcal{N} $SB to be a $ k $-folded $ \mathcal{N} $-idempotent. Finally, relations between $ k $-folded $ \mathcal{N} $-intersection and $ k $-folded $ \mathcal{N} $-product are displayed, and how the image and inverse image of a $ k $-F$ \mathcal{N} $SB become a $ k $-F$ \mathcal{N} $SB is studied.</p></abstract>

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Algebraic Perspective of Cubic Multi-Polar Structures on BCK/BCI-Algebras

Cited by 3 publications

References 39 publications

Interval Valued Intuitionistic Fuzzy β-Filters on β-Algebras

Interval Valued Intuitionistic Fuzzy β-Filters on β-Algebras

Groups and Structures of Commutative Semigroups in the Context of Cubic Multi-Polar Structures

Operational algebraic properties and subsemigroups of semigroups in view of $ k $-folded $ \mathcal{N} $-structures

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