A study of (α, β)-complex fuzzy hyperideals in non-associative hyperrings

Gulistan, Muhammad; Yaqoob, Naveed; Nawaz, Shah; Azhar, Muhammad

doi:10.3233/jifs-181829

Cited by 11 publications

(8 citation statements)

References 18 publications

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“…The algebraic structure between fuzzy sets and normed rings were proposed in [28]. Gulistan et al [29] presented the notion of (α, β)-complex fuzzy hyper-ideal and investigated many algebraic properties of this phenomena. Liu and Shi [30] presented a novel framework to fuzzification of lattice, which is known as an M-hazy lattice.…”

Section: Introductionmentioning

confidence: 99%

A Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups

Alolaiyan

Alshehri

Mateen

et al. 2021

Entropy

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A complex fuzzy set is a vigorous framework to characterize novel machine learning algorithms. This set is more suitable and flexible compared to fuzzy sets, intuitionistic fuzzy sets, and bipolar fuzzy sets. On the aspects of complex fuzzy sets, we initiate the abstraction of (α,β)-complex fuzzy sets and then define α,β-complex fuzzy subgroups. Furthermore, we prove that every complex fuzzy subgroup is an (α,β)-complex fuzzy subgroup and define (α,β)-complex fuzzy normal subgroups of given group. We extend this ideology to define (α,β)-complex fuzzy cosets and analyze some of their algebraic characteristics. Furthermore, we prove that (α,β)-complex fuzzy normal subgroup is constant in the conjugate classes of group. We present an alternative conceptualization of (α,β)-complex fuzzy normal subgroup in the sense of the commutator of groups. We establish the (α,β)-complex fuzzy subgroup of the classical quotient group and show that the set of all (α,β)-complex fuzzy cosets of this specific complex fuzzy normal subgroup form a group. Additionally, we expound the index of α,β-complex fuzzy subgroups and investigate the (α,β)-complex fuzzification of Lagrange’s theorem analog to Lagrange’ theorem of classical group theory.

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Section: Introductionmentioning

confidence: 99%

A Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups

Alolaiyan

Alshehri

Mateen

et al. 2021

Entropy

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“…Azhar and his colleagues [31][32][33][34] developed the structures of partially ordered LAsemihypergroups. Nawaz and his colleagues [35][36][37][38][39][40][41] developed and studied many nonassociative structures. The concept of almost ideals in semigroups was provided by Grosek and Satko [42,43] in 1980 and 1981, respectively.…”

Section: Introductionmentioning

confidence: 99%

On the Left and Right Almost Hyperideals of LA-Semihypergroups

Nawaz¹,

Gulistan²,

Kausar³

et al. 2021

IJFIS

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“…Alolaiyan and Abbas [29] established a stability of complete fuzzy hypergraphs and used it to find a safe and scientific way in computerized tomography (CT) scans. Gulstan et al [30] expounded the notion ( , ) complex fuzzy hyperideal. The algebraic structure of weakly and almost T-ABSO fuzzy modules was studied in [31].…”

Section: Introductionmentioning

confidence: 99%

Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings

Gulzar¹,

Mateen²,

Chu³

et al. 2021

IJCIS

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The objective of this article is to present the notion of direct product of two complex intuitionistic fuzzy subrings. We show that the direct product of two complex intuitionistic fuzzy subrings is also complex intuitionistic fuzzy subring and discuss its various algebraic aspects. We also define the level subsets of the direct product of two complex intuitionistic fuzzy subsets and prove that the level subset of the direct product of two complex intuitionistic fuzzy subring is subring and prove some fundamental result of this phenomena. We show that the homomorphic image (preimage) of the direct product of complex intuitionistic fuzzy subrings is a complex intuitionistic fuzzy subring by using the notion of classical homomorphism.

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A study of (α, β)-complex fuzzy hyperideals in non-associative hyperrings

Cited by 11 publications

References 18 publications

A Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups

A Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups

On the Left and Right Almost Hyperideals of LA-Semihypergroups

Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings

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