On Fundamental Theorems of Fuzzy Isomorphism of Fuzzy Subrings over a Certain Algebraic Product

Altassan, Alaa; Mateen, M. Haris; Pamučar, Dragan

doi:10.3390/sym13060998

Cited by 7 publications

(3 citation statements)

References 45 publications

(45 reference statements)

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“…By direct calculations, it is observed that µ satisfies the conditions of a fuzzy Lie subalgebra, making it a fuzzy Lie algebra (cf. [18][19][20]).…”

Section: Fuzzy Lie Algebrasmentioning

confidence: 99%

S-Embedding of Lie Superalgebras and Its Implications for Fuzzy Lie Algebras

Assiry,

Mansour,

Baklouti

2023

Axioms

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This paper performed an investigation into the s-embedding of the Lie superalgebra (→S1∣1), a representation of smooth vector fields on a (1,1)-dimensional super-circle. Our primary objective was to establish a precise definition of the s-embedding, effectively dissecting the Lie superalgebra into the superalgebra of super-pseudodifferential operators ( SψD⊙) residing on the super-circle S1|1. We also introduce and rigorously define the central charge within the framework of (→S1∣1), leveraging the canonical central extension of SψD⊙. Moreover, we expanded the scope of our inquiry to encompass the domain of fuzzy Lie algebras, seeking to elucidate potential connections and parallels between these ostensibly distinct mathematical constructs. Our exploration spanned various facets, including non-commutative structures, representation theory, central extensions, and central charges, as we aimed to bridge the gap between Lie superalgebras and fuzzy Lie algebras. To summarize, this paper is a pioneering work with two pivotal contributions. Initially, a meticulous definition of the s-embedding of the Lie superalgebra (→S1|1) is provided, emphasizing the representationof smooth vector fields on the (1,1)-dimensional super-circle, thereby enriching a fundamental comprehension of the topic. Moreover, an investigation of the realm of fuzzy Lie algebras was undertaken, probing associations with conventional Lie superalgebras. Capitalizing on these discoveries, we expound upon the nexus between central extensions and provide a novel deformed representation of the central charge.

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“…By direct calculations, it is observed that µ satisfies the conditions of a fuzzy Lie subalgebra, making it a fuzzy Lie algebra (cf. [18][19][20]).…”

Section: Fuzzy Lie Algebrasmentioning

confidence: 99%

S-Embedding of Lie Superalgebras and Its Implications for Fuzzy Lie Algebras

Assiry,

Mansour,

Baklouti

2023

Axioms

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“…In [6], Altassan et al defined the concept of a ω-fuzzy set, ω-fuzzy subring, and ωfuzzy ideal, where they also looked into various fundamental outcomes of this phenomenon. Furthermore, they developed a quotient ring with respect to this specific fuzzy ideal analogue to the classical quotient ring and proposed the idea of a ω-fuzzy coset.…”

Section: Introductionmentioning

confidence: 99%

Neutrosophic 𝔑-Structures in Semimodules over Semirings

Muhiuddin,

Abughazalah,

Elavarasan

et al. 2023

Symmetry

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The study of symmetry is a fascinating and unifying subject that connects various areas of mathematics in the twenty-first century. Algebraic structures offer a framework for comprehending the symmetries of geometric objects in pure mathematics. This paper introduces new concepts in algebraic structures, concentrating on semimodules over semirings and analysing the neutrosophic structure in this context. We explore the properties of neutrosophic subsemimodules and neutrosophic ideals after defining them. We discuss, utilizing neutrosophic products, the representations of neutrosophic ideals and subsemimodules, as well as the relationship between neutrosophic products and intersections. Finally, we derive equivalent criteria in terms of neutrosophic structures for a semiring to be fully idempotent.

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“…The new development about Q-complex fuzzy subring was introduced in [40]. For other useful results of fuzzy subgroups not mentioned in the article, readers are referred to [41][42][43][44][45][46][47].…”

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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On Fundamental Theorems of Fuzzy Isomorphism of Fuzzy Subrings over a Certain Algebraic Product

Cited by 7 publications

References 45 publications

S-Embedding of Lie Superalgebras and Its Implications for Fuzzy Lie Algebras

S-Embedding of Lie Superalgebras and Its Implications for Fuzzy Lie Algebras

Neutrosophic 𝔑-Structures in Semimodules over Semirings

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

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