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

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 se...

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Bibliographic Details
Published in:	Entropy (Basel, Switzerland) Vol. 23; no. 8; p. 992
Main Authors:	Alolaiyan, Hanan, Alshehri, Halimah A., Mateen, Muhammad Haris, Pamucar, Dragan, Gulzar, Muhammad
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 30-07-2021 MDPI
Subjects:	(α,β)-complex fuzzy normal subgroup (α,β)-complex fuzzy set (α,β)-complex fuzzy subgroup Algebra Algorithms Commutators complex fuzzy set Decision making Fuzzy logic Fuzzy sets Group theory Machine learning Quotients Subgroups Theorems
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Summary:	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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	1099-4300 1099-4300
DOI:	10.3390/e23080992