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

Abstract

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.

Algebraic Properties of ω , θ -Complex Fuzzy Subgroups

“…Each concept introduced in this paper is explained with clear examples. is algebraic structure will play an important role to handle many other group theory problems under a new complex fuzzy environment [37,38].…”

“…Verma [36] et al discussed a systematic review on the advancement in study of fuzzy variational problems. Alolaiyan et al [38] developed the structure of (α, β)-complex fuzzy subgroups.…”

Identification and Prioritization of DevOps Success Factors Using Bipolar Complex Fuzzy Setting With Frank Aggregation Operators and Analytical Hierarchy Process

“…Thus, handling such sort of information is very complicated for a decisionmaker, for this, every expert has needed to change the range of FS, therefore, the main theory of complex FS was diagnosed by Ramot et al [35]. Certain applications of CFS have been done in shape, called distance measures [36], complex fuzzy hypersoft sets [37], neighborhood operators for CFS [38], algebraic structure [39], and entropy measures [40][41][42]. By utilizing the two-dimension data, the comprehensive data can be expected in one set, and hence, loss of data can be prevented.…”

On the Algebraic Characteristics of Fuzzy Sub e-Groups

“…Abuhijleh et al [24] worked on complex fuzzy subgroups in 2021. Alolaiyan et al [25] studied algebraic structure of ðα, βÞ -complex fuzzy subgroups. Alolaiyan et al [26] developed bipolar fuzzy subrings in 2021.…”