On conjunctive complex fuzzification of Lagrange's theorem of <i>ξ</i>−CFSG

Aneeza Imtiaz; Umer Shuaib; Aneeza Imtiaz; Umer Shuaib

doi:10.3934/math.2023961

AIMS Mathematics

2023, Volume 8, Issue 8: 18881-18897. doi: 10.3934/math.2023961

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On conjunctive complex fuzzification of Lagrange's theorem of ξ−CFSG

Aneeza Imtiaz ,
Umer Shuaib ^,

Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan

Received: 18 March 2023 Revised: 20 May 2023 Accepted: 24 May 2023 Published: 05 June 2023
MSC : 08A72, 20N25, 03E72

The application of a complex fuzzy logic system based on a linear conjunctive operator represents a significant advancement in the field of data analysis and modeling, particularly for studying physical scenarios with multiple options. This approach is highly effective in situations where the data involved is complex, imprecise and uncertain. The linear conjunctive operator is a key component of the fuzzy logic system used in this method. This operator allows for the combination of multiple input variables in a systematic way, generating a rule base that captures the behavior of the system being studied. The effectiveness of this method is particularly notable in the study of phenomena in the actual world that exhibit periodic behavior. The foremost aim of this paper is to contribute to the field of fuzzy algebra by introducing and exploring new concepts and their properties in the context of conjunctive complex fuzzy environment. In this paper, the conjunctive complex fuzzy order of an element belonging to a conjunctive complex fuzzy subgroup of a finite group is introduced. Several algebraic properties of this concept are established and a formula is developed to calculate the conjunctive complex fuzzy order of any of its powers in this study. Moreover, an important condition is investigated that determines the relationship between the membership values of any two elements and the membership value of the identity element in the conjunctive complex fuzzy subgroup of a group. In addition, the concepts of the conjunctive complex fuzzy order and index of a conjunctive complex fuzzy subgroup of a group are also presented in this article and their various fundamental algebraic attributes are explored structural. Finally, the conjunctive complex fuzzification of Lagrange's theorem for conjunctive complex fuzzy subgroups of a group is demonstrated.
Citation: Aneeza Imtiaz, Umer Shuaib. On conjunctive complex fuzzification of Lagrange's theorem of ξ−CFSG[J]. AIMS Mathematics, 2023, 8(8): 18881-18897. doi: 10.3934/math.2023961

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Abstract

The application of a complex fuzzy logic system based on a linear conjunctive operator represents a significant advancement in the field of data analysis and modeling, particularly for studying physical scenarios with multiple options. This approach is highly effective in situations where the data involved is complex, imprecise and uncertain. The linear conjunctive operator is a key component of the fuzzy logic system used in this method. This operator allows for the combination of multiple input variables in a systematic way, generating a rule base that captures the behavior of the system being studied. The effectiveness of this method is particularly notable in the study of phenomena in the actual world that exhibit periodic behavior. The foremost aim of this paper is to contribute to the field of fuzzy algebra by introducing and exploring new concepts and their properties in the context of conjunctive complex fuzzy environment. In this paper, the conjunctive complex fuzzy order of an element belonging to a conjunctive complex fuzzy subgroup of a finite group is introduced. Several algebraic properties of this concept are established and a formula is developed to calculate the conjunctive complex fuzzy order of any of its powers in this study. Moreover, an important condition is investigated that determines the relationship between the membership values of any two elements and the membership value of the identity element in the conjunctive complex fuzzy subgroup of a group. In addition, the concepts of the conjunctive complex fuzzy order and index of a conjunctive complex fuzzy subgroup of a group are also presented in this article and their various fundamental algebraic attributes are explored structural. Finally, the conjunctive complex fuzzification of Lagrange's theorem for conjunctive complex fuzzy subgroups of a group is demonstrated.

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