 Incorporating £-Complex Intuitionistic Fuzzy Set to Sylow Theorems in Group TheoryMuhammad Jawad, Sarka Hoskova-Mayerova, Niat Nigar, Sanaa Ahmed Bajri and Muhammad Haris Mateen Journal of Mathematics, 2026, vol. 2026, 1-14 Abstract: The complex intuitionistic fuzzy (CIF) set is an advanced version of the regular intuitionistic fuzzy set. It is made to better show the uncertainty and complexity that arise in real-life problems. The grading and nongrading degrees in the CIF set are shown by complex-valued functions that are defined on the unit disc of the complex plane. A CIF set combines both magnitude and phase terms to establish a more robust mathematical framework to understand and address, such as decision-making and pattern detection, where conventional intuitionistic fuzzy sets may be insufficient. The £-CIF set is the generalization of the CIF set. The extension of the traditional Sylow theorems in the context of £-CIF brings in the idea of the £-CIF conjugate element within the £-CIF subgroup of a group. In this paper, we introduce the paradigmatic idea of £-CIF subgroups of a group, and various features of this concept are demonstrated. Furthermore, the construction of the £-CIF version of the Cauchy theorem is derived. Finally, we look into the £-CIF Sylow p subgroup for a finite group and show how Sylow’s theorems can be extended in a £-CIF environment. Date: 2026 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6650937 DOI: 10.1155/jom/6650937 Access Statistics for this article More articles in Journal of Mathematics from Hindawi |
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