当前位置: X-MOL 学术Complex Intell. Syst. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Hybrid structure of maximal ideals in near rings
Complex & Intelligent Systems ( IF 5.0 ) Pub Date : 2024-06-15 , DOI: 10.1007/s40747-024-01486-0
B. Jebapresitha

A hybrid structure is an arrangement that makes use of many hierarchical reporting structures and is applied to algebraic structures such as groups and rings. In the discipline of abstract algebra, an ideal of a near-ring is a unique subset of its elements in ring theory. Ideals generalize specific subsets of integers, such as even numbers or multiples of three. Researchers have been using mathematical theories of fuzzy sets in ring theory to explain the uncertainties that emerge in various domains such as art and science, engineering, medical science, and in environment. By fusing soft sets and fuzzy sets, a new mathematical tool that has significant advantages in dealing with uncertain information is provided. Consequently, there is always some discrepancy between reality's haziness and its mathematical model's precision. Hence ring theory has been widely used in many researches but there is some uncertainty in converting the fuzzy sets to a hybrid structure of any algebraic structure. Many approaches were done in groups. Therefore, the Hybrid structure of fuzzy sets in near rings is introduced, in which the fuzzy ideals are converted to hybrid ideals and fuzzy maximal ideals are converted to hybrid maximal ideals. For hybridization, firstly the hybrid structure is established and then sub-near rings and near rings are also determined. Then the hybrid structure of sub-near rings and ideals is introduced. This converts the fuzzy ideals and fuzzy maximal ideals to hybrid ideals and hybrid maximal ideals. The result obtained by the proposed model efficiently solved the uncertainty problems and the effectiveness of the proposed approach shows the best class, mean, worst class, and time complexity.



中文翻译:


近环极大理想杂化结构



混合结构是一种利用许多分层报告结构的安排,并应用于代数结构,例如群和环。在抽象代数学科中,近环的理想是环理论中其元素的独特子集。理想概括了整数的特定子集,例如偶数或三的倍数。研究人员一直在使用环理论中模糊集的数学理论来解释艺术和科学、工程、医学和环境等各个领域中出现的不确定性。通过融合软集和模糊集,提供了一种在处理不确定信息方面具有显着优势的新数学工具。因此,现实的模糊性与其数学模型的精确性之间总是存在一些差异。因此环理论在许多研究中得到了广泛的应用,但将模糊集转换为任何代数结构的混合结构都存在一定的不确定性。许多方法都是分组进行的。因此,引入了近环模糊集的混合结构,将模糊理想转化为混合理想,将模糊极大理想转化为混合极大理想。对于杂化,首先建立杂化结构,然后还确定亚近环和近环。然后介绍了亚近环与理想的混合结构。这将模糊理想和模糊最大理想转换为混合理想和混合最大理想。所提出的模型获得的结果有效地解决了不确定性问题,并且所提出的方法的有效性显示了最佳类、平均数、最差类和时间复杂度。

更新日期:2024-06-15
down
wechat
bug