二元关系应用于粗糙环境下的量子模糊子结构

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2024-01-01 DOI:10.1515/dema-2023-0109

Saqib Mazher Qurashi, Bander Almutairi, Qin Xin, Rani Sumaira Kanwal, Aqsa

{"title":"二元关系应用于粗糙环境下的量子模糊子结构","authors":"Saqib Mazher Qurashi, Bander Almutairi, Qin Xin, Rani Sumaira Kanwal, Aqsa","doi":"10.1515/dema-2023-0109","DOIUrl":null,"url":null,"abstract":"\n Binary relations (BIRs) have many applications in computer science, graph theory, and rough set theory. This study discusses the combination of BIRs, fuzzy substructures of quantale, and rough fuzzy sets. Approximation of fuzzy subsets of quantale with the help of BIRs is introduced. In quantale, compatible and complete relations in terms of aftersets and foresets with the help of BIRs are defined. Furthermore, we use compatible and complete relations to approximate fuzzy substructures of quantale, and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough fuzzy quantale. Finally, using BIRs, quantale homomorphism is used to build a relationship between the approximations of fuzzy substructures of quantale and the approximations of their homomorphic images.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Binary relations applied to the fuzzy substructures of quantales under rough environment\",\"authors\":\"Saqib Mazher Qurashi, Bander Almutairi, Qin Xin, Rani Sumaira Kanwal, Aqsa\",\"doi\":\"10.1515/dema-2023-0109\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n Binary relations (BIRs) have many applications in computer science, graph theory, and rough set theory. This study discusses the combination of BIRs, fuzzy substructures of quantale, and rough fuzzy sets. Approximation of fuzzy subsets of quantale with the help of BIRs is introduced. In quantale, compatible and complete relations in terms of aftersets and foresets with the help of BIRs are defined. Furthermore, we use compatible and complete relations to approximate fuzzy substructures of quantale, and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough fuzzy quantale. Finally, using BIRs, quantale homomorphism is used to build a relationship between the approximations of fuzzy substructures of quantale and the approximations of their homomorphic images.\",\"PeriodicalId\":10995,\"journal\":{\"name\":\"Demonstratio Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Demonstratio Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/dema-2023-0109\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Demonstratio Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/dema-2023-0109","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

二元关系（BIR）在计算机科学、图论和粗糙集理论中有很多应用。本研究讨论了二元关系、量子的模糊子结构和粗糙模糊集的结合。在 BIRs 的帮助下，介绍了量子态模糊子集的逼近。在 Quantale 中，借助 BIRs 定义了后集和前集的兼容关系和完整关系。此外，我们还利用兼容关系和完整关系来近似量子态的模糊子结构，并用后集和前集解释这些近似。这一概念概括了粗糙模糊量子模型的概念。最后，利用 BIRs，我们利用量子同态建立了量子模糊子结构的近似与其同态图像的近似之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Binary relations applied to the fuzzy substructures of quantales under rough environment

Binary relations (BIRs) have many applications in computer science, graph theory, and rough set theory. This study discusses the combination of BIRs, fuzzy substructures of quantale, and rough fuzzy sets. Approximation of fuzzy subsets of quantale with the help of BIRs is introduced. In quantale, compatible and complete relations in terms of aftersets and foresets with the help of BIRs are defined. Furthermore, we use compatible and complete relations to approximate fuzzy substructures of quantale, and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough fuzzy quantale. Finally, using BIRs, quantale homomorphism is used to build a relationship between the approximations of fuzzy substructures of quantale and the approximations of their homomorphic images.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.