广义线性相关模糊空间中模糊分数阶演化方程的可观测性

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-08-27 DOI:10.1016/j.fss.2025.109573

Nguyen Thi Thu Huyen , Nguyen Thi Kim Son , Hoang Thi Phuong Thao , Nguyen Phuong Dong

{"title":"广义线性相关模糊空间中模糊分数阶演化方程的可观测性","authors":"Nguyen Thi Thu Huyen , Nguyen Thi Kim Son , Hoang Thi Phuong Thao , Nguyen Phuong Dong","doi":"10.1016/j.fss.2025.109573","DOIUrl":null,"url":null,"abstract":"<div><div>The work is devoted to studying the observability of fuzzy fractional evolution equations in the space of generalized linearly correlated fuzzy numbers, namely the space <span><math><mrow><mi>LC</mi></mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>. Firstly, we develop an analysis of functions taking values in <span><math><mrow><mi>LC</mi></mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>. Next, we present some conditions to ensure that the Cauchy problem for the proposed fuzzy fractional evolution equations admits a unique integral solution. Furthermore, by constructing an appropriate observability Gramian matrix, we obtain a sufficient condition such that the proposed fuzzy fractional evolution equations are observable. The concepts of derivative, fractional derivative and integral of the linearly correlated fuzzy functions in the space <span><math><mrow><mi>LC</mi></mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> are introduced via the construction of the mapping <span><math><mi>ψ</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>→</mo><mrow><mi>LC</mi></mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>. The necessary and sufficient conditions for the mapping <em>ψ</em> to be an isomorphism are also mentioned.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109573"},"PeriodicalIF":2.7000,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The observability of fuzzy fractional evolution equations in the generalized linearly correlated fuzzy spaces\",\"authors\":\"Nguyen Thi Thu Huyen , Nguyen Thi Kim Son , Hoang Thi Phuong Thao , Nguyen Phuong Dong\",\"doi\":\"10.1016/j.fss.2025.109573\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The work is devoted to studying the observability of fuzzy fractional evolution equations in the space of generalized linearly correlated fuzzy numbers, namely the space <span><math><mrow><mi>LC</mi></mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>. Firstly, we develop an analysis of functions taking values in <span><math><mrow><mi>LC</mi></mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>. Next, we present some conditions to ensure that the Cauchy problem for the proposed fuzzy fractional evolution equations admits a unique integral solution. Furthermore, by constructing an appropriate observability Gramian matrix, we obtain a sufficient condition such that the proposed fuzzy fractional evolution equations are observable. The concepts of derivative, fractional derivative and integral of the linearly correlated fuzzy functions in the space <span><math><mrow><mi>LC</mi></mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> are introduced via the construction of the mapping <span><math><mi>ψ</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>→</mo><mrow><mi>LC</mi></mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>. The necessary and sufficient conditions for the mapping <em>ψ</em> to be an isomorphism are also mentioned.</div></div>\",\"PeriodicalId\":55130,\"journal\":{\"name\":\"Fuzzy Sets and Systems\",\"volume\":\"520 \",\"pages\":\"Article 109573\"},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2025-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fuzzy Sets and Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165011425003124\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165011425003124","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了广义线性相关模糊数空间（LC(A1,A2)）中模糊分数阶演化方程的可观测性。首先，我们对LC（A1,A2）中取值的函数进行了分析。其次，我们给出了保证所提出的模糊分数阶演化方程的Cauchy问题存在唯一积分解的条件。此外，通过构造一个适当的可观测格兰曼矩阵，我们得到了所提出的模糊分数进化方程是可观测的充分条件。通过构造映射ψ:R2→LC(A1,A2)，引入了空间LC（A1,A2）中线性相关模糊函数的导数、分数阶导数和积分的概念。给出了映射ψ是同构的充分必要条件。

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

The observability of fuzzy fractional evolution equations in the generalized linearly correlated fuzzy spaces

The work is devoted to studying the observability of fuzzy fractional evolution equations in the space of generalized linearly correlated fuzzy numbers, namely the space

LC (A_{1}, A_{2})

. Firstly, we develop an analysis of functions taking values in

LC (A_{1}, A_{2})

. Next, we present some conditions to ensure that the Cauchy problem for the proposed fuzzy fractional evolution equations admits a unique integral solution. Furthermore, by constructing an appropriate observability Gramian matrix, we obtain a sufficient condition such that the proposed fuzzy fractional evolution equations are observable. The concepts of derivative, fractional derivative and integral of the linearly correlated fuzzy functions in the space

LC (A_{1}, A_{2})

are introduced via the construction of the mapping

ψ : R^{2} \to LC (A_{1}, A_{2})

. The necessary and sufficient conditions for the mapping ψ to be an isomorphism are also mentioned.

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

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.