弱对偶(M)-积分的性质与等式

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-05-28 DOI:10.1016/j.fss.2025.109473

Wenxuan Wang, Siqi Chen, Xuanming Ye, Xiaoyang Chen, Yao Ouyang

{"title":"弱对偶(M)-积分的性质与等式","authors":"Wenxuan Wang, Siqi Chen, Xuanming Ye, Xiaoyang Chen, Yao Ouyang","doi":"10.1016/j.fss.2025.109473","DOIUrl":null,"url":null,"abstract":"<div><div>The weak dual (M)-property of monotone measures is introduced and its relationship with the dual (M)-property is discussed in detail. This newly introduced concept proved to be not only sufficient but also necessary for the coincidence of the pan-integral from above and the Choquet integral.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109473"},"PeriodicalIF":3.2000,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weak dual (M)-property and equality of integrals\",\"authors\":\"Wenxuan Wang, Siqi Chen, Xuanming Ye, Xiaoyang Chen, Yao Ouyang\",\"doi\":\"10.1016/j.fss.2025.109473\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The weak dual (M)-property of monotone measures is introduced and its relationship with the dual (M)-property is discussed in detail. This newly introduced concept proved to be not only sufficient but also necessary for the coincidence of the pan-integral from above and the Choquet integral.</div></div>\",\"PeriodicalId\":55130,\"journal\":{\"name\":\"Fuzzy Sets and Systems\",\"volume\":\"517 \",\"pages\":\"Article 109473\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2025-05-28\",\"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/S016501142500212X\",\"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/S016501142500212X","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

介绍了单调测度的弱对偶(M)-性质，并详细讨论了它与对偶(M)-性质的关系。这个新引入的概念证明了上述泛积分与Choquet积分的一致性不仅是充分的，而且是必要的。

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

Weak dual (M)-property and equality of integrals

The weak dual (M)-property of monotone measures is introduced and its relationship with the dual (M)-property is discussed in detail. This newly introduced concept proved to be not only sufficient but also necessary for the coincidence of the pan-integral from above and the Choquet integral.

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.