{"title":"模糊 n 单元数值函数的子差分及其在优化问题中的应用","authors":"Samira Fatemi, Ildar Sadeqi, Fridoun Moradlou","doi":"10.1016/j.fss.2024.109189","DOIUrl":null,"url":null,"abstract":"<div><div>We give the concept of subdifferentiability for a fuzzy <em>n</em>-cell number-valued function. Then we state some theorems related to the subdifferentiability based on the new definition. Finally, we present some applications focused on optimization problems, including the Lagrangian dual problem and the composite minimization problem.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109189"},"PeriodicalIF":3.2000,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Subdifferential of fuzzy n-cell number-valued functions and its applications in optimization problems\",\"authors\":\"Samira Fatemi, Ildar Sadeqi, Fridoun Moradlou\",\"doi\":\"10.1016/j.fss.2024.109189\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We give the concept of subdifferentiability for a fuzzy <em>n</em>-cell number-valued function. Then we state some theorems related to the subdifferentiability based on the new definition. Finally, we present some applications focused on optimization problems, including the Lagrangian dual problem and the composite minimization problem.</div></div>\",\"PeriodicalId\":55130,\"journal\":{\"name\":\"Fuzzy Sets and Systems\",\"volume\":\"499 \",\"pages\":\"Article 109189\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2024-11-12\",\"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/S016501142400335X\",\"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/S016501142400335X","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
我们给出了模糊 n 单元数值函数的次微分性概念。然后，我们根据新定义阐述了与次微分性相关的一些定理。最后，我们介绍了优化问题的一些应用，包括拉格朗日对偶问题和复合最小化问题。
Subdifferential of fuzzy n-cell number-valued functions and its applications in optimization problems
We give the concept of subdifferentiability for a fuzzy n-cell number-valued function. Then we state some theorems related to the subdifferentiability based on the new definition. Finally, we present some applications focused on optimization problems, including the Lagrangian dual problem and the composite minimization problem.
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.
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