{"title":"Higher-order derivative of uncertain process and higher-order uncertain differential equation","authors":"Kaixi Zhang, Baoding Liu","doi":"10.1007/s10700-024-09422-0","DOIUrl":null,"url":null,"abstract":"<p>This paper initializes higher-order uncertain calculus that deals with higher-order differentiation and multiple integration of uncertain process based on uncertainty theory. Fubini theorem and fundamental theorem of higher-order uncertain calculus are derived. Finally, this paper rigorously defines higher-order uncertain differential equations and introduces some analytic methods for solving these equations.</p>","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":"8 1","pages":""},"PeriodicalIF":4.8000,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Optimization and Decision Making","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10700-024-09422-0","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
This paper initializes higher-order uncertain calculus that deals with higher-order differentiation and multiple integration of uncertain process based on uncertainty theory. Fubini theorem and fundamental theorem of higher-order uncertain calculus are derived. Finally, this paper rigorously defines higher-order uncertain differential equations and introduces some analytic methods for solving these equations.
期刊介绍：
The key objective of Fuzzy Optimization and Decision Making is to promote research and the development of fuzzy technology and soft-computing methodologies to enhance our ability to address complicated optimization and decision making problems involving non-probabilitic uncertainty.
The journal will cover all aspects of employing fuzzy technologies to see optimal solutions and assist in making the best possible decisions. It will provide a global forum for advancing the state-of-the-art theory and practice of fuzzy optimization and decision making in the presence of uncertainty. Any theoretical, empirical, and experimental work related to fuzzy modeling and associated mathematics, solution methods, and systems is welcome. The goal is to help foster the understanding, development, and practice of fuzzy technologies for solving economic, engineering, management, and societal problems. The journal will provide a forum for authors and readers in the fields of business, economics, engineering, mathematics, management science, operations research, and systems.
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