Calculus of linear fuzzy-number-valued functions using the generalized derivative and the Riemann integral of fuzzy n-cell-number-valued functions x2729;

doi:10.1016/j.fss.2020.12.001

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	Calculus of linear fuzzy-number-valued functions using the generalized derivative and the Riemann integral of fuzzy n-cell-number-valued functions x2729;
	Hai, Shexiang 1; Gong, Zengtai 2
刊名	FUZZY SETS AND SYSTEMS
	2022-02-15
卷号	429 页码:188-211
关键词	Fuzzy-number-valued functions Fuzzy differentiability Fuzzy integral Fuzzy calculus
ISSN号	0165-0114
DOI	10.1016/j.fss.2020.12.001
英文摘要	We study the differentiability, integral, and calculus of linear fuzzy-number-valued functions. Special emphasis is placed on the linear fuzzy-number-valued function Fxfffd;(t) = uxfffd;1f1(t) + uxfffd;2f2(t) + middot middot middot + uxfffd;mfm(t), where u'1, uxfffd;2, ... , uxfffd;m denote fuzzy n-cell numbers and f1, f2, ... , fm represent real functions of a real variable. The concepts of the limit and continuity of fuzzy n-cellnumber-valued functions are defined, which are the basis for studying the calculus of linear fuzzy-number-valued functions. Using the fuzzy generalized difference introduced by Gomes and Barros (2015) [8], we define a generalized difference for fuzzy ncell numbers. Then a generalized differentiability of fuzzy n-cell-number-valued functions is proposed, and a sufficient condition for generalized differentiability of linear fuzzy-number-valued functions is given by means of real function theory. Furthermore, a Riemann integral of fuzzy n-cell-number-valued functions is introduced, and some properties of the integral are discussed. Finally, the relationship between generalized differentiability and the Riemann integral of the linear fuzzy-number-valued function Fxfffd;(t) = uxfffd;1f1(t) + uxfffd;2f2(t) + middot middot middot + uxfffd;mfm(t) is derived.
WOS研究方向	Computer Science ; Mathematics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000752567200008
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/154788]
专题	理学院
作者单位	1.Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Peoples R China; 2.Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China
推荐引用方式 GB/T 7714	Hai, Shexiang,Gong, Zengtai. Calculus of linear fuzzy-number-valued functions using the generalized derivative and the Riemann integral of fuzzy n-cell-number-valued functions x2729;[J]. FUZZY SETS AND SYSTEMS,2022,429:188-211.
APA	Hai, Shexiang,&Gong, Zengtai.(2022).Calculus of linear fuzzy-number-valued functions using the generalized derivative and the Riemann integral of fuzzy n-cell-number-valued functions x2729;.FUZZY SETS AND SYSTEMS,429,188-211.
MLA	Hai, Shexiang,et al."Calculus of linear fuzzy-number-valued functions using the generalized derivative and the Riemann integral of fuzzy n-cell-number-valued functions x2729;".FUZZY SETS AND SYSTEMS 429(2022):188-211.