模糊数对角算子宽度
Width of Fuzzy Number Diagonal Operator
DOI: 10.12677/ORF.2021.111012, PDF,    科研立项经费支持
作者: 贺小航, 吴圣伟：西华大学理学院，四川 成都
关键词: 模糊数；n-宽度；Zadeh扩张；对角算子；Fuzzy Numbers； n-Widths； Zadeh’s Extension； Diagonal Operator
摘要: 在经典宽度理论基础上，将模糊数构成的集合作为被逼近集，讨论对角矩阵宽度的渐近阶得到1≤s<∞相应结论。本文继以上工作，利用函数的扎德扩张原理及Hausdorff距离讨论模糊对角矩阵宽度当s=∞时的渐近阶。特别地，当模糊数集合限制在实数集合上时，这个误差估计和经典宽度理论相应的结果是一致的。
Abstract: Based on the classical width theory, the set of fuzzy numbers is regarded as the approximated set. The asymptotic order of the width of diagonal matrix is discussed to 1≤s<∞ . This paper continues the above work. Using the function’s Zadeh’s expansion principle to discuss the width of diagonal matrix asymptotic order when s=∞ . In particular, when fuzzy number set restrictions in real number set, the error estimation and the classical theory of the width of the corresponding results are consistent.
文章引用：贺小航, 吴圣伟. 模糊数对角算子宽度[J]. 运筹与模糊学, 2021, 11(1): 97-104. https://doi.org/10.12677/ORF.2021.111012

参考文献

[1] Kolmogoroff, A. (1936) Uber die beste Annäherung von Funktionen einer gegebenen Funkionenklasse. Annals of Mathematics, 37, 107-110. [Google Scholar] [CrossRef] 
[2] Pietsch, A. (1974) s-Numbers of Operators in Banach Spaces. Studia Mathematica, 51, 21-33. [Google Scholar] [CrossRef] 
[3] Mityagin, B.S. and Tichomirov, V.M. (1964) Asymptotic Charac-teristic of Compact Sets in Linear Spaces. In: Proceedings Fourth All-Union Soviet Math. Congress, Vol. II. Sectional Lecture, Vol. 299, Nauka, Leningrad.
[4] Sofman, L.B. (1969) Diameters of Octahedra. Mathematical Notes of the Academy of Sciences of the USSR, 5, 258-262. [Google Scholar] [CrossRef] 
[5] Tichomirov, V.M. and Babadjanov, S.B. (1967) On the Width of a Functional Class in the Space Lp (p ≥ 1). Izvestiia Akademii nauk SSSR. Seriia Fiziko-Matematicheskikh, 2, 24-30.
[6] Hutton, C.V., Morrell, J.S. and Retherford, J.R. (1976) Diagonal Operators, Approximation Numbers, and Kolmogoroff Diameters. Journal of Approximation Theory, 16, 48-80. [Google Scholar] [CrossRef] 
[7] Pinkus, A. (1979) Matrices and n-Widths. Linear Algebra and Its Applications, 27, 245-278. [Google Scholar] [CrossRef] 
[8] Melkman, A.A. (1984) The Distance of a Subspace of Rm from Its Axes and n-Widths of Octahedra. Journal of Approximation Theory, 42, 245-256. [Google Scholar] [CrossRef] 
[9] Kašin, B.S. (1977) Diameters of Some Finite-Dimensional Sets and Classes of Smooth Functions. Mathematics of the USSR-Izvestiya, 11, 317-333. [Google Scholar] [CrossRef] 
[10] Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353. [Google Scholar] [CrossRef] 
[11] Chang, S.S.L. and Zadeh, L.A. (1972) On Fuzzy Mapping and Control. IEEE Transactions on Systems, Man and Cybernetics, SMC-2, 30-34. [Google Scholar] [CrossRef] 
[12] Han, Y.J., Liang, L. and Chen, G.G. (2019) Asymptotic Esti-mates for n-Width of Fuzzy Numbers. Journal of Inequalities and Applications, 2019, Article No. 86. [Google Scholar] [CrossRef] 
[13] Pinkus, A. (1985) n-Widths in Approximation Theory II. Springer, Berlin. [Google Scholar] [CrossRef] 
[14] 吴从炘, 赵治涛, 任雪昆. 模糊分析学与特殊泛函空间[M]. 哈尔滨: 哈尔滨工业大学出版社, 2013: 33-61.

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