模糊Riesz空间上模糊序有界线性算子的研究
A Study of Fuzzy Ordered Bounded Linear Operators on Fuzzy Riesz Spaces
摘要: 本文首先研究了模糊Riesz空间上模糊线性算子的一些性质，其次讨论了具有模糊主投影性质的模糊Riesz空间上任意两个模糊序有界线性算子的上确界和下确界的存在性，最后给出了模糊线性泛函是模糊序有界的刻画。
Abstract: In this paper, we first study some properties of fuzzy linear operators on fuzzy Riesz spaces. Secondly, we discuss the existence of supremum and infimum of any two fuzzy ordered bounded linear operators on fuzzy Riesz spaces with fuzzy principal projection properties. Finally, we give a characterization that fuzzy linear functionals are fuzzy ordered bounded.
文章引用：陈强, 周姮媛, 刘艳丽. 模糊Riesz空间上模糊序有界线性算子的研究[J]. 理论数学, 2024, 14(3): 74-82. https://doi.org/10.12677/pm.2024.143086

参考文献

[1] Zadeh, L.A. (1965) Fuzzy Sets. Information Control, 8, 338-353. [Google Scholar] [CrossRef] 
[2] Zadeh, L.A. (1971) Similarity Relations and Fuzzy Orderings. Information Sciences, 3, 177-200. [Google Scholar] [CrossRef] 
[3] Venugopalan, P. (1992) Fuzzy Ordered Sets. Fuzzy Sets and Systems, 46, 221-226. [Google Scholar] [CrossRef] 
[4] Beg, I. and Islam, M.U. (1995) Fuzzy Ordered Linear Spaces. Fuzzy Mathematics, 3, 659-670.
https://www.researchgate.net/publication/266311007
[5] Beg, I. and Islam, M.U. (1994) Fuzzy Riesz Spaces. Fuzzy Mathematics, 2, 211-228.
https://www.researchgate.net/publication/256471147
[6] Beg, I. and Islam, M. (1997) Fuzzy Archimedean Spaces. Fuzzy Mathematics, 5, 413-423.
https://www.researchgate.net/publication/233757745
[7] Beg, I. (1997)-Complete Fuzzy Riesz Spaces. Results in Mathematics, 31, 292-229. https://www.researchgate.net/publication/257289053 [Google Scholar] [CrossRef] 
[8] Beg, I. (1998) Extenssion of Fuzzy Positive Linear Operator. Fuzzy Mathematics, 6, 849-855.
https://www.researchgate.net/publication/262611976
[9] Hong, L. (2015) Fuzzy Riesz Subspaces, Fuzzy Ideals, Fuzzy Bands, and Fuzzy Band Projections. Seria Matematica-Informatica, 53, 77-108. [Google Scholar] [CrossRef] 
[10] Park, C., Movahednia, E., Mosadegh, S.M.S.M. and Mursaleen, M. (2018) Riesz Fuzzy Normed Spaces and Stability of a Lattice Preserving Functional Equation. Journal of Computational Analysis Applications, 24, 569-579.
[11] Iqbal, M. and Bashir, Z. (2020) The Existence of Fuzzy Dedekind Completion of Archimedean Fuzzy Riesz Space. Computational and Applied Mathematics, 39, 116. [Google Scholar] [CrossRef] 
[12] Guirao, J., Iqbal, M., Bashir, Z. and Rashid, T. (2021) A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces. Mathematics, 9, 1512. [Google Scholar] [CrossRef] 
[13] Cheng, N., Liu, X. and Dai, J. (2022) Extension of Fuzzy Linear Operators on Fuzzy Riesz Spaces. Bulletin des Sciences Mathématiques, 179, 103168. [Google Scholar] [CrossRef] 
[14] 刘宵. 模糊Riesz空间中收敛序列性质的研究[D]: [硕士学位论文]. 成都: 西华大学理学院, 2022.

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