模糊赋范Riesz空间上模糊算子的研究
Research on Fuzzy Operators on Fuzzy Normed Riesz Space
摘要: 本文在模糊赋范Riesz空间中引入-α范数，给出弱模糊范数有界线性泛函的定义。研究了模糊序有界线性泛函与弱模糊范数有界线性泛函之间的关系。在模糊Banach格上，模糊序有界线性泛函和弱模糊范数有界线性泛函是等价的。
Abstract: In this paper, α-norm is introduced in fuzzy normed Riesz space, and the definition of fuzzy weak norm bounded linear functional is given. The relationship between fuzzy ordered bounded linear functionals and fuzzy weakly norm bounded linear functionals is studied. On fuzzy Banach lattices, fuzzy order bounded linear functionals and fuzzy weak norm bounded linear functionals are equivalent.
文章引用：陈强, 周姮媛. 模糊赋范Riesz空间上模糊算子的研究[J]. 理论数学, 2024, 14(5): 237-244. https://doi.org/10.12677/pm.2024.145181

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] Katsaras, A.K. (1984) Fuzzy Topological Vector Spaces I. Fuzzy Sets Systems, 6, 85-95. [Google Scholar] [CrossRef] 
[4] Venugopalan, P. (1992) Fuzzy Ordered Sets. Fuzzy Sets and Systems, 46, 221-226. [Google Scholar] [CrossRef] 
[5] Felbin, C. (1992) Finite Dimensional Fuzzy Normed Linear Space. Fuzzy Sets Systems, 48, 239-248. [Google Scholar] [CrossRef] 
[6] Beg, I. and Islam, M.U. (1995) Fuzzy Ordered Linear Spaces. Fuzzy Mathematics, 3, 659-670.
[7] Beg, I. and Islam, M.U. (1994) Fuzzy Riesz Spaces. Fuzzy Mathematics, 2, 211-228. [Google Scholar] [CrossRef] 
[8] Bag, T. and Samanta, S.K. (2003) Finite Dimensional Fuzzy Normed Linear Spaces. Fuzzy Mathematics, 11, 687-705.
[9] Bag, T. and Samanta, S.K. (2005) Fuzzy Bounded Linear Operators. Fuzzy Sets and Systems, 151, 513-547. [Google Scholar] [CrossRef] 
[10] Hong, L. (2015) Fuzzy Riesz Subspaces, Fuzzy Ideals, Fuzzy Bands, and Fuzzy Band Projections. Seria Matematica- Informatica, 53, 77-108. [Google Scholar] [CrossRef] 
[11] Park, C., Movahednia, E., Mosadegh, S.M.S.M., et al. (2018) Riesz Fuzzy Normed Spaces and Stability of a Lattice Preserving Functional Equation. Journal of Computational Analysis Applications, 24, 569-579.
[12] 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] 
[13] Guirao, J., Iqbal, M., Bashir, Z., et al. (2021) A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces. Mathematics, 9, 1512. [Google Scholar] [CrossRef] 
[14] Bashir, Z. and Iqbal, M. (2022) The Unbounded Fuzzy Norm Convergence in Fuzzy Banach Lattices. Soft Computing, 26, 25-31. [Google Scholar] [CrossRef] 
[15] 赵家锐, 李浩, 潘相宇. 模糊赋范Riesz空间的性质[J]. 应用数学进展, 2022, 11(4): 2017-2023. [Google Scholar] [CrossRef] 
[16] 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. [Google Scholar] [CrossRef] 
[17] Zaanen, A.C. (1997) Introduction to Operator Theory in Riesz Spaces. Springer, Berlin Heidelberg. [Google Scholar] [CrossRef] 

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