模糊Riesz空间上序稠密集的研究
The Study of Order Dense Sets in Fuzzy Riesz Spaces
摘要: 本文主要讨论了模糊Riesz空间中的模糊序稠密集，模糊quasi序稠密集和模糊super序稠密集的一些基本性质。首先给出模糊理想A在模糊理想B中模糊quasi序稠密的等价条件和模糊理想A和模糊理想B的交是模糊quasi序稠密的必要条件以及A在B中模糊super序稠密的等价条件。其次用模糊quasi序稠密集刻画模糊Archimedean Riesz空间。最后给出Archimedean Riesz空间中模糊理想是模糊super序稠密的充要条件和模糊Archimedean Riesz空间中模糊Riesz子空间是模糊super序稠密的等价条件。
Abstract: This paper discusses some fundamental properties of fuzzy order dense sets, fuzzy quasi order dense sets, and fuzzy super order dense sets in fuzzy Riesz spaces. Firstly, it presents equivalent conditions for fuzzy ideals to be fuzzy quasi order dense in fuzzy ideals, necessary conditions for the intersection of fuzzy ideals to be fuzzy quasi order dense, and equivalent conditions for fuzzy super order density. Then, it characterizes fuzzy Archimedean Riesz spaces using fuzzy quasi order dense sets. Lastly, it provides necessary and sufficient conditions for fuzzy ideals to be fuzzy super order dense in Archimedean Riesz spaces and equivalent conditions for fuzzy Riesz subspaces to be fuzzy super order dense in fuzzy Archimedean Riesz spaces.
文章引用：张也. 模糊Riesz空间上序稠密集的研究[J]. 理论数学, 2024, 14(6): 122-132. https://doi.org/10.12677/pm.2024.146233

参考文献

[1] Zadeh, L.A. (1965) Fuzzy Sets. Information and 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. (1994) Fuzzy Riesz Spaces. The Journal of Fuzzy Mathematics, 2, 211-241.
[5] Beg, I. and Islam, M.U. (1995) Fuzzy Ordered Linear Spaces. The Journal of Fuzzy Mathematics, 3, 659-670.
[6] Beg, I. (1997) σ-Complete Fuzzy Riesz Spaces. Results in Mathematics, 31, 292-299. [Google Scholar] [CrossRef] 
[7] Beg, I. and Islam, M.U. (1997) Fuzzy Archimedean Spaces. The Journal of Fuzzy Mathematics, 5, 413-423.
[8] Hong, L. (2015) Fuzzy Riesz Subspaces, Fuzzy Ideals, Fuzzy Bands and Fuzzy Band Projections. Annals of West University of Timisoara-Mathematics and Computer Science, 53, 77-108. [Google Scholar] [CrossRef] 
[9] 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] 
[10] Cheng, N. and Chen, G.G. (2021) Fuzzy Rieszhomomophism on Fuzzy Riesz Space. arxiv: 2104.07498v1.
[11] Cheng, N., Liu, X. and Dai, J. (2022) Extension of Fuzzy Linear Operators on Fuzzy Riesz Spaces. Bulletin des Sciences Mathématiques, 179, Article 103168. [Google Scholar] [CrossRef] 
[12] 赵娟娟, 程娜. 模糊Riesz空间中模糊不相交补和模糊投影带性质的研究[J]. 理论数学, 2022, 12(12): 2178-2188. [Google Scholar] [CrossRef] 
[13] Singh, S. and Tiwari, S.P. (2023) L-Fuzzy Automata Theory: Some Characterizations via General Fuzzy Operators. Fuzzy Sets and Systems, 460, 103-142. [Google Scholar] [CrossRef] 
[14] Zaanen, A.C. (1997) Introduction to Operator Theory in Riesz Spaces. Springer.
[15] Luxemburg, W.A.J. and Zaanen, A.C. (1971) Riesz Spaces.

为你推荐