模糊完全分配格的代数表示
Algebraic Representation of Fuzzy Completely Distributive Lattices
DOI: 10.12677/PM.2026.1610217, PDF,    科研立项经费支持
作者: 孙艺洋, 魏晓伟*, 付阳健, 葛芸彤, 徐艺萌：天津理工大学数学科学学院，天津
关键词: Monad结构；Eilenberg-Moore范畴；模糊完全分配格；Monad Structure； Eilenberg-Moore Category； Fuzzy CD-Lattice
摘要: 设L为完全分配格。本文研究强L-上集monad结构所对应的Eilenberg一Moore代数的刻画。首先，给出强L-上集的定义。其次，利用强L-上集构造一个monad结构。最后证明该monad结构对应的Eilenberg-Moore代数恰好是模糊完全分配格。
Abstract: Let L be a completely distributive lattice. This paper mainly investigates the characterization of Eilenberg-Moore algebras associated with the monad of strong L-upper sets. First, we introduce the notion of a strong L-upper set. Next, we construct a monad structure based on strong L-upper sets. Finally, we prove that the Eilenberg-Moore algebras corresponding to this monad structure are precisely fuzzy completely distributive lattices.
文章引用：孙艺洋, 魏晓伟, 付阳健, 葛芸彤, 徐艺萌. 模糊完全分配格的代数表示[J]. 理论数学, 2026, 16(10): 99-114. https://doi.org/10.12677/PM.2026.1610217

参考文献

[1] Manes, E.G. (1974) Compact Hausdorff Objects. General Topology and Its Applications, 4, 341-360. [Google Scholar] [CrossRef] 
[2] Hofmann, D. and Tholen, W. (2006) Kleisli Compositions for Topological Spaces. Topology and Its Applications, 153, 2952-2961. [Google Scholar] [CrossRef] 
[3] Day, A. (1975) Filter Monads, Continuous Lattices and Closure Systems. Canadian Journal of Mathematics, 27, 50-59. [Google Scholar] [CrossRef] 
[4] Hofmann, D. and Seal, G.J. (2015) A Cottage Industry of Lax Extensions. Categories and General Algebraic Structures, 3, 113-151.
[5] Yue, Y. (2025) Scott Algebraic Closure Space and Its Applications. Fuzzy Sets and Systems, 498, Article ID: 109127. [Google Scholar] [CrossRef] 
[6] Pang, B. (2023) Quantale-Valued Convex Structures as Lax Algebras. Fuzzy Sets and Systems, 473, Article ID: 108737. [Google Scholar] [CrossRef] 
[7] Wei, X. (2025) Algebraic Representation of Finite-Complete L-Ordered Sets by Monad. Hacettepe Journal of Mathematics and Statistics, 55, 638-654. [Google Scholar] [CrossRef] 
[8] Wei, X. and Yue, Y. (2025) Algebraic Representations of (Fuzzy) Completely Distributive Lattices. Fuzzy Sets and Systems, 503, Article ID: 109245.[CrossRef] 
[9] Birkhoff, G. (1967) Lattice Theory, vol. XXV. American Mathematical Society.
[10] Goguen, J.A. (1967) L-Fuzzy Sets. Journal of Mathematical Analysis and Applications, 18, 145-174. [Google Scholar] [CrossRef] 
[11] Adamek, J., Herrlich, H. and Strecker, G.E. (1990) Abstract and Concrete Categories. Wiley.
[12] Hofmann, D., Seal, G.J. and Tholen, W. (2013) Monoidal Topology: A Categorical Approach to Order, Metric, and Topology. Cambridge University Press.
[13] Zhang, D.X. and Liu, Y.M. (1994) L-Fuzzy Modification of Completely Distributive Lattices. Mathematische Nachrichten, 168, 79-95. [Google Scholar] [CrossRef] 

为你推荐