We introduce the concept of a fuzzy countable semicontinuous lattice on a fuzzy complete lattice, and discuss some of its properties besides providing its characterization.

fuzzy countable semiprime ideal, fuzzy countable semiwaybelow relation, fuzzy countable semicontinuous lattices.

Received: July 17, 2023;  Accepted: November 21, 2023; Published: December 11, 2023

How to cite this article: Chongyun Zhao and Guanghao Jiang, Fuzzy countable semicontinuous lattices, Advances and Applications in Discrete Mathematics 41(1) (2024), 41-55. http://dx.doi.org/10.17654/0974165824003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] K. H. Hofmann and J. D. Lawson, Irreducibility and generation in continuous lattices, Semigroup Forum 13(1) (1976), 307-353.
[2] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, Continuous Lattices and Domains, Cambridge University Press, Cambridge, 2003.
[3] Y. Rav, Semiprime ideals in general lattices, J. Pure Appl. Algebra 56(2) (1989), 105-118.
[4] Qiye Zhang, L-fuzzy domain theory, Capital Normal University, Beijing, 2002.
[5] Wei Yao, Fuzzy Scott topology on fuzzy posets and specialization L-order of fuzzy topological space, Beijing institute of Technology, Beijing, 2008.
[6] Yanwei Han, Fuzzy semicontinuous lattice and its category properties, Shaanxi Normal University, Xi’an, 2011.
[7] Zhilian Guo, Studies on consistently semicontinuous domain and fuzzy semicontinuous domain, Shaanxi Normal University, Xi’an, 2012.
[8] Guanghao Jiang and Li Zhou, Fuzzy order-homomorphism of fuzzy countable continuous lattices, Fuzzy Systems Math. 30(6) (2016), 39-46.
[9] Li Zhou and Guanghao Jiang, Order homomorphisms of countable semicontinuous lattices, Tianjin Normal University (Nature Science Edition) 31(2) (2017), 50-56.
[10] Guanghao Jiang and Bailing An, Join semicontinuous lattices and join semicontinuous functions, Advances and Applications in Discrete Mathematics 25(1) (2020), 23-39.
[11] Bailing An and Guanghao Jiang, Fuzzy uniform domain and its applications, J. Interdiscip. Math. 24(3) (2021), 567-577.