Automorphism group of \(L\)-fuzzy topologies when \(L\) is a diamond-type lattice
Downloads
DOI:
https://doi.org/10.26637/MJM0803/0040Abstract
We determined the group of all automorphisms of the lattice of all \(L\)-fuzzy topologies on a fixed set \(X\), when \(L\) is a diamond-type lattice.
Keywords:
Automorphism group, homomorphism, Lattice, Fuzzy TopologyMathematics Subject Classification:
Mathematics- Pages: 961-965
- Date Published: 01-07-2020
- Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Pub., Third Edn., 1967.
C. L. Chang, Fuzyy Topological Spaces, J. Math. Anal. Appl., 24(1968), 182-190.
Dexue Zhang and Hongliang Lai, Fuzzy Preorders and Fuzzy topology, Fuzzy Sets and Systems, 157(2006), $1865-1885$.
G. Elsamony, Connecting Fuzzifying Topologies And Generalized Ideals by means of Fuzzy Preorders, Int. J. of Mathematics and Mathematical Sciences, Volume 2009 , Article ID 567482,16 page.
J. D. Farely, The Automorphism group of a function lattice, Algebra Universalis, 36 (1996), 8-45.
Gerald Schrag, Every finite group is the Automorphism group of some finite orthomodular lattice, Proceedings of the American Mathematical Society, 55 (1976), 243-249.
J. Hartmanis, On The Lattice of Topologies, Cand. J. Math., 10 (1958), 547-553.
Jinming Fang and Piwei Chen, One to one correspondencebetween fuzzifying topologies and fuzzy preorders, Fuzzy Sets and Systems, 158 (2007), 1814-1822.
Jiri Adamek Horst Herrlich and George E. Strecker, Abstract and Concrete Categories The Joy of Cats, Free Online Edn., http:// katmat.math, uni.bremen.de/acc, (2004).
R. E. Larson and S. J. Andima, The Lattice of Topologies a Survey, Rocky Mountain J. Math., 5 (1975), 177-198.
Liu Ying Ming and Liu Mao Kang, Fuzzy Topology, World Scientific Pub. Singapore, 1997.
N. M. Madhavan Namboothiri, Order Induced L-Fuzzy Topological Properties, Advances in Fuzzy Sets And Systems, 9 (2011), 167-197.
S. E. Rodabaugh, A Categorical Accomadation to Various Notions of Fuzzy Topology, Fuzzy Sets and Systems, 9 (1983), 241-265.
Susan J. Andima and W. J. Thron, Order-Induced Topological Properties, Pacific J. Math., 75(2)(1978), 297318.
I. Uljane, On the Order Type L-valued Relations on Lpowersets, Mathware and Soft Computing, 14 (2007), $183-199$.
L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338-353.
- NA
Similar Articles
- Indiwar Singh Chauhan, T.S. Chauhan, Weyl-semi symmetric special Para-Sasakian manifold , Malaya Journal of Matematik: Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
