Non-deterministic-M-fuzzy Lattices
DOI:
https://doi.org/10.23755/rm.v48i0.1270Keywords:
Nd-M-fuzzy subset, Nd-M-fuzzy Relation, Nd-M-fuzzy lattice.Abstract
Goran Trajakoviski and Tepavcevic´invented the L-fuzzy lattice in which a ´ bounded lattice is fuzzified using a complete lattice. Using a complete consistent distributive multilattice M, we broaden the concept of L-fuzzy lattice to Nd-M-fuzzy lattice in this study. We also introduce the idea of Nd-M-order relation on a set X. Additionally, we demonstrated that the equivalent condition for a Nd-M-fuzzy subset to be a Nd-M-fuzzy sublattice of a bounded lattice L.References
N. Ajmal and K. Thomas. Fuzzy lattices. Information Sciences, 79(3-4):271–291, 1994.
A. Avallone. Modular functions on multilattices. Czechoslovak Mathematical Journal, 52:499–512, 2002.
G. Birkhoff. Lattice theory, volume 25. American Mathematical Society, 1940.
P. Cordero, G. Gutiérrez, J. Martínez, M. Ojeda-Aciego, and I. de las Penas. Congruence relations on multilattices. In Computational Intelligence in Decision and Control, pages 139–144. World Scientific, 2008.
K. Gireesan and T. Thrivikraman. Non-deterministic Fuzzification using Multilattices. PhD thesis, Cochin University of Science and Technology, 2015.
J. A. Goguen. L-fuzzy sets. Journal of Mathematical Analysis and Applications, 18(1):145–174, 1967.
I. J. Johnston. Some results involving multilattice ideals and distributivity. Discrete Mathematics, 83(1):27–35, 1990.
K. K. Gireesan. Non-deterministic L-fuzzy topological spaces. Bulletin of Kerala Mathematical Association, 11(2):121–125, 2014.
G. Klir and B. Yuan. Fuzzy Sets and Fuzzy Logic, volume 4. Prentice Hall, New Jersey, 1995.
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calvino. Multi-lattices as a basis for generalized fuzzy logic programming. Lecture Notes in Computer Science, 3849:61, 2006.
A. Tepavčević and G. Trajkovski. L-fuzzy lattices: an introduction. Fuzzy Sets and Systems, 123(2):209–216, 2001.
Downloads
Published
Issue
Section
License
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:
- Free access for all users worldwide
- Increased visibility and readership
- Rapid publication
- No spatial constraints
- Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)
Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.