Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/4197
Title: | Ω-Lattices | Authors: | Eghosa Edeghagba E. Šešelja B. Tepavčević, Andreja |
Issue Date: | 15-Mar-2017 | Journal: | Fuzzy Sets and Systems | Abstract: | © 2016 Elsevier B.V. In the framework of Ω-sets, where Ω is a complete lattice, we introduce Ω-lattices, both as algebraic and as order structures. An Ω-poset is an Ω-set equipped with an Ω-valued order which is antisymmetric with respect to the corresponding Ω-valued equality. Using a cut technique, we prove that the quotient cut-substructures can be naturally ordered. Introducing notions of pseudo-infimum and pseudo-supremum, we obtain a definition of an Ω-lattice as an ordering structure. An Ω-lattice as an algebra is a bi-groupoid equipped with an Ω-valued equality, fulfilling particular lattice-theoretic formulas. On an Ω-lattice we introduce an Ω-valued order, and we prove that particular quotient substructures are classical lattices. Assuming Axiom of Choice, we prove that the two approaches are equivalent. | URI: | https://open.uns.ac.rs/handle/123456789/4197 | ISSN: | 01650114 | DOI: | 10.1016/j.fss.2016.10.011 |
Appears in Collections: | PMF Publikacije/Publications |
Show full item record
SCOPUSTM
Citations
6
checked on May 3, 2024
Page view(s)
19
Last Week
2
2
Last month
0
0
checked on May 10, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.