Authors: Edeghagba, Elijah Eghosa
Šešelja, Branimir
Tepavčević, Andreja 
Title: Representation theory for complete L-lattices
Journal: Journal of Multiple-Valued Logic and Soft Computing
Volume: 33
Issue: 6
First page: 593
Last page: 617
Issue Date: 1-Jan-2019
Rank: M22
ISSN: 1542-3980
Abstract: 
In the framework of L-valued (fuzzy) sets, where L is a complete lattice, we introduce complete L-lattices, based on L-structures investigated by the authors. An L-poset is a set equipped with an L-valued equality E and an L-valued transitive relation R, which is antisymmetric with respect to E. A complete L-lattice is an L-poset in which every subset has a so called pseudo-supremum and a pseudo-infimum. Several properties concerning special elements of these L-structures are investigated. Among our main results, we prove that an L-poset is a complete L-lattice if and only if particular quotient substructures with respect to the L-valued equality are classical complete lattices. As another important result obtained by using closure systems, we present a Representation theorem dealing with a general construction of L-posets and Lcomplete lattices.
Keywords: Closure system | Complete L-lattice | L-equality | L-lattice | L-poset | L-set
Publisher: Old City Publishing
Project: Development of methods of computation and information processing: theory and applications 

Show full item record

Page view(s)

32
checked on Jan 31, 2023

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.