Authors: Šešelja, Branimir
Tepavčević, Andreja 
Title: L-E-Fuzzy Lattices
Journal: International Journal of Fuzzy Systems
Volume: 17
Issue: 3
First page: 366
Last page: 374
Issue Date: 1-Sep-2015
Rank: M23
ISSN: 1562-2479
DOI: 10.1007/s40815-015-0057-9
Abstract: 
A new definition of a fuzzy lattice (L-E-fuzzy lattice) as a particular fuzzy algebraic structure is introduced in the framework of fuzzy equalities and fuzzy identities. The membership values structure is a complete lattice. An L-E-fuzzy lattice is defined on a bi-groupoid M, as its fuzzy sub-bi-groupoid μ equipped with a fuzzy equality E, fulfilling fuzzy lattice identities. It is proved that the new notion is a generalization of known lattice-valued structures. Basic properties of the introduced new fuzzy lattices are presented. In particular, it is proved that the quotients of cuts of μ over the corresponding cuts of E are classical lattices. By a suitable example, it is shown how the new introduced structures can be applied.
Keywords: Complete lattice | Fuzzy congruence | Fuzzy equality | Fuzzy identity | Fuzzy lattice
Publisher: Springer Link
Project: Development of methods of computation and information processing: theory and applications 
Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, Grant “Ordered structures and applications”

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