Paper Info
Title
Representation of lattices by fuzzy sets
Abstract
We prove that every lattice L of finite length can be represented by a fuzzy set on the collection X of meet-irreducible elements of L. A decomposition of this fuzzy set gives a family of isotone functions from X to 2=({0,l}, less-than-or-equal-to), the lattice of which is isomorphic to L. More generally, conditions under which any collection of isotone functions from a finite set into 2 corresponds to a decomposition of a fuzzy set are given. As a consequence, the representation theorem for a finite distributive lattice by the lattice of all isotone functions is obtained.The collection of all lattices characterized by the same fuzzy set turns out to be a lattice with the above-mentioned distributive lattice as the greatest element.
Year
DOI
Venue
1994
10.1016/0020-0255(94)90117-1
Inf. Sci.
Keywords
DocType
Volume
fuzzy set
Journal
79
Issue
ISSN
Citations 
3-4
0020-0255
17
PageRank 
References 
Authors
3.49
0
2
Name
Order
Citations
PageRank
Branimir Šešelja117023.33
Andreja Tepavčevic2398.83