Authors: Šešelja, Branimir
Tepavčević, Andreja 
Title: Representing ordered structures by fuzzy sets: An overview
Journal: Fuzzy Sets and Systems
Volume: 136
Issue: 1
First page: 21
Last page: 39
Issue Date: 16-May-2003
Rank: M22
ISSN: 0165-0114
DOI: 10.1016/S0165-0114(02)00366-4
Abstract: 
We present a survey on representations of ordered structures by fuzzy sets. Any poset satisfying some finiteness condition, semilattice, lattice belonging to a special class, e.g., distributive, Noetherian, complete and others - can be represented by a single function, i.e., by a fuzzy set. Its domain and co-domain are particular subsets of the same structure, and consist of irreducible elements. The representation is minimal in the sense that another representation could not be obtained by replacing the domain of the former by its proper subset. By this approach, the structure itself is uniquely represented by the collection of cuts ordered dually to inclusion. © 2002 Elsevier Science B.V. All rights reserved.
Keywords: Cut sets | Fuzzy set | Meet-irreducible | Partially ordered set
Project: Serbian Ministry of Science and Technology, Grant No. 1227

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