Fuzzy posets on sets
type: Item
instance of: scholarly article
title: Fuzzy posets on sets
zbMATH Open document ID: 0968.03061
DOI: 10.1016/S0165-0114(98)00249-8
author: J. Neggers
author: Hee Sik Kim
published in: Fuzzy Sets and Systems
publication date: 2001-09-11T00:00:00Z
review text: The principal notions introduced and studied in this paper are the notions of fuzzy posets and fuzzy dimensions (for a special class of fuzzy posets). A set \(X\) equipped with functions \(L\), \(G\), \(P\) (``less than'', ``greater than'' respectively ``parallel'', or incompatibility functions) defined on \(X\times X\) and having \([0,1]\) as value set, satisfying the condition \(L+G+P=1\), is called a fuzzy poset. Several standard theorems for posets are proved in the setting of fuzzy posets. Furthermore, using a rounding-off procedure, the skeleton of a fuzzy poset is defined, and results on the behaviour of deformations of skeletons of fuzzy posets as it relates to the structure of these fuzzy posets are proved. The fuzzy dimension is defined as the intersection of the least number of fuzzy chains which yield the fuzzy poset. It is clear that it is possible to arrive in this manner at a reasonable theory of fuzzy posets.
reviewed by: I. Tofan
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 1563543
zbMATH Keywords: fuzzy poset
zbMATH Keywords: fuzzy dimension
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1563543