Partitions and fuzziness
type: Item
instance of: scholarly article
title: Partitions and fuzziness
zbMATH Open document ID: 0595.94028
DOI: 10.1016/0022-247X(86)90049-1
author: Bernadette Bouchon
author: Gérard Cohen
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: This paper presents properties of classical or generalized partitions. First of all, fuzzy binary relations are defined on a finite set, satisfying an extension of the transitivity property and associated with a distance. Characterizations of such relations by matricial properties are given. Partitions are then constructed by means of cliques and spheres associated with the corresponding distance. The case of fuzzy partitions is specially investigated, quasi-partitions are connected with ultrametricity properties. The gain of information resulting from the replacement of a given fuzzy partition by another one is presented, with respect to a given threshold, and it provides a good tool to choose a fuzzy partition in a family or to improve a given classification of the studied population, for example.
Mathematics Subject Classification ID: 94D05
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 05B40
Mathematics Subject Classification ID: 03E20
zbMATH DE Number: 3959295
zbMATH Keywords: fuzzy relations
zbMATH Keywords: fuzzy binary relations
zbMATH Keywords: distance
zbMATH Keywords: matricial properties
zbMATH Keywords: cliques
zbMATH Keywords: spheres
zbMATH Keywords: fuzzy partitions
zbMATH Keywords: quasi-partitions
zbMATH Keywords: ultrametricity properties
zbMATH Keywords: gain of information
zbMATH Keywords: classification
MaRDI profile type: Publication
cites work: Fuzzy partitions and relations; an axiomatic basis for clustering
cites work: Q3338121
cites work: Q3748967
cites work: Q4749834
cites work: Four fundamental parameters of a code and their combinatorial significance
cites work: q-coverings, codes and line graphs
cites work: Ultrametrics and matrix theory
cites work: Similarity relations and fuzzy orderings
full work available at URL: 0022-247x(86)90049-1
OpenAlex ID: W2025953262
description: scientific article; zbMATH DE number 3959295