Quotients with respect to similarity relations
type: Item
instance of: scholarly article
title: Quotients with respect to similarity relations
zbMATH Open document ID: 0666.18002
DOI: 10.1016/0165-0114(88)90080-2
author: Ulrich Höhle
published in: Fuzzy Sets and Systems
publication date: 1988-01-01T00:00:00Z
review text: The problem of the quotient w.r.t. a similarity relation is closely related to Poincaré's paradox and central problems in cluster analysis. Amazingly this problem remains open for more than 30 years. As a generalization of strong M-categories we introduce the concept of M- valued sets, which leads to the definition of the category M-SET. In M- SET we give a complete solution of the quotient problem.
Mathematics Subject Classification ID: 18B10
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 18D15
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 94D05
Mathematics Subject Classification ID: 03C90
zbMATH DE Number: 4089770
zbMATH Keywords: partition trees
zbMATH Keywords: local equalities
zbMATH Keywords: integral cl-monoids
zbMATH Keywords: vague equivalence
zbMATH Keywords: similarity relation
zbMATH Keywords: Poincaré's paradox
zbMATH Keywords: cluster analysis
zbMATH Keywords: strong M-categories
zbMATH Keywords: M-valued sets
zbMATH Keywords: category M-SET
zbMATH Keywords: quotient problem
MaRDI profile type: Publication
full work available at URL: 0165-0114(88)90080-2
OpenAlex ID: W2000594950
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description: scientific article; zbMATH DE number 4089770