On an independence condition for consensus \(n\)-trees
type: Item
instance of: scholarly article
title: On an independence condition for consensus \(n\)-trees
zbMATH Open document ID: 0709.90008
DOI: 10.1016/0893-9659(89)90121-3
author: J. P. Barthélemy
author: F. R. McMorris
published in: Applied Mathematics Letters
publication date: 1989-01-01T00:00:00Z
review text: Methods for the aggregation of several tree-structured data into a single ``consensus'' tree are being extensively studied, especially in the field of numerical taxonomy where comparing and constructing trees of various types are everyday activities. A typical example is when several tree construction algorithms, e.g., clustering algorithms, operating on the same data set produce different trees, and it is desired to try to capture the agreement of all these trees by forming a consensus tree. In addition to the actual construction of consensus functions, there have been theorems modeled after Arrow's Impossibility Theorem that show the inconsistency of some reasonably looking axioms. In this note we outline the proof of such a theorem for n-trees (which are a type of hierarchical classification) hereby settling an open problem of \textit{D. A. Neumann} [Math. Biosci. 63, 271--289 (1983; Zbl 0539.62073)].
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91C15
Mathematics Subject Classification ID: 91C20
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 4167787
zbMATH Keywords: independence condition
zbMATH Keywords: aggregation of several tree-structured data
zbMATH Keywords: consensus tree
zbMATH Keywords: hierarchical classification
MaRDI profile type: Publication
full work available at URL: 0893-9659(89)90121-3
OpenAlex ID: W2030540566
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description: scientific article; zbMATH DE number 4167787