On the semilattice of weak orders of a set
type: Item
instance of: scholarly article
title: On the semilattice of weak orders of a set
zbMATH Open document ID: 0554.90002
DOI: 10.1016/0165-4896(84)90098-2
published in: Mathematical Social Sciences
publication date: 1984-01-01T00:00:00Z
review text: A weak order on a set X is a binary relation P that is reflexive, transitive and total in that for x,y\(\in X\), xPy or yPx. Order theoretic and combinatorial properties of the semilattice of weak orders on a set are developed. In the case of a finite set, an order theoretic characterization of this semilattice is obtained. Though it is not specifically mentioned in the paper, it follows from property (F2) on p. 234, that the semilattice of weak orders on a finite set X is isomorphic to the semilattice of chains from \(\emptyset\) to X in the power set of X.
Mathematics Subject Classification ID: 91B08
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 06E10
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 3883874
zbMATH Keywords: residuated mapping
zbMATH Keywords: preference relation
zbMATH Keywords: weak order
zbMATH Keywords: binary relation
zbMATH Keywords: semilattice
author: Melvin F. Janowitz
MaRDI profile type: Publication
full work available at URL: 0165-4896(84)90098-2
OpenAlex ID: W2070442029
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description: scientific article; zbMATH DE number 3883874