On the (numerical) ranking associated with any finite binary relation

Michel Regenwetter; Elena Rykhlevskaia

doi:10.1016/j.jmp.2004.03.003

On the (numerical) ranking associated with any finite binary relation

Research output: Contribution to journal › Article › peer-review

Abstract

We generalize the concept of a 'ranking associated with a linear order' from linear orders to arbitrary finite binary relations. Using the concept of differential of an object in a binary relation as theoretical primitive, we axiomatically introduce several measurement scales, some of which include the generalized ranking as a special case. We provide a computational formula for this generalized ranking, discuss its many elegant properties and offer some illustrating examples.

Original language	English (US)
Pages (from-to)	239-246
Number of pages	8
Journal	Journal of Mathematical Psychology
Volume	48
Issue number	4
DOIs	https://doi.org/10.1016/j.jmp.2004.03.003
State	Published - Aug 2004

Keywords

Binary relation
Digraph
Order
Rank position
Ranking
Scale

ASJC Scopus subject areas

General Psychology
Applied Mathematics

Online availability

10.1016/j.jmp.2004.03.003

Library availability

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title = "On the (numerical) ranking associated with any finite binary relation",

abstract = "We generalize the concept of a 'ranking associated with a linear order' from linear orders to arbitrary finite binary relations. Using the concept of differential of an object in a binary relation as theoretical primitive, we axiomatically introduce several measurement scales, some of which include the generalized ranking as a special case. We provide a computational formula for this generalized ranking, discuss its many elegant properties and offer some illustrating examples.",

keywords = "Binary relation, Digraph, Order, Rank position, Ranking, Scale",

author = "Michel Regenwetter and Elena Rykhlevskaia",

note = "Funding Information: We thank the National Science Foundation for partially funding this research through NSF Grant SBR 97-30076 to Regenwetter and the University of Illinois Research Board for funding our collaboration. We are indebted to John Boyd, Bill Batchelder, Peter Fishburn, Tony Marley, Sasa Peke{\v c} and Don Saari for helpful pointers and comments on various aspects of this work. We are also grateful to the action editor and two referees for their helpful feedback.",

year = "2004",

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AU - Regenwetter, Michel

AU - Rykhlevskaia, Elena

N1 - Funding Information: We thank the National Science Foundation for partially funding this research through NSF Grant SBR 97-30076 to Regenwetter and the University of Illinois Research Board for funding our collaboration. We are indebted to John Boyd, Bill Batchelder, Peter Fishburn, Tony Marley, Sasa Pekeč and Don Saari for helpful pointers and comments on various aspects of this work. We are also grateful to the action editor and two referees for their helpful feedback.

PY - 2004/8

Y1 - 2004/8

N2 - We generalize the concept of a 'ranking associated with a linear order' from linear orders to arbitrary finite binary relations. Using the concept of differential of an object in a binary relation as theoretical primitive, we axiomatically introduce several measurement scales, some of which include the generalized ranking as a special case. We provide a computational formula for this generalized ranking, discuss its many elegant properties and offer some illustrating examples.

AB - We generalize the concept of a 'ranking associated with a linear order' from linear orders to arbitrary finite binary relations. Using the concept of differential of an object in a binary relation as theoretical primitive, we axiomatically introduce several measurement scales, some of which include the generalized ranking as a special case. We provide a computational formula for this generalized ranking, discuss its many elegant properties and offer some illustrating examples.

KW - Binary relation

KW - Digraph

KW - Order

KW - Rank position

KW - Ranking

KW - Scale

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JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

IS - 4

ER -

On the (numerical) ranking associated with any finite binary relation

Abstract

Keywords

ASJC Scopus subject areas

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