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A Metric and an Ordering on Sets

Published online by Cambridge University Press:  01 January 2025

Frank Restle
Frank Restle*
Affiliation:
Michigan State University
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Abstract

Beginning with sets of arbitrary elements, concepts of distance and betweenness of sets are defined. Since betweenness as defined is not transitive, an investigation is made of the conditions which ensure desirable regularity. It is found that a straight line or linear array of sets is a generalization of nested sets (Guttman scales). Close relationships among the notions of distance, betweenness, and linear arrays are demonstrated. Parallel and perpendicular arrays, dimensions, and multidimensional spaces are characterized.

Type
Original Paper
Information
Psychometrika , Volume 24 , Issue 3 , September 1959 , pp. 207 - 220
Copyright
Copyright © 1959 The Psychometric Society

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