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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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References

Attneave, F. Dimensions of similarity. Amer. J. Psychol., 1950, 63, 516–556.CrossRefGoogle ScholarPubMed
Burke, C. J. Some problems in discrimination models. Amer. Psychologist, 1956, 11, 483–483.Google Scholar
Bush, R. R. and Mosteller, F.. A model for stimulus generalization and discrimination. Psychol. Rev., 1951, 58, 413–423.CrossRefGoogle Scholar
Galanter, E. H. An axiomatic and experimental study of sensory order and measure. Psychol. Rev., 1956, 63, 16–28.CrossRefGoogle ScholarPubMed
Hays, W. L. An approach to the study of trait implication and trait similarity. In Tagiuri, R., Petrullo, L. (Eds.), Person perception and interpersonal behavior, Stanford: Stanford Univ. Press, 1958.Google Scholar
Landahl, H. D. Neural mechanisms for the concepts of difference and similarity. Bull. math. Biophysics, 1945, 7, 83–88.CrossRefGoogle Scholar
Munroe, M. E. Introduction to measure and integration, Cambridge, Mass.: Addison Wesley, 1953.Google Scholar
Restle, F. A theory of discrimination. Unpublished doctoral dissertation, Stanford Univ., 1953.Google Scholar