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Psychometrika

, Volume 51, Issue 2, pp 209–240 | Cite as

Differential ordering of objects and attributes

  • J. P. Sutcliffe
Article

Abstract

By reference to nominated attributes, a genus, being a population of objects of one specified kind, may be partitioned into species, being subpopulations of different kinds. A prototype is an object representative of its species within the genus. Using this framework, the paper describes how objects can be relatively differentiated with respect to attributes, and how attributes can be relatively differentiating with respect to objects. Methods and rationale for such differential ordering of objects and attributes are presented by example, formal development, and application.

For a genus Θ comprisingn species of object there is a subsetP ofn distinct prototypes. With respect tom nominated attributes, each object in Θ has anm-element characterization. Together these determine ann ×m objects × attributes matrix, the rows of which are the characterizations of the prototypical objects. Over then species in Θ, an associated relative frequency vector gives the distribution of objects (and of their characterizations). The matrix and vector associate the objects in Θ with points in a metric space (P, δ); and it is with respect to various sums of distances in this attribute space that one can differentially order objects and attributes.

The definition of the distance functionδ is generalized across kinds of difference, types of characterization, scale-types of measurement, Minkowskiindex ≧ 1, and any form of distribution of objects over species. Explanatory and taxonomic applications in psychology and other fields are discussed, with focus on classification, identification, recognition, and search. The Braille code and the identification of its characters provide illustration.

Key words

numerical taxonomy information storage and retrieval classification identification recognition search genus species prototype object x attribute matrix datum Minkowski metric distance similarity differentiation distinguishing feature tree key Braille 

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Copyright information

© The Psychometric Society 1986

Authors and Affiliations

  • J. P. Sutcliffe
    • 1
  1. 1.Department of PsychologyUniversity of SydneySydneyAustralia

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