Categorization Generated by Extended Prototypes - An Axiomatic Approach

Journal of Mathematical Psychology Vol. 51 pp. 14-28, 2007

Posted: 25 Jun 2008

See all articles by Yaron Azrieli

Yaron Azrieli

Ohio State University (OSU) - Economics

Ehud Lehrer

Tel Aviv University - School of Mathematical Sciences

Abstract

We suggest a model of categorization based on prototypes. A set of entities, identified with some finite dimensional Euclidian space, is partitioned into a finite number of categories. Such a categorization is said to be generated by extended prototypes if there is a set of distinguished entities, one for each category, such that the categorization is determined by proximity to these prototypical entities. The prototypes are called extended since they are described by points in a higher dimensional space than the entities. Sufficient conditions for a categorization to be generated by extended prototypes are provided. These conditions are also necessary if the prototypes are in general position.

Keywords: Categorization, Prototypes, Conceptual spaces, Prototype-oriented decision making

Suggested Citation

Azrieli, Yaron and Lehrer, Ehud, Categorization Generated by Extended Prototypes - An Axiomatic Approach. Journal of Mathematical Psychology Vol. 51 pp. 14-28, 2007, Available at SSRN: https://ssrn.com/abstract=1148206

Yaron Azrieli (Contact Author)

Ohio State University (OSU) - Economics ( email )

Columbus, OH 43210-1172
United States

Ehud Lehrer

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

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