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Fuzzy Set Inclusion

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  • Michael Smithson

    (Australian National University, Canberra)

Abstract

The concept of set inclusion has remained insufficiently developed in the fuzzy set literature to be of much use to social scientists. However, a fully fledged concept of fuzzy set inclusion, along with appropriate statistical methods for evaluating it, could be very useful in the social sciences. This article combines fuzzy set and statistical methods, in the form of a cumulative distribution-based approach to evaluating fuzzy set inclusion without making strong assumptions about measurement levels. It establishes criteria for distinguishing an “inclusion relation†from independence plus skew as well as from other kinds of relationships. A measure of inclusion is developed that is sensitive to the degree to which individual cases violate a strict inclusion rule. A technique for modeling localized inclusion relations in contingency tables and scatter plots is also presented. Finally, the connections between the fuzzy set approach to set inclusion and mainstream statistical techniques are briefly adumbrated.

Suggested Citation

  • Michael Smithson, 2005. "Fuzzy Set Inclusion," Sociological Methods & Research, , vol. 33(4), pages 431-461, May.
    • Handle: RePEc:sae:somere:v:33:y:2005:i:4:p:431-461
    DOI: 10.1177/0049124105274497
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    References listed on IDEAS

    as
    1. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    2. repec:ucp:bkecon:9780226702766 is not listed on IDEAS
    3. Ragin, Charles C., 2000. "Fuzzy-Set Social Science," University of Chicago Press Economics Books, University of Chicago Press, edition 1, number 9780226702773, August.
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