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Fuzzy Set Inclusion: Linking Fuzzy Set Methods With Mainstream Technique
Oleh:
Smithson, Michael
Jenis:
Article from Bulletin/Magazine
Dalam koleksi:
Sociological Methods and Research vol. 33 no. 04 (May 2005)
,
page 431.
Topik:
Fuzzy Set theory
;
data analysis
;
set inclusion
;
comulative distribution function
Isi artikel
The concept of set inclusion has remainded inssuficiently developed in the fuzzy set literature to be of much use to social scientists. However, a Fully fledget 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 anout measurements levels. It established 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.
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