A measure-theoretic axiomatization of fuzzy sets

Using measurement theory, this paper examines three empirical structures that underlie the representation of fuzzy sets: the fuzzy membership structure, the fuzzy component structure, and the fuzzy system structure. These qualitative structures justify the use of the standard min-max system to repre...

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Bibliographic Details
Published in:Fuzzy sets and systems 1993-12, Vol.60 (3), p.295-307
Main Authors: Bollmann-Sdorra, P., Wong, S.K.M., Yao, Y.Y.
Format: Article
Language:English
Subjects:
Axiomatization of fuzzy sets
Exact sciences and technology
fuzzy component structure
fuzzy membership structure
fuzzy sets
fuzzy system structure
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
measurement theory
Sciences and techniques of general use
Set theory
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Summary:Using measurement theory, this paper examines three empirical structures that underlie the representation of fuzzy sets: the fuzzy membership structure, the fuzzy component structure, and the fuzzy system structure. These qualitative structures justify the use of the standard min-max system to represent fuzzy sets. The results of this study facilitate the development of a sound measurement-theoretic axiomatization of fuzzy systems.
ISSN:0165-0114
1872-6801
DOI:10.1016/0165-0114(93)90440-S