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A measure-theoretic axiomatization of fuzzy sets |
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| Authors: | P. Bollmann-Sdorra S.K.M. Wong Y.Y. Yao |
| Affiliation: | Technische Universitat, Berlin, Germany Department of Computer Science, University of Regina, Sask., Canada S4S 0A2 Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ont., Canada P7B 5E1 |
| Abstract: | 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. |
| Keywords: | Axiomatization of fuzzy sets fuzzy component structure fuzzy membership structure fuzzy sets fuzzy system structure measurement theory |
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