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.