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Unlike the Mamdani and TS fuzzy systems, a Boolean fuzzy system, type-1 or type-2, employs a fuzzy implication to interpret its rules. There exist three families of type-2 fuzzy implications-R-implication, S-implication and QL-implication. In this paper, using the same technique that we developed previously [22, 23], we constructively prove that all the interval type-2 Boolean fuzzy systems, regardless...
Whether a rule-based fuzzy system has the ability to approximate any multivariate continuous function arbitrarily well is an important issue, especially for fuzzy control and fuzzy modeling. The answer to this issue concerning various Mamdani and Takagi-Sugeno (TS) fuzzy systems employing type-1 fuzzy sets is affirmative and well documented in the literature. As for type-2 (T2) fuzzy systems, the...
Fuzzy systems using type-2 fuzzy sets and fuzzy logic are important and are indeed gaining increasing attention in the literature (e.g., type-2 fuzzy controllers and fuzzy models). A fundamental question is whether a type-2 fuzzy system is a universal approximator in that it is capable of uniformly approximating any real continuous function on a compact domain to any degree of accuracy. Up to date,...
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