Kernel shapes of fuzzy sets in fuzzy systems for function approximation
Information Sciences: an International Journal
Consistent Sobolev regression via fuzzy systems with overlapping concepts
Fuzzy Sets and Systems
Approximation properties of piece-wise parabolic functions fuzzy logic systems
Fuzzy Sets and Systems
Some approximation properties of adaptive fuzzy systems with variable universe of discourse
Information Sciences: an International Journal
Analysis and design of time-variant fuzzy systems based on dynamic fuzzy inference
Computers & Mathematics with Applications
Fuzzy hyperbolic neural network with time-varying delays
Fuzzy Sets and Systems
A robust fault-tolerant control strategy for networked control systems
Journal of Network and Computer Applications
Center-of-gravity fuzzy systems based on normal fuzzy implications
Computers & Mathematics with Applications
Adaptive fuzzy approach to function approximation with PSO and RLSE
Expert Systems with Applications: An International Journal
Universal fuzzy controllers based on generalized T--S fuzzy models
Fuzzy Sets and Systems
Information Sciences: an International Journal
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In this paper, the approximation problem of SISO fuzzy systems is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basic functions (FBF's), we first give a systematic and detailed analysis of FBF's and present five properties of FBF's: structure similarity and compatibility between the membership functions and FBF's, complementarity and less fuzziness of FBF's, and composition of fuzzy systems. These properties provide a clear picture of the shape and features of FBF's. Based on these properties of FBF's, we obtain some basic approximation properties of fuzzy systems: basic approximation property, uniform approximation property, uniform convergent property and universal approximation property. These results reveal the basic approximation mechanism of fuzzy systems and verify a few basic ideas in the design of fuzzy systems