A new type of fuzzy logic system for adaptive modelling and control
We present a new type of fuzzy controller constructed with the B-spline model and its applications in modelling and control. Unlike the other normalised parameterised set functions for defining fuzzy sets, B-spline basis functions do not necessarily span from membership value 0 to 1, but possess the property “partition of unity”. These B-spline basis functions are automatically determined after the input space is partitioned. By using “product” as fuzzy conjunction, “centroid” as defuzzification, “fuzzy singletons” for modelling output variables and adding marginal linguistic terms, fuzzy controllers can be constructed which have advantages like smoothness, automatic design and intuitive interpretation of controller parameters. Furthermore, both theoretical analysis and experimental results show the rapid convergence for tasks of data approximation and unsupervised learning with this type of fuzzy controller.
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