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Fuzzy controller: Further limit theorems for linear control rules. (English) Zbl 0719.93059
It is shown that for any type of unimodal fuzzy numbers used to define the linguistic variable in the fuzzy control rules, for any type of fuzzy logic used to evaluate the fuzzy control rules, and for any reasonable defuzzifier, a defuzzified output approaches a linear function of all the inputs as the number of rules grow, if this output is a linear function of the cells in the fuzzy control table. This result is a type of central limit theorem for the fuzzy controller.
Reviewer: J.Sustal (Cottbus)

MSC:
93C42 Fuzzy control/observation systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
03E72 Theory of fuzzy sets, etc.
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[1] Buckley, J.J.; Ying, H., Fuzzy controller theory: limit theorems for linear fuzzy control rules, Automatica, 25, 469-472, (1989) · Zbl 0685.93003
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