Equality relations as a basis for fuzzy control. (English) Zbl 0785.93059

Summary: The aim of this paper is to introduce a fuzzy control model with well- founded semantics in order to explain the concepts applied in fuzzy control. Assuming that the domains of the input and output variables for the process are endowed with equality relations, that reflect the indistinguishability of values lying closely together, the use of triangular and trapezoidal membership functions can be justified and max- \(\sqcap\) inference where \(\sqcap\) is a \(t\)-norm turns out to be a consequence of our model. Distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like MOM or COA are appropriate or lead to undesired results.


93C42 Fuzzy control/observation systems
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