An Introduction to Fuzzy Control by Prof. Dr. Dimiter Driankov, Dr. Hans Hellendoorn, Dr.

By Prof. Dr. Dimiter Driankov, Dr. Hans Hellendoorn, Dr. Michael Reinfrank (auth.)

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The set R = {red, orange, yellow, green, blue} is an example of a finite set that is described by its elements. h. , the set of positive integers, is an example of a countable set that is described by a property. c. The real interval [0,1] is an example of an uncountable set. Two sets are very important, namely, the universe U, containing all elements of the universe of discourse, and the empty set 0, containing no elements at all. They complement each other. , equality is defined extensionally.

This is a frequently used standard domain. If the domain used is the real interval [-1,1], then we have the so-called nor- :1 ,. ,. ,m hot 15 16 17 18 19 20 21 22 23 24 25 26 Fig. 5. The whole domain. 1 Introduction: Fuzzy Sets 49 malized domain (Chapter 4). However, we will use the notion of normalized domain to refer to both normalized and standard domains. Furthermore, it is usual to have functions with straight lines, instead of functions with curves as were given in the temperature domain.

Long delay monotone 8. long delay oscillatory. The description of the open-loop process as a "short", "medium", or "long" delay is done on the basis of the ratio of the pure time delay in the process and the dominant time constant. 4 Knowledge Representation in KBCs 23 y spr---------------~=_-------- No delay monotone No delay oscillatory ysp time Medium delay monotone time Medium delay oscillatory time t--------=======--- Short delay monotone Short delay oscillatory time time Long delay monotone Long delay oscillatory Fig.

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