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

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Furthermore, the membership degrees of the borderline cases will naturally lie between 0 and 1. In other words, the more an element or object is characteristic of F, the closer to 1 is its degree of membership. Thus, the use of a numerical scale, as the interval [0,1], allows for a convenient representation of the gradation of membership. However, three things should be made clear here. First, precise membership' degrees do not exist by themselves, but are only tendency indices that are subjectively assigned by an individual or a group of individuals.

In DECS the KBS is used in a closed loop, thus replacing completely the conventional control element. 3 Knowledge Based Controllers 19 Plant DECS Fig. 2. The structure of a DECS. change-of-error, etc. The need for such a KBS is motivated if the nature of the process under control is such that appropriate analytic models do not exist or are inadequate, but the process operator can manually control the process to a satisfactory degree. The scope of the KBS can be anywhere between single-loop and plant-wide operation.

4 Knowledge Representation in KBCs 25 y~~--------------------------- Y~~--r-----~~~--------~~ time Overshoot, no undershoot time Too low monotone y~~--------------------------- Too low oscillatory time y ~ ~-t'-----T------r------"~---T Overshoot, undershoot Y~~--~--------------------- Overshoot monotone time Ysp ~--T-------------- time Overshoot oscillatory time y~~--~~----------~~------- No overshoot, undershoot time Over safety limit Y~~--------~====----------- No overshoot, no undershoot time Fig.

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