A Consistency Criterion for Optimizing Defuzzification in Fuzzy Control

An Overview of Fuzzy Control Theory

“…As we have seen in [85], the Consistency Criterion 5.1.10 is not fulfilled; the third example will learn us that this can never be the case when we consider the identity mapping between the same rule bases. Notice also that it is impossible to drive the output to its full potential of 100% output range.…”

“…Also, in that case we are considering fuzzy real numbers, which means that all theory developed for the treatment of the fuzzy real line can be used. We have included in the bibliography a number of references dealing with the implementation of a structure on the fuzzy real line; especially the work of D. Dubois In [85] and [86] we have been working on two new criteria, only applicable on compact subsets X ⊆ R or subsets thereof, which nevertheless seem to be important. Suppose a controller is given by a rule base consisting of a finite number of fuzzy variables A = {α 1 , ..., α n } ⊆ F(X).…”

“…As mentioned in [69], when we consider a single-input, single-output controller, we can control the shape of the surface to a certain extent by manipulating the membership functions. In [85] and [86], we studied the behavior of the identity mapping between two fuzzy antecedent rule bases, and whether or not it yields an identity mapping between the input before fuzzification and the output after defuzzification. We found that this was not the case.…”