Page 310 - Electrical Engineering Dictionary

fuzzy H-infinity control H-infinity con- fuzzy inference a fuzzy logic principle of
trol involving fuzzy logic concepts or fuzzy combining fuzzy IF-THEN rules in a fuzzy
control to achieve an H-infinity controller rule base into a mapping from a fuzzy set in
performance index. the input universe of discourse to a fuzzy set
in the output universe of discourse. A typical
fuzzy H-infinity filter an H-infinity filter example is a composition inference.
involving fuzzy logic concepts or a fuzzy fil-
ter to achieve an H-infinity filter performance fuzzy inference engine a device or com-
index. ponent carrying out the operation of fuzzy in-
ference, that is, combining fuzzy IF-THEN
fuzzy hierarchical systems fuzzy sys-
rules in a fuzzy rule base into a mapping
tems of hierarchical structures. A typical
from a fuzzy set in the input universe of dis-
example is a two-level fuzzy system with
course to a fuzzy set in the output universe of
a higher level of fuzzy inference rules and
discourse. See also approximate reasoning,
lower level of analytical linear models.
fuzzy inference system, fuzzy rule.
fuzzy identification a process of deter-
fuzzy inference system a computing
mining a fuzzy system or a fuzzy model. A
framework based on fuzzy set theory, fuzzy
typical example is identification of fuzzy dy-
IF-THEN rules, and approximate reasoning.
namic models consisting of determination of
There are two principal types of fuzzy infer-
the number of fuzzy space partitions, deter-
ence systems:
mination of membership functions, and de-
termination of parameters of local dynamic 1. Fuzzy inference systems mapping
models. fuzzy sets into fuzzy sets (pure fuzzy infer-
ence systems) that are composed of a knowl-
fuzzy IF-THEN rule rule of the form edge base containing the definitions of the
fuzzy sets and the database of fuzzy rules
IF x is A THEN y is B
provided by experts; and a fuzzy inference
where A and B are linguistic values defined engine that performs the fuzzy inferences.
by fuzzy sets on universe of discourse X and 2. Fuzzy inference systems performing
Y respectively (abbreviated as A −→ B). non-linearmappingfromcrisp(nonfuzzy)in-
The statement “x is A” is called the an- put data to crisp (nonfuzzy) output data. In
tecedent or premise, while “y is B” is called the case of a Mamdani fuzzy system, in ad-
the consequence or conclusion. A fuzzy IF- dition to a knowledge base and a fuzzy in-
THEN rule can be defined as a binary fuzzy ference engine, there is a fuzzifier that rep-
relation. The most common definition of a resents real-valued inputs as fuzzy sets, and
fuzzy rule A −→ B is as A coupled with B, a defuzzifier that transforms the output set to
i.e., a real value. In the case of a Sugeno fuzzy
R = A −→ B = A × B, system, special fuzzy rules are used, giving a
crisp (nonfuzzy) conclusion, and the output
or of the system is given by the sum of those
crisp conclusions, weighted on the activation
µ A×B (x, y) = µ A (x)?µ B (y) ,
of the premises of rules. Some fuzzy sys-
tems of this type hold the universal function
where ? is a triangular norm.
approximation property.
Seealsofuzzyrelation, fuzzyset, linguistic
variable, triangular norm. See also defuzzifier, fuzzifier, fuzzy
set, fuzzy IF-THEN rule, fuzzy reasoning,
fuzzy implication See fuzzy IF-THEN Sugeno fuzzy rule, universal function appro-
rule. ximation property.

c
2000 by CRC Press LLC