Computational Intelligence

De veloping a Fuzzy Controller 311

some or all of these same input variables are used in the fuzzy antecedents of the

rules. As deve loped by Takagi, Sugeno, and Kang, the function is affine (the output

is a linear plus a constant function of the inputs), but the method has been extended

to nonlinear functions.

The general form of a fuzzy rule in a TSK model, then, is

If x

1

is S

1

and , . . ., and x

k

is S

k

then y = u(x

1

,...,x

k

) = a

0

+ a

1

x

1

+ a

2

x

2

+ ···+ a

k

x

k

(7.6)

where y is the consequent (output) variable whose value is inferred, each x

i

is an

input variable (an antecedent) that may also appear in the consequent part of the

rule, each S

i

is a fuzzy set represented ...