Fuzzy Logic Approach - Computational Intelligence in Time Series Forecasting - page 163

1

THEN

1 1

x "

1

x

y

TT T 0 1 n

TS 1 n

R 2 : IF x 1 is G 2

1 and ..... and x n is G 2 n

2

THEN y

2 2

x "

2

x

TT T

0 1 n

TS 1 n

: : : : :

R M : IF x 1 is G M

1 and ..... and x n is G M n

M

THEN y

MM

x "

M
n

x

TT T

0 1

TS 1 n

Therefore, for a given set of inputs the corresponding Takagi-Sugeno inference
will be

M

l l

E y

¦

11 2 2 MM

E y E y " E y

Ts

Ts Ts Ts

y

l 1

(4.7)

0

M

1 2 M

EE " E

l

E

¦

l 1

l

E is the degree of fulfilment or firing strength of the l th rule, which is
computed for the n -(multiple) input system using the product operator as

where

n

l

E P P u P u u " P . (4.8)

– x x x x

l l l l

G

i

G

1

G

2

G

n

i 1

i 1 2 n

Therefore,

11 2 2 MM

y J y J y " J y , (4.9)

0 TS TS TS

where the normalized degree of fulfilment for l th rule is

l l

E E

l

J , (4.10)

M

1 2 M

"

E E E

l

¦ E

l 1

or the corresponding Takagi-Sugeno inference for s th training sample will be

1

y J TT

1 1

x "

1

x

T 0 1 n

0 s s 1_ s ns _

2

2 2 2

(4.11)

J TT x " x ......

T

0 1 n

s 1_ s n _ s

M MM M

n

J x " x .

TT T

0 1

s 1_ s n _ s

Now, by appending 1 along with n inputs in XIe s , which takes care of

T from the

0

rule consequent, the s th extended training sample is given as (4.12)