Transparent Fuzzy/Neuro-fuzzy Modelling - Computational Intelligence in Time Series Forecasting - page 286

Algorithm 7.1. Algorithm of iterative merging

Given a rule base ^

`

" with l th rule as R l : If x 1 is G l 1 and, ..., and x n
is G l n then y l = f ( x 1 , ..., x n ), where G l i , with inputs i = 1, 2,..., n , are fuzzy sets with
membership functions

l
RRl 1, 2, , M . ,

>@

P :

x

o 0,1 , select three thresholds OJK . ,, 0,1

l
G i

Repeat for inputs i =1, 2, ..., n

Step 1 : Selection of the most similar fuzzy sets

- ½

° °

, pq

L l

S

l

,

m

S GGGG

®

max GG

¾

i i i i i i

°

pq
pq

z

°

¯ ¿

, 1,..., M

Step 2 : Merging of Selected fuzzy sets

If S GG

l

,

m

! O ,

l

,

m L

:

GG G

i i i i i

C L l L l C

Merge ( , , t

G G G G G G i i i i i i

Until : S GG O

l

,

m

.

i i

Step 3 : Removal of fuzzy sets similar to universal set
for i = 1, 2, ...., n
for l = 1, 2, ..., M

SU

l

,

l

U

l

* U ,

G G G i i i

i i i

If

remove G l i from the antecedent of rule R l .

SU

l
i

, ! J ,

G

i

end
end
where 1,

P x x .

i Ui

i

Step 4 : Removal of redundant inputs
for j = 1, 2, ...., n-1
for k = 1, 2, ....., n
S jk = min l S

GG "

l

,

l

, l , , , M ;

j k

If S ! remove x j from the premise. ,

jk

end
end

Step 5 : Merging of rules with equal premise parts
for l = 1, 2, ...., M-1
for m = 1, 2, ...., M
if Merge ( R l , R m ).

l m

, i ,

GG i i

end
end

Step 6 : Re-estimation of TS rule consequents by LSE method