Research Article

A Proposal to Speed up the Computation of the Centroid of an Interval Type-2 Fuzzy Set

Table 2

KMA2 algorithm flow.

KMA2

The KM algorithm for finding the minimum extreme point of the centroid of an interval type-2 fuzzy set over with upper membership function and lower membership function can
be restated as follows:
The KM algorithm for finding the maximum extreme point of the centroid of an interval type-2 fuzzy set over xi with upper membership function and lower membership function can be reexpressed as follows:

Sort in ascending order and call the sorted by the same name, but now . Match the weights with their respective and renumber them so that their index corresponds to the renumbered .
Precomputation:
       (43)
       (44)
     (45)
     (46)
with .
       (47)
.        (48)
Set Set
(49) (56)
Find so thatFind so that
(50) (57)
(51) (58)
.(52) . (59)
Find such that Find such that
. .
If , stop and set , else continue. If , stop and set , else continue.
Set Set
(53) (60)
(54) (61)
. (55) . (62)
Set , and go to step 4. Set , and go to step 4.