Advances in Fuzzy Systems

Research Article

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

Table 1

IASC2 algorithm flow.
IASC2
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 computed using the following procedure: The maximum extreme point of the centroid of an interval type-2 fuzzy set over with upper membership function and lower membership function can be computed by the following procedure:
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:
    (15)
    (16)
    (17)
    (18)
with .
    (19)
    (20)
Initialization: Initialization:
  (21) (32)
Find so that Find so that  
   
  (22) (33)
  (23) (34)
  (24) (35)
  (25) (36)
  (26) (37)
.   (27) .(38)
Recursion: Recursion:
  (28) (39)
  (29) (40)
  (30) (41)
.  (31) .(42)
If , then , and go to step 4 else and stop. If , then and go to step 4 else and stop.