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Computing the centroid of a general type-2 fuzzy set by means of the centroid-flow algorithm

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2 Author(s)
Daoyuan Zhai ; Ming Hsieh Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA ; Mendel, J.M.

Previous studies have shown that the centroid of a general type-2 fuzzy set (T2 FS) à can be obtained by taking the union of the centroids of all the α-planes (each raised to level α) of Ã. Karnik-Mendel (KM) or the enhanced KM (EKM) algorithms are used to compute the centroid of each α-plane. The iterative features in KM/EKM algorithms can be time-consuming, especially when the algorithms have to be repeated for many α-planes. This paper proposes a new method named centroid-flow (CF) algorithm to compute the centroid of à without having to apply KM/EKM algorithms for every α-plane. Extensive simulations have shown that the CF algorithm can reduce the computation time by 75%-80 % and 50% -75%, compared with KM and EKM algorithms, respectively, and still maintains satisfactory computation accuracy for various T2 FSs when the primary variable x and α -plane are discretized finely enough.

Published in:

Fuzzy Systems, IEEE Transactions on  (Volume:19 ,  Issue: 3 )