Computing the Centroid of a General Type-2 Fuzzy Set by Means of the Centroid-Flow Algorithm

Authors:
Daoyuan Zhai;J. M. Mendel
Affiliations:
Ming Hsieh Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2011

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Abstract

Previous studies have shown that the centroid of a general type-2 fuzzy set (T2 FS) Ã 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 Ã 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.