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New results about the centroid of an interval type-2 fuzzy set, including the centroid of a fuzzy granule |
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| Authors: | Jerry M Mendel Hongwei Wu |
| Affiliation: | a Signal and Image Processing Institute, Department of Electrical Engineering, University of Southern California, 3740 McClintock Avenue, Los Angeles, CA 90089-2564, United States b Computational Biology Institute, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States c Computational Systems Biology Laboratory, Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA 30602, United States |
| Abstract: | The centroid of an interval type-2 fuzzy set (IT2 FS) provides a measure of the uncertainty of such a FS. Its calculation is very widely used in interval type-2 fuzzy logic systems. In this paper, we present properties about the centroid of an IT2 FS. We also illustrate many of the general results for a T2 fuzzy granule (FG) in order to develop some understanding about the uncertainty of the FG in terms of its vertical and horizontal dimensions. At present, the T2 FG is the only IT2 FS for which it is possible to obtain closed-form formulas for the centroid, and those formulas are in this paper. |
| Keywords: | Centroid Centroid properties Interval type-2 fuzzy set Type-2 fuzzy set Fuzzy granule |
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