Title :
Properties of the Centroid of an Interval Type-2 Fuzzy Set, Including the Centroid of a Fuzzy Granule
Author :
Mendel, Jerry M. ; Wu, Hongwei
Author_Institution :
Dept. of Electr. Eng., Southern California Univ., Los Angeles, CA
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 fit is possible to obtain closed-form formulas for the centroid, and those formulas are in this paper
Keywords :
fuzzy logic; fuzzy set theory; fuzzy systems; uncertainty handling; IT2 FS; T2 fuzzy granule; closed-form formulas; fuzzy granule centroid; fuzzy set theory; fuzzy systems; interval type-2 fuzzy set centroid; type-2 fuzzy logic systems; Application specific integrated circuits; Extraterrestrial measurements; Frequency selective surfaces; Fuzzy logic; Fuzzy sets; Fuzzy systems; Image processing; Measurement uncertainty; Signal processing; Upper bound;
Conference_Titel :
Fuzzy Systems, 2005. FUZZ '05. The 14th IEEE International Conference on
Conference_Location :
Reno, NV
Print_ISBN :
0-7803-9159-4
DOI :
10.1109/FUZZY.2005.1452417
