Title :
Cardinality, Fuzziness, Variance and Skewness of Interval Type-2 Fuzzy Sets
Author :
Mendel, Jerry M. ; Wu, Dongrui
Author_Institution :
Ming Hsieh Dept. of Electr. Eng., Southern California Univ., Los Angeles, CA
Abstract :
Centroid, cardinality, fuzziness, variance and skewness are all important concepts for an interval type-2 fuzzy set (IT2 FS) because they are all measures of uncertainty, i.e. each of them is an interval, and the length of the interval is an indicator of the uncertainty. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use the Mendel-John representation theorem for IT2 FSs. Formulas for computing the cardinality, fuzziness, variance and skewness of an IT2 FS are derived. Unlike the formulas for the centroid of an IT2 FS, which must be computed by iterative Karnik-Mendel algorithms, these new formulas have closed-form expressions, so they can be computed very fast. These definitions are useful not only for measuring the uncertainties of an IT2 FS, but also in measuring the similarity between two IT2 FSs
Keywords :
fuzzy set theory; geometry; iterative methods; Mendel-John representation theorem; cardinality computing; centroid computing; fuzziness computing; interval type-2 fuzzy sets; iterative Karnik-Mendel algorithms; skewness computing; variance computing; Bismuth; Closed-form solution; Computational intelligence; Frequency selective surfaces; Fuzzy set theory; Fuzzy sets; Iterative algorithms; Length measurement; Measurement uncertainty; Particle measurements;
Conference_Titel :
Foundations of Computational Intelligence, 2007. FOCI 2007. IEEE Symposium on
Conference_Location :
Honolulu, HI
Print_ISBN :
1-4244-0703-6
DOI :
10.1109/FOCI.2007.371499
