By Luis Collantes, Rajkumar Roy (auth.), Yukinori Suzuki, Seppo Ovaska DSc, Takeshi Furuhashi D.Eng, Rajkumar Roy PhD, Yasuhiko Dote PhD (eds.)
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Barnett. The ordering of multivariate data. A, Vol. 139, Part 3, p. 318-355, 1976. 2. Bloch, H. Maitre. Fuzzy mathematical morphologies: A comparative study. Pattern Recognition 28 (9), pp. 1341-1387, 1995. 3. Ch. Busch, M. Eberle. Morphological operations for color-coded Images. Proc. EUROGRAPHICS'95, Computer Graphics Forum, Vol. 14, No. 3, pp. C193204, 1995. 4. L. J. Delp. An empirical study of morphological operators in color image enhancement. Proc. SPIE Conf. Image Processing Algorithms and Techniques III, Vol.
In this paper, for the sake of reducing the size of covariance matrix, which will be used for RLS method, a Virtual Higher-Resolution Fuzzy Model (VHR-FM) [4,5] will be used for circumvent this situation. Each cell of the rule-base will be expanded into 2n cells (where n is number of input variables). Therefore, the Ordinary Fuzzy System (0-FS) is now implicitly divided into n TI Ni Separated Local Fuzzy Systems (SLFS) i=l (where Ni is the number of fuzzy subset of input i). Then, the size of the covariance matrix can be reduced significantly.
A fuzzy set A defined in a universe of discourse X is expressed by its membership function IJA: X-+ [0,1] where IJA(x) expresses the extent to which x fulfils the category specified by A: A= { x, pA(x) }, '<:/x eX For an intuitive description of the fuzzy mapping the input and output universes of discourse are divided by fuzzy sets that represents linguistic terms. Based on these linguistic terms, the mapping is described by a set of if-then rules like if Xt is A~J) and x2 is A~J) and ... and Xn is Ail) then y is B(i) .
