Download Soft Computing in Industrial Applications by Luis Collantes, Rajkumar Roy (auth.), Yukinori Suzuki, Seppo PDF
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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N=O i=I I Moreover, the update of the VHR-FRT can easily be carried out by standard leastsquares technique (see the Appendix). 33 The step-by-step procedures for implementation of the proposed fuzzy identifier are as follows: 1. Select the universe of discourse, the shape and number of the membership functions of the fuzzy linguistic variables. 2. Design the center of the input variables' membership functions. 3. If no a priori information is available, go to 5 4. Fill the cell of 0-FRT from a priori expert knowledge.
Update Law Since the number of fuzzy subsets of each input variable remail\ unchanged by using VHR-FM. -FM with a minor change. From equation (2), we can see that we only need to multiply the fuzzy index of the output consequence by 2. I I - (/lx2+¢})...... (/nx2+~n) n - (/;+~;) II X· E ..... E Y i=I ~n ={) ~PI={) y =. :. (2) n _ I I I E ..... L, fPI=O (/;~;) IIx. ~n=O i=I I Moreover, the update of the VHR-FRT can easily be carried out by standard leastsquares technique (see the Appendix). 33 The step-by-step procedures for implementation of the proposed fuzzy identifier are as follows: 1.
Initially, a fuzzy set A was considered as a subset offuzzy set B, when for all membership values a; ~ b; was fulfilled [22). Kosko extended the concept to degrees of subsethood. This degree is derived geometrically from the assigned hyperrectangles. It equals 46 the ratio of the volume of the intersection of both hyperrectangles to the volume of one hyperrectangle. Thus, even the whole set is a subset of each of its subsets to a certain degree 1 . g. color images). e. for the position z the set of all points z + b with b E B) are considered as fuzzy sets.