tailieunhanh - Fuzzy Systems Part 9

Tham khảo tài liệu 'fuzzy systems part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Information Extraction from Text - Dealing with Imprecise Data 151 one fuzzy output from each fuzzy model and then weights these outputs based on the membership values of the given input vector in each cluster. Let xk yk denote each training data point where Xkịxik. .xnv k is the kth input vector of nv dimensions yk is their output value pik E 0 1 represent the membership value of kth vector to cluster i c be the total number of clusters m be the level of fuzziness parameter. The learning algorithm of type-1 FIS with the Improved Fuzzy Functions approach Celikyilmaz Turksen 2007 2008b c is processed as follows Step 1 IFC is a dual-structure clustering method combining FCM Bezdek 1984 and fuzzy c-regression algorithms Hoppner Klawonn 2003 within one clustering schema and has the following objective function min jmC X 1 IL K 1 Xh mEik 4 In 4 dik xk-vi represents the Euclidean distance of each xk to each cluster center vi. The error Eik yk-gi rik 2 is the total squared deviation between of the approximated fuzzy models namely the interim fuzzy functions gi T of cluster i and the actual output. The novelty of each gi ĩì is that corresponding membership values and their possible transformations are the only predictors of interim fuzzy functions while excluding original variables. The aim is to calculate the membership values that can be candidate input variables when used to estimate the local models. An example interim fuzzy function can be formed using gi 1i Wi w0i w1iti w2i 1 exp -P 5 In 5 wi represents the vector of regression coefficients. IFC minimizes the objective function JmỈFC. The second term of the objective function can be minimized if optimum functions can be found. Thus the algorithm searches for the best interim fuzzy functions gi ĩl . From the Lagrange transformation of the objective function in 4 the membership values are calculated with a new membership value update equation as follows Í -i t t d2 E2 d E2k 1 m-1 t 1 6 1 j 1 J i 1 i k . .