tailieunhanh - Fuzzy Systems Part 8

Tham khảo tài liệu 'fuzzy systems part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Fuzzy Filtering A Mathematical Theory and Applications in Life Science 131 If X1 is A1 and and Xn is An then yf s. Here xi . Xr are the model input variables yf is the filtered output variable Al . An are the linguistic terms which are represented by fuzzy sets and s is a real scalar. Given a universe of discourse Xj a fuzzy subset Aj of Xj is characterized by a mapping pA Xj 0 1 where for Xj e Xj Pa Xj can be interpreted as the degree or grade to which Xj belongs to Aj. This mapping is called as membership function of the fuzzy set. Let us define for jth input Pj non-empty fuzzy subsets of Xj represented by A1j A2j . Ap j . Let the ith rule of the rulebase is represented as Ri If X1 is Ai 1 and andXnisAinthenyf si where Aịi e A11 Ap 1 e A12 Ap 2 and so on. Now the different choices of Ai1 Ai2 . Ain leads to the K nn iPj number of fuzzy rules. For a given input X the degree of fulfillment of the ith rule by modelling the logic operator and using product is given by gi X n P Xj . j 1 The output of the fuzzy model to input vector X e X is computed by taking the weighted average of the output provided by each rule K K n ts .A X tsi npAv Xj i 1 i 1 j 1 2 yf K K n 2 tgi X tnPA Xj i 1 i 1j 1 Let us define a real vector 0 such that the membership functions of any type . trapezoidal triangular etc can be constructed from the elements of vector 0. To illustrate the construction of membership functions based on knot vector 0 consider the following examples Trapezoidal membership functions Let 0 iap tf- P -2 b1 - an t1 - t2 Pn-2 bn such that for ith input Xi e ai bi ữị t1 t2p 2 bị holds V i 1 . n. Now pi trapezoidal membership functions for ith input Pa . Pa . Pa . can be defined as 132 Fuzzy Systems Hau xi 1 if xi e ai t1 -Xi t 2 r 1 2-1 2 1 if xi e ti ti t t 0 otherwise xi i t2 j 2 t2 j-3 1 -xi t2 j t2j - t2j 1 0 Ha xi if Xi e t2j-3 t2j-2 if x e t2j 2 t2j 1 if Xi e t2j 1 t2j otherwise 2P 3 x - ifx. e t2P 3 t2p 2 12P 2 t2p 3 if xi e ti ti HaPị1 xi ỡ 1 ifx e t2p