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Nghiên cứu bộ điều khiển thông minh trên cơ sở tích hợp mạng nơron mờ với subethood và ứng dụng

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Nghiên cứu bộ điều khiển thông minh trên cơ sở tích hợp mạng nơron mờ với subethood và ứng dụng

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Trong bài báo này nhóm tác giả nghiên cứu thiết kế bộ điều khiển thông minh trên cơ sở tích hợp mạng nơron mờ với subsethood (NFS). NFS gồm 5 lớp sử dụng các hàm thành viên mờ Gausian và được huấn luyện với thuật truyền ngược. Đồng thời mức độ ảnh hưởng của các luật mờ lên phần kết luận bởi các kết nối mờ cũng được định lượng dựa trên phép đo subsethood tương hỗ. bộ điều khiển này cho phép phát sinh tập luật mờ một cách tự động từ dữ liệu huấn luyện thay vì sử dụng tri thức chuyên gia.

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Nội dung Text: Nghiên cứu bộ điều khiển thông minh trên cơ sở tích hợp mạng nơron mờ với subethood và ứng dụng

  1. Tiiu ban: Cong nghi thong tin - Tir dong hod - Cong nghe I'ii tru ISBN: 978-604-913-010-6 NGHIEN ClTU B O DIEU KHIEN THONG MINH TREN CO SO TICH HOP MANG NO RON MOf VOI SUBSETHOOD VA iTNG DUNG Ha Manh Dao, Thai Quang Vinh Vien Cdng nghe thdng tin 18-Hoang Qudc Viet, Ciu Giiy, Ha Ndi Email: hmdao(a),ioit.ac.vn. tqvinh@ioit.ac.vn Tom tat: Trong bdi bdo ndy chiing tdi se nghiin ciru thiit ki bd dieu khiin thdng minh tren ca sd tich hgp mgng na ron md vdi subsethoodfNFS). NFS gdm 5 lap sic dung cdc hdm thdnh viin md Gausian vd duo'c hudn luyen vdi thudt truyin nguac. Ddng thdi muc do dnh hudng cua cdc lugt md lin phdn kit ludn bdi cdc kit ndi md ciing duac dinh luang dug trin phep do subsethood tuang hd. Bd diiu khiin ndy cho phep phdt sinh tgp lugt md mgt cdch tu ddng tir du lieu hudn luyin thay vi su dung tri thirc chuyin gia. Bd diiu khiin NFS thi hiin nhiiu uu diim han so vdi edc bd diiu khiin su dung mgng na ron md thdng thudng. Cudi ciing bdi bdo ciing se di cdp din cdc vdn di dng dung cita bd diiu khiin NFS vd thuc hiin md phdng. Abstract: In this paper, we are design a intelligence controller based the integration Neuro-Fuzzy Network with mutual Subsethood (NFS). NFS includes five layers, which used gaussian membership function. NFS is used to train by the gradient descent algorithm. In this manner, NFS fully considers the contribution of input variables to the joint firing strength of fuzzy rules. Afterwards, the investigated fuzzy neural network quantifies the impacts of fuzzy rules on the consequent parts by fuzzy connections based on mutual subsethood. This controller allow automatically generate fuzzy rules from training data instead using expert knowledge. The NFS controller has many better than the conventional fuzzy neural networks. Finally, To demonstrate the capability of the NFS, simulations in control area is conducted. \. Dat van de Bd dieu khien md hien dugc img dung rdng rai trong dilu khiln, nhan dang, phan ldp mau...Van de mau chdt ciia bd dieu khien md la xay dung dugc tap luat ciia bd dilu khiln. Tap luat phai dam bao bao het cac trudng hgp ciia bai toan, dam bao sd luat la tdi thilu va sd lugng tinh toan it nhat. De thiet ke bd dilu khiln md, theo truyen thdng can phai cd tri thirc chuyen gia \'e linh vuc, nhung dieu nay trong nhilu bai toan thuc te la chua dap iing dugc vi nliieu ITnh vuc viec tim chuyen gia la khd, qua trinh thu thap tri thiic mat nhieu thdi gian va chi thich hgp vdi sd dau vao it. Trong cac bai toan phiic tap, nhieu dau vao, ngudi chuyen gia nhieu khi klidng bao duac hit cac trudng hgp thuc tl dan den bd dieu khien md ban chi muc do chinh xac va pham vi giai bai toan. D I giai quyet van de nay, cac nghien cim gan day da dl 122
  2. Hoi nghi Khoa hoc k\- niim 35 ndm I 'iin Khoa hoc vd Cong nghi Viet Nam - Hd Noi 10 2010 xuat nhilu thuat toan tu ddng nit ra tap luat md tir tap dir lieu %'ao/ ra ciing \'di mdt sd tri thirc biet trudc. Cac thuat toan nay chu NIU dua vao \'iec phan nhdm dii lieu dau \ao \a sir dung mang no ron \'a mang na ron md. Gan da)', dl nang eao chit lugng \'a tdi uu tap luat md. cac thuat toan phat sinh tap luat md tu ddng dua tren dii: lieu \ ao/ra da dugc cai thien bang each sir dung subsethood \'a thuat tien hoa. Vdi each sir dung phep do subsethood phai ke den cac cdng trinli[2]-[15] ciia C H . Kao[2000]. Song Hengjie at al[2009]. K. A. Rasmani. Q. Shen [2002]. Sandeep Paul. Satish Kumar[2004]. Michelle Galea, Qiang Shen[2002]..., Trong bai bao nay chiing tdi se de cap den viec xa)' dung tap luat md dua tren dii lieu \'ao/ ra bang each su dung mang na ron md \'di phep do subsethood va. md phdng chung. Phan tiep theo ciia bai loan bao gdm phan 2 trinh bay \'e phep do subsethood, khao sat mang na ron md tren ca sd phep do subsethood(NFS), cap nhat tham sd \a tinh toan subsethood ciia cac lien ket md[3]; phan 3 thuc hien cai dat cac ham de khdi tao NFS va huan luyen phat sinh tap luat md sir dung mdi trudng Matlab; phan 4 thuc hien md phong . danh gia md phdng. Cudi cimg phan 5 la ket luan. 2. Xay dung bo dieu khien md sir dung no ron md dua tren subsethood(NFS) 2.1. Phep do subsethood Phep do subsethood cd ngudn gdc tir dinh ly P)'thagorean cd the dugc dinh nghia nhu sau[l,14,15]: Cho A. B la cac tap md thugc khdng gian U vdi ham lien thuoc PA va pe tuong img: • Phep do subsethood md S(A.B) do mirc do ma A la tap con ciia B dugc dinh nghia nhu sau: y min(/^,(z/),//„(w)) M(A) Z/'N) Vdi S{A,B)&[Q,V[. Sau day chiing tdi se sir dung djuh nghia \a cac tinh chat cua subsethood dinh nghTa d tren vao de tinh lien ket md ciia bd dieu khien mang no ron md. 2.2. Bg dieu khien nff ron ma sir dung subsediood(NFS) 2.2.1. Mo ta NFS Trong phan nay chiing tdi se khao sat bd dieu khien mang na ron md dugc de xuat bdi S. Hengjie at al.[3]. Bd dieu khien mang na ron md su dung phep do subsethood duac the hien nhu hinh ^'e 1. Cau triic ciia bd dieu khien nay gdm 5 ldp. Ldp 1 la ldp vao. ldp 2 la ldp dieu kien, moi mit la mdt gia tri ngdn ngir ciia bien \'ao. Ldp 3 la ldp luat. Ldp 4 la ldp bieu dien phin kit luan ciia luat, mdi nut la mdt nhan ngdn ngir ciia bien ra \'a nd thuc hien giai md. Ldp 5 la ldp diu ra. Cac nut ldp 2. 3 deu su dung ham thanh vien md dang Gaussian. Diem dac biet ciia mang no ron md nay so \'di cac mang no ron md khac la nd sir dung cac lien ket md di)' dii giira ldp luat \'a ldp meiih de ket luan. Cac lien ket md nay the hien mirc dp tac ddng ciia moi phan dieu kien trong moi luat den phan ket luan nhu the nao. Mdi lien ket md ciing su dung ham thanh \'ien md dang Gaussian va xac dinh mirc do gidng nhau giira nd vdi 123
  3. Tieu ban: Cong nghe thong tin - Tir dong hod - Cong nghi Vii tru ISBN: 978-604-913-010-6 tap md ciia luat Rk tuong img bang each sir dung phep do subsethood md. Mang diu vao va ra ciia moi mit trong cac ldp dugc trinh bay trong bang 1. Output Laver Consequent leaver Rule Laver Antecedent Laver Input Laver Hinh I. cdu true mgng na ron md su dung subsethood(NFS) Ldp Tenldp Mang dau vao Mang dau ra 1 Input layer /"'=^, >^;'*=r 2 Antecedent layer /,?=-U"'-c„,)^ (2, ^J' -^^''-.,^'^'
  4. Hoi nghi Khoa hoc ky niim 35 ndm I 'iin Khoa hoc vd Cong nghi Viet Nam - Hd Noi 10 2010 • Wk. ILi"': La trong Heu ket tir ldp dieu kien den ldp luat. Nd xac dinh trong sd ddng gdp cua niit ngdn ngir IL"'i(i=l .2....N va Uj thugc Nj) cau thanh phan IF ciia luat md R^ • Rk : Luat md IF-THEN thir k \a la mdt nut cua ldp 3 dung ham thanh \'ien Gausian dugc dinh nghTa la Rk(Ck. Ok). • OLj"^' ) La mdt nut ciia ldp 4. Mdi niit bieu dien mdt gia tri ngdn ngii: thir mj cua bien dau ra yj • voLj'""',k : Trgng lien ket md tir niit luat Rk tdi gia tri ngdn ngir dau ra OLj""-'. NO ciing sir dung ham thanh vien dang Gaussian vdi tam V'^OLJ'""' k va he sd dd trai V'^OLI"^"' k va dugc djnh nghTa bdi voLrik(v'oLrlk .v^oy'^k )• • £(voLj"'lk, Rk): Phep do subsethood tuong hd trgng lien ket md. Nd do miirc do gidng nhau ciia cac tap md de dinh luong mirc dd tac ddng ciia luat md Rk len phin kit luan OLj'J. • ^j.mj! la trgng crisp tir gia tri ngdn ngir diu ra OLj"^-* tdi nut thir j ciia ldp diu ra. Luat md cd dang: Rj:IFx,is A"' aiul...Xi is A''' and x^ is A^r THEN y is / with s' Co che suy dien: Input: IF xi is Ai and... x\ is A\ Ri'.IFxiis Al'' and...Xi is A''' and xy is ^^- THEN y is / with s' Rj:IFx,is A"' and...Xi is A"'' and XN is A'^- THEN y is / with s' RM: IF X, is A'f'' and... Xi is Af and xy is Af THEN y is / with s" Output: >^ = X 4 A ( / ) t=i Vdi: A(_y*) bieu dien su giai md ciia gia tri ngdn ngir y'^. Van de dat ra ddi vdi mang nay la lam thi nao dl phat sinh tap luat va tdi uu tap luat do tren ca sd tap dtr lieu huan luyen vao/ra. Van dl nay se duac xet chi tilt trong phin thuat cap nhat tham sd va tinh subsethood trong phan tiep theo. 2.2.2. Tinh subsethood cho lien kit md giira ldp 3 vd ldp 4 Xet lien ket md giira luat Rk vdi nut gia tri ngdn ngir ciia ldp 4 la OLj""-*. Trgng lien kit md md ta mirc do tac ddng ciia cac luat len cac gia tri ngdn ngir dau ra va nd dugc do bdi subsethood tuong ho £{\' „,^ ,R^). Hay ndi each khac£-(v' ,„ ,R^.) do su gidng nhau giira cac luat md Rk va tap md Q^'"; ^ . Tir dinh nghTa subsethood (1) chiing ta xac dinh dugc subsethood tuang ho ^(i' ,„ .7?.) nhu sau: OL,'.k ''' 125
  5. Tieu ban: Cong nghe thong tin - Tir dong hod - Cong nghe Vii tru ISBN: 978-604-913-010-6 vdi f (v „ , i?,) e [0,1]. Ham thude Gaussian cua Rk va ^^,'"/ , cd thi xay ra sir gdi len nhau cua cac tap md thanh phan. Tir bieu thiic ciia £{v „,^ , R^,) ciing xac dinh dugc cac dai OL/ .k' ^ Ol"'.k k^> ^ OL/.k' " ' luong : -p , • ^ dv^ „ dv\, OL/.k OL/.k Sau day chiing tdi se sir dung cac cdng thuc subsethood de xac dinh cac luat cap nhat tham sd va trgng lien ket. 2.2.2. Thuat cap nhat tham sd cho cdc l&p NFS Gia sir NFS duac huan luyen vdi T cap dir lieu vao ra ( X {T),D (r)),r = 1,2.., T Gia sir ggi yj(T) la tin hieu dau ra thuc sir thir j , ham gia E cua mang dugc dinh nghTa nhu sau: E(T) = ^f^{d^{T)-y^iT)f (3) 2 ;=: Vdi mang no ron tren, cac tham sd mang NFS dugc cap nhat den gia tri tdi uu theo thuat giam gradient. Cdng thirc cap nhat tham sd va trgng lien ket ciia cac ldp nhu sau: Ldp 5'.^^.„,^(T + l) = ^^.,„^(r)-TiidEiT)I dv;^„,^^^(r)) (4) Ldp4:v;^„^(r + l) = . ; . ^ ^ ( r ) - , ( a £ ( r ) / 5 v ; ^ , ^ ( r ) ) (5) Ldp 3: c,{T-^\) = c,{T)-fl(dE(T)/dc,(T)) (7) (J,{T + \) = CT,iT)-JlidE{T)/da,iT)) (8) 126
  6. Hoi nghi Khoa hoc Icy- niim 35 ndm Viin Khoa hgc vd Cong nghi Viet .\am - Hd Noi 10 2010 Begin 1 Khoi tao mang NFS ir Kho'i tao gia tri ban dau cho cac tham so mans, ngiro'na sai so E. Dat mau huan luyen thu- k vao mang Thuc hien Ian truven toi dau ra k=k-H Tinh sai so dau ra Error Thuc hien pha Ian truyen nguo'c tin hieu sai so, tinh subsethood va cap nhat cac tham so echo=echo-i-l Thu tap tham so cuoi ciing, cac tham so ham thuoc, phat sinh tap luat mo' voi FIS vdi cac lien ket giua lop 2 voi 3 va lop 3 voi 4 ton tai. Ket thuc fPinh 2. Thudt todn phdt sinh tap lugt Ldp 2: CD^^^,, (r +1) = 0)^^^,., (r) - r]{dE(T) I dco^^^,, (r)) (9) c^^„,(r + l) = c^^,„(r)-^(a£(r)/ac^^„,(r)) (10) G^^,, (r +1) = CT^^„, (r) - ri{dE{T) I CG^^,, (r)) (11) Vdi r| la hang sd hgc. 127
  7. Tieu ban: Cong nghi thong tin - Tir dong hod - Cong nghe I 'ii tru ISBN: 978-604-913-010-6 2.3. Thuat todn phdt sinh tu dong tap luat md Tap luat md dugc phat sinh tu ddng thdng qua qua trinh huin luyen. Qua trinh huan luyen nay dugc td chiic thanh 2 pha: Pha thii nhit: cac dir lieu sd vao va ra dugc nhdm lai thanh cac cum, sau dd nidi cum se dugc khai trien thanh cac luat md. Pha thir 2: khdi tao cho mang phat sinh va ap dung phuang phap huin luyen de thich nghi tdi uu boat ddng ciia he thdng. Tir dd thuat toan phat sinh luat tu ddng dugc thuc hien qua cac budc sau: Thuat toan dilu chinh cac tham sd mang NFS va ham thanh vien md dugc thue hien nhu luu dd thuat toan hinh 3. 3. Cai dat mang NFS bing Matlab Trong bai bao nay, mang nna ron md sir dung subsethood dugc cai dat thdng qua cac ham sau: STT Ten ham Mo ta 1 [xl,fl]=layerl(x) Cai dat ldp vao 2 [x2,f2]=layer2(xl,c2,sima2) Cai dat ldp menh de dieu kien 3 [x3 ,fi]=layer3 (x2,ome,c3 ,sima3) Cai dat ldp luat 4 [x4,f4]=layer4(x3,eps,nuyc,nuys) Cai dat ldp menh de dieu kien 5 [y5,f5]=layer5(x4,muy) Cai dat ldp ra 6 [esp,depc,deps]=epsi(ck,sima,nuyc,nuys) Ham cai dat lien ket md va thuc [cr,dcrc,dcrs]=muy2(ck,sima,nuyc,nuys,gamal,gam hien phep do subsethood a2) [cr,dcrc,dcrs]=muy3(ck,sima,nuyc,nuys,gamal,gam a2) 7 estd=ern (x) Ham sai sd chuan 1 ek=E(yk,dk) Ham tinh sai sd dau ra 2 muy=bp5 (yk,dk,eta,x4,muyc) Ham cap nhat tham sd ldp ra 3 Ham cap nhat tham sd cho ldp [nuyc,nuys]=bp4(yk,dk,eta,muy,nuycc, menh de ket luan va tham sd nuysc,f4,x3,esp,depc,deps) subsethood (THEN) 4 [ck,sima,ome]= Ham cap nhat tham so cho ldp bp3 (yk,dk,eta,muy,nuyc,nuys, luat c3,simac3,omec,esp,depc,deps,f4,f3,x3,x2) 5 [ck,sima]=bp2(yk,dk,eta,muy,nuyc,nuys, Ham cap nhat tham sd cho ldp ome,c3 ,sima3,c2,sima2,f4,f3 ,f2,epsi,x 1) menh de dieu kien(IF) 1 TrainNFSO Ham huan luyen 2 GenFisO Ham phat sinh tap luat Bang 2. Cac ham xay dung NFS bang Matlab 128
  8. Hgi nghj Khoa hoc ky niim 35 ndm I 'iin Khoa hoc vd Cong nghi Viet Nam - Hd Noi 10/2010 4. Mo phong Trong md phdng ciia chiing tdi chiing tdi sir dung bd dilu khien NFS md ta phan 2 xdi 2 tin hieu dau vao va mdt tin hieu dau ra. Trong md phdng 1, chiing tdi sir dung md hinh nghich dao de huan luyen mang. Trong md hinh 2, chiing tdi ciing sir dung tap dir lieu cd dugc tir md hinh toan hgc eiia he thdng dieu khien miic nude de huan luyen phat sinh tap luat. Kit qua md phdng dugc so sanh vdi kit qua ciia md phdng dd khi sir dung bd dilu khiln ANFIS. 4.1. Mo phdng diiu khiin nhiet do bon mrdc tdm 4.1.1. Md hinh diiu khiin Md hinh dieu khiln nhiet cua bdn tim cd dang sau: y{k + l) = a{T)y{k) + b{T)uik) + {l-a{T))Y, (25) l + exp(0.5X^)-r) Vdi: fl(r) = e x p ( - « r ) va b{T)=^^^^^P^ ^ ^ ^ \ tham sd cua mo hinh duac dat la: a a = 1x10"', p = 8.7x10--', r = 40, Fo = 25"C. Tin hieu vao la u(k) gidi ban tir 0 din 5 vdn. Chu ky cit mau T dat la 25giay. 4.1.2. Thiit ke vd hudn luyin bd diiu khiin NFS *'y(k + \) = f(ii(k),y(k)) ii(k) Hinh 3. Md hinh hudn luyen NFS Trong md phdng nay chiing tdi sir dung bd dilu khiln vdi 2 tin hieu diu vao la e(k) va de(k), tin hieu dau ra la u(k). Cac tin hieu diu vao e(k) md hoa thanh 5 tap md: VL(Very Large), L(Large), M( Moderate), S(Small), VS(Very Small); de(k) thanh cac tap md VH(Very High), H(High), M(Moderate). L(Low), VL(Very Low) va sir dung ham thanh vien md Gaussian. Tin hieu dau ra dugc md hoa thanh cac tap md: NL(Negative Large), NM(Negative Moderate), NS( Negative Small), AZ(Appraximately Zero), (PS) Positive Small, PM(Positive Moderate), PL( Positive Large). Trong md phdng chiing tdi sir dung phuong phap dieu khien nghich dao ddi tugng dilu khiln pha huin luyen nhu hinh 4. 129
  9. Tiiu ban: Cong nghi thong tin - Tir dong hod - Cong nghe Vii tru ISBN: 978-604-913-010-6 4.1.3. Md phdng vd kit qud md phdng Sau khi pha hgc kit thuc, bd dilu khiln da dugc huin luyen se dugc sir dung nhu bd dieu khien ddi tugng dieu khien nhu hinh 2: Z-' yik) uik) NFS Plant, f v(^ + l) Hinh 4. Md hinh dieu khien nhiet do NFS Qua trinh thuc hien md phdng thuc hien nhu sau: Md phdng vdi bd dieu khien ANFIS, ket qua cho nhu hinh 6a - Md phdng vdi bg dieu khien NFS, ket qua nhu hinh 6b. l i i U ' I J ilflg Hinh 6a. Kit qud chgy md phdng vdi bd diiu khien ANFIS ^^^^^^^^^S!^^^v^^S^h^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ (l^^j^n 1 ,. J .>J .JL* • C* . -, - ^ ^y ^SJ ^ J ,*£ - ! CS. ; • 53 r:i ten T i n h i e u RQf- T I M h.ou r« i h u c Tin hieu dieu k h i e n yo ...i N. j _J i L.-rr:j B O so •a t V.'^' H ^ --'•--' i - -^ ^ 30 -j'-''- •--\ --] f- h [ i {---- - -- ?n - -1 i r '' 'i--- i i l O -f^' -IO s - \ 60 OO I \ 1 0\0 i 1:20 ^1 1J0 I E5O IE Xhol gion cat mou/bMOc l-TT T — 2 G =-ocor-.cJ = Hinh 6b. Kit qud chay md phdng vdi bd diiu khiin NFS 4.2. Danh gia ket qua md phdng Qua ket qua md phdng. so sanh phuong phap NFS vdi bd dilu khien ANFIS thi NFS cd nhilu uu diem ban: • NFS cung cap mdt sir udc luge cudng do ghep ndi cua cac luat md tdt hon.Trong NFS tat ca cac luat md dugc dinh nghTa nhu tap md tuong img vdi gia tri ngdn ngir ciia cac bien dau vao ciia cac luat da cho va md ta ham thanh vien Gausian vdi trgng tam va do trai khac nhau. Trong ca ehl nay NFS xem xet day dii sir ddng gdp ciia cac biln diu vao tdi cudng do ghep ndi ciia cac luat md va cho su udc luge hieu qua ban so vdi ANFIS. 130
  10. Hoi nghi Khoa hoc ky niim 35 ndm Viin Khoa hoc vd Cong nghi Viet Nam - Hd Noi 10/2010 • NFS truyin tac ddng cua cac luat md len phin kit luan theo cac ket ndi md va dinh lugng tac ddng su dung subsethood tuong hd cho phep hieu chinh cac tham sd ham thanh vien eiia tap md tot hon, kit qua chinh xac va tron ban bg dieu khien ANFIS. • Bd dieu khiln NFS cho sai sd dilu khien nhd ban, dn dinh hon. 5. Ket luan Bd dieu khien mang na ron md sir dung phep do subsethood da cho phep phat sinh tap luat tu dgng vdi nhieu uu diem hon so vdi cac bd dieu mang na ron md truyen thdng. Chinh vi vay cac ket qua nghien ciin mdi cdng bd day cang chung td nd thu hiit sir quan tam cua cdng ddng nghien cuu trong nhieu ITnh 'vuc. Bd dieu khien nay dugc sir dung nhieu trong cac ITnh vuc nhan dang mau, dieu khien, chuan doan y te, phan loai mau... Qua bai bao nay chiing tdi da thuc hien khao sat mang na ron miro sir dung phep do subsethood khac nhau va tap trung vao mang NFS vdi ket ndi md. Sau dd chiing tdi da thiet ke cac ham matlab de thuc hien cai dat NFS ciing nhu thuc hien huan luyen NFS. Cudi ciing chiing tdi da sir dung NFS vao thiet ke bd dieu khien nhiet do cua bdn tam va so sanh ket qua vdi bd dieu khien ANFIS ma da d-wocj nhieu tac gia thuc hien. Cudi ciing, qua bai bao nay chiing tdi cung cam on su hd trg tir de tai "Chuang trinh KHCN Vu tru" VT-06. TAI LIEU THAM KHAO 1. Bari Kosko ; Addition as Fuzzy Mutual £«rro/7y ; Information Sciences 73,273- 2&t (1993); 2. C H . Kao, 'A new method to generate fuzzy rules from training data containing noise for handling classification problems". Master Thesis, Department of Electronic Engineering, National Tai-wan University of Science and Technology, Taipei, Taiwan, R.O.C., 2000. 3. Song Hengjie, Miao Chunyan, Shen Zhiqi, Miao Yuan, Bu-Sung Lee; A fuzzy neural network with fuzzy impact grades; Neurocomputing 72 (2009) 3098-3122. 4. K. A. Rasmani, Q. Shen ; Modifying Weighted Fuzzy Subsethood-based Rule Models with Fuzzy Quantifiers; Fuzz-IEEE 2004; 25-29 July, 2004 Budapest, Hungary 5. Sandeep Paul and Satish Kumar, Member, IEEE; Subsethood-Produet Fuzzy Neural Inference System(SuPFuNIS); IEEE Transactions on Neural Networks, vol. 13, No. 3, May 2002. 6. Michelle Galea and Qiang Shen; Fuzzy Rules from Ant-Inspired Computation; 25-29 July, 2004 Budapest, Hungary 7. Yu-Hai Lilj, Feng-Ian Xiong, Subsethood on intuitionisticFuzzy sets. Proceedings of the First International Conference an Machine Learning and Cybernetics, Beijing, 4- 5 November 2002. 8. John T. (Terry) Rickard, Senior Member, IEEE, Janet Aisbett, and Greg Gibbon; Fuzzy Subsethood for Fuzzy Sets of Type-2 and Generalized Type-n; IEEE Transactions on Neural Networks, \'ol. 17, No. 1, May 2009. 13]
  11. Tieu ban: Cong nghe thong tin - Tir dong hod - Cong nghe \ it tru ISBN: 978-604-913-010-6 9. Sandeep Paul, Member, IEEE, Satish Kumar Senior Member, IEEE, Lotika Singh, Student Member, IEEE; A Novel Evolutionary TSK-Subsethood Model and its Parallel Implementation', 978-1-4244-1819-0/08/$25.00 ©2008 IEEE 10. A. Sala and P. Albertos; Fuzzy Systems Evaluation; The Inference Error Approach; IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYC. BERNETICS, VOL. 28, NO. 2, APRIL 1998 11. Shunmuga Velayutham and Satish Kumar; Some Applications of an Asymmetric Subsethood Product Fuzzy Neural Inference System; The IEEE International Conference on Fuzzy Systems ; 0-7803-7810-5/03/517.00 ©2003 IEEE 12. H. Bustince, V. Mohedano, E. Barrenechea, M. Pagola; A method for constructing V. Young's fuzzy subsethood measures and fuzzy entropies; 3rd International IEEE Conference Intelligent Systems, September 2006. 13. Sandeep Paul, Satish Kumar ; Fuzzy Neural Inference System Using Mutual Subsethood Products with Applications in Medical Diagnosis and Control; 2001 lEEJZ International Fuzzy Systems Conference; 0-7803-7293-W01/$ 17.00 ©2001 EEE. 132

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