Design of a rule-driven architecture for a genetic T-norm
Abstract
Rule-Driven processing has been proved as a way of achieving high speed in fuzzy hardware. Up to now, rule-driven architectures were designed to work with minimum or product as T-norm. This paper proposes two new rule-driven models designed for any T-norm (programmable T-norm) and any kind of membership function. The first one gives a valid theory for rule-driven processing with programmable T-norm and stablishes the background for the second model. The second model has been designed taking into account its implementation characteristics and for normalized membership functions with an overlap factor of two. The architecture proposed can be implemented either by hardware or software.
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n1E e 3?sR F pZ$?9 m 3 3t?stI9 e-s8}jU p$%t BC ) w x z ,x ,-,h,\,;,p,-B,-B L ,{,5 D s PZ99k RkR8 b$Y z )1 ,p ) w p d ,p 1 ,p n ,p ; D U p d U {W { d 7X \ d , d yzQ { 1 7X \ 1 , d x_z . 7X . d p 1 U {W { d 7X \ d , d yzQ { 1 7X \ 1 , 1 x_z . 7X . 1 p n U {W { d 7X \ d , 1 yzQ { 1 7X \ 1 , d x_z . 7X . n p ; U {W { d 7X \ d , 1 yzQ { 1 7X \ 1 , 1 x_z . 7X . ; qY 88ARY$} PZt{$BtR s w \ d , d ,\ d , 1 D stI w \ 1 , d ,\ 1 , 1 D IhtI $t { d stI { 1 R}{$%jk qY V{$%s$Bt yt%sjR b$jj A w R 3$ 1 D U \{ d ) w > ( ,\ D , > \,4 D , > 4,g D , > ;,o H D \{ 1 ) w >( ,\ 1 D , > \ 1 ,4 1 D , > 4 1 ,g 1 D , > g 1 ,; 1 D , > ; 1 ,o 1 H D qY }s$$Bt h BP C b$jj A w R 3$ 1 D U h ) w h d ,h 1 ,333,h 1x D ) w w >( ,\ D , >( ,\ 1 D D , w >( ,\ D , > \ 1 ,4 1 D D , w >( ,\ D , > 4 1 ,g 1 D D ,333 D qY ]jsRR$h{s$Bt BP iZjR gp b$jj A w R 3$ 1 D U gp ) w w p 1 D , w p 1 D , w p d ,p 1 D , w p d D , w p d D , w p 1 D , w p 1 D , w p d ,p 1 D , w p d D , w p d D ,333 D G qY ]jsRR$h{s$Bt BP iZjR gp RYBbR PB s t${ qTtB8 Y 8s-$8Z8 tZ8T A BP s{$% ZjR Ys {st A -{ZI PB st $t}Z { $t{jZII $t s {jj h > _s${Zjsjk Y$R 8s-$8Z8 R b$jj A JZsj B Y sj R BP s{$% ZjR $P Y qTtB8 $R }BIZ{ B 8$t$8Z8 n1 V{$%s$Bt Vs BP s qTtB8 stI s iZj qY V{$%s$Bt Vs BP s qTtB8 $R IhtI sR Y $Bt bY Y %sjZ BP x z $R A$ Yst 9B y $R IhtI Ak Y R BP $tJZsj$$R w B d ,B 1 ,B n D bY${Y Iht Y ABI BP x z 3$ n RYBbR Y s}Y BP Y NZ{,sR$b${9 qTtB8U x z ) Ey? w ( , w y L K d D D 3$ ; RYBbR $t bY$ Y V{$% Vs BP Y NZ{,sR$b${9 qTtB8 stI PB8 Ys w B d ,B 1 ,B n D {stABAs$tIU B d w ,V D U L V d ( B 1 w ,V D U Ld ( B n w ,V D U V Ld ( p$%t BC ) w x z ,x ,-,h,\,;,p,-B,-B L ,{,5 D b$Y gyQ w { D )1 gp i Y R BP ZjR sRRB{$sI b$Y Y {jj h i w -B 7, d ,333,-B d ,7 L t D stI
*R$t BP s iZjT*$%t V{Y${Z PB s pt${ qTtB8 n1 3$Z nU NZ{,sR$b${9 qTtB8 3$Z ;U V{$%s$Bt ss BP s NZ{,T sR$b${9 3$Z xU V{$%s$Bt Vs BP p 1 $t h d w -B 1 ,7 1 ,333,-B 1 ,7 1 L t D Y R BP 88ARY$} PZt{$BtR $t{jZII $t Y V{$%sT $Bt yt%sjR Ys Iht Y {jj h i BP h stI p > s Zj BP gp i IhtI Ak Y 88ARY$} PZt{$BtR w -B d ,7 ,-B 1 ,7 1 D U Y V{$%s$Bt Vs BP Y Zj p > $t Y {jj h i \\ w p > ,h i D $R IhtI sR Y Zt$Bt $%t Ak Y $tJZsj$$RU B d w ,V D ( B 1 w ,V D ( B n w ,V D ( bY ) -B d ,7 stI V ) -B 1 ,7 1 \\ w p > ,h i D $tI${sR Y ss BP h i $t bY${Y p > $R s{$% 3$ x RYBbR Y V{$%s$Bt Vs BP Y Zj p 1 $t Y {jj h d \\ w p 1 ,h d D BP Y }%$BZR -s8}j w R 3$ 1 D qY }%$BZR }B{RR RYBZjI A IBt PB s{Y Zj p 7 $t{jZII $t gp i bY${Y b$jj A IhtI Ak s {BZ}j BP 88ARY$} PZt{$BtR w -B d ,> ,-B 1 ,i D qY$R -}jsts$Bt YsR At $%t PB s bB I$8tR$Btsj RkR8 qY -tR$BtR BP YR $IsR B s t${ tTI$8tR$Btsj RkR8 b$jj A IBt ZR$t Y Iht$$Bt BP s tTI$8tR$Btsj qTtB8 >MH nn 7$8}j$h{s$Bt BP Y V{$%s$Bt VsR es{Y Zj p > BP gp i b$jj Ys% st V{$%s$Bt Vs $t Y {jj h i \\ w p > ,h i D es{Y {jj h i YsR 1 z {jjR b$Y s {B88Bt ABI p$%t h 7 stI h i bB {jjR BP h b$Y s {B88Bt ABI bY${Y %$Pk Ys Ys% s Zj $t {B88Bt gp 7 gp i W ) ! p 1 Bt BP Y {B88Bt ZjR \\ w p 1 ,h 7 D Y RZ{Z Ys IT R{$AR Y V{$%s$Bt Vs BP p 1 $t Y {jj h 7 stI \\ w p 1 ,h i D Y RZ{Z Ys
n1M e 3?sR F pZ$?9 m 3 3t?stI9 3$Z EU V{$%s$Bt Vs BP p 1 $t C IhtR p 1 $t h i $ {st A BAs$tI Y V{$%s$Bt Vs BP p 1 $t Y Zt$Bt BP ABY {jjRU \\ w p 1 ,h 7 h i D ) \\ w p 1 ,h 7 D L \\ w p 1 ,h i D V tsj$9s$Bt BP Y }%$BZR RZj sjjBbR B {BtR$IU \\ w p 1 , gyQ w h D ! 7 )d h 7 D ) \\ w p 1 D qYs bsk $ {st A {BtR$II Y V{$%s$Bt Vs BP Y Zj p 1 $t Y $t}Z R}s{ RkR8 C p\ w p 1 D 3B -s8}j \\ w p 1 D $t Y }%$BZR -s8}j w R 3$ 1 D {st A BAs$tI sRU \\ w p 1 D ) \\ w p 1 ,h d D L \\ w p 1 ,h 1 D L \\ w p 1 ,h n D L \\ w p 1 ,h E D L \\ w p 1 ,h D L \\ w p 1 ,h M D L \\ w p 1 ,h dd D L \\ w p 1 ,h d1 D L \\ w p 1 ,h dn D qY$R -}R$Bt $R Y Zt$Bt BP sjj Y V{$%s$Bt VsR $t bY${Y p 1 $R $t{jZII 3$ E RYBbR s}Y${sjjk Y htsj RZj \\ w p 1 D RYBbR Y }s BP Y $t}Z R}s{ C $t bY${Y Y Zj p 1 $R s{$% PB Y Rj{I qTtB8 y YsR B A }B$t BZ Ys $t Ys {sR b s tB bB,$t b$Y Y }s$$Bt h AZ Btjk b$Y Y $t}Z R}s{ C ; y8}j8ts$Bt BP Y BIj qY sjB$Y8 Ys $8}j8tR Y Bt j$t }B{RR$t BP Y }B}BRRI 8BIj $R %k R$8}j A{sZR Y {B8}j-$k $R 8s$tjk $t Y B & j$t }B{RR$t 3$ }RtR Y sjB$Y8 PB Y BtTj$t $8}j8ts$Bt BP Y 8BIj \\ w p % D $R s RZ{Z BAs$tI $t Y B& j$t }B{RR$t }YsR Ys {Bts$tR sjj Y t{RRsk $tPB8s$Bt B IR{$A Y V{$% Vs BP s $%t Zj qY }B}BRRI sjB$Y8 {st A $8}j8tI ZR$t }ssjj$R8 stI R8ts$Bt qY R8ts$Bt $R I$%$II $t bB R}R Y hR Bt {sj{ZjsR $P s Zj $R s{$% stI Y R{BtI Bt $P t{RRsk -{ZR $ qYBR R}R {st A $8}j8tI b$Y }ssjj$R8 A{sZR Y R yP { 1 ; \\ w p % D PB s{Y Zj stI Y -{Z$Bt BP s{Y Zj Ys% tB I}tIt{k s8Bt Y8
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nn( e 3?sR F pZ$?9 m 3 3t?stI9 qY }RZIB iZjT*$%t 8BIj $R AsRI Bt 7tR$Aj VsR V 7tR$Aj Vs > C\ > $R IhtI Ak Y $Bt BP Y {jj h > stI Y R BP sRRB{$sI ZjR gp > e-s8}jU p$%t BC ) w x z ,x ,-,h,\,;,p,-B,-B L ,{,5 D s PZ99k RkR8 b$Y z )1 stI p ) w p d ,p 1 ,p n ,p ; D U p d U {W { d 7X \ d , d yzQ { 1 7X \ 1 , d x_z . 7X . d p 1 U {W { d 7X \ d , 1 yzQ { 1 7X \ 1 , d x_z . 7X . 1 p n U {W { d 7X \ d , d yzQ { 1 7X \ 1 , 1 x_z . 7X . n p ; U {W { d 7X \ d , 1 yzQ { 1 7X \ 1 , 1 x_z . 7X . ; 3$ M RYBbR Y 7tR$Aj VsR BP Ys RkR8 b$Y s t${ qTtB8 stI Y R BP ZjR Ys {Yss{$9 Y8 bY C\ x ) w p d ,p 1 ,p n ,p ; D G qY tsj s}}sst{ BP Y 7tR$Aj VsR BP s bBT$t}Z RkR8 b$Y s}T 9B$Isj 88ARY$} PZt{$Bt stI s }Bs88sAj qTtB8 $R $%t $t 3$ qY$R }s$$Bt $R Y Rs8 PB stk k} BP 88ARY$} PZt{$BtR qY s PBZ I$&t k}R BP 7tR$Aj VsR w 7V D U 6 7V 8s,I b$Y d Ys% Btjk Bt Zj sRRB{$sI 6 7V 8s,I b$Y 1 stI n Ys% bB ZjR sRRB{$sI 6 7V 8s,I b$Y ; Ys% PBZ ZjR sRRB{$sI qY sRBt PB ts8$t Y 8BIj _RZIB iZjT*$%t {B8R PB8 Ys%$t PBZ ZjR sRRB{$sI b$Y Y k} BP 7tR$Aj Vs ; qYR PBZ ZjR sRRB{$sI s $t tsj tB sjbskR s{$% stI A{sZR Y 8BIj IsjR b$Y s }Bs88sAj qTtB8 Y $R tB bsk BP $It$Pk$t Y tBtTs{$% BtR yt BI B I8$t ^{$tjk Y R BP s{$% ZjR s 8{Yst$R8 B BAs$t Y$R R PB8 st $t}Z $R tII qY s{Y${Z }B}BRRI $R I$%$II $t bB }YsRR s {B8}$js$Bt stI st BtTj$t }YsR xd ]B8}$js$Bt _YsR qY BA`{$% BP Ys }YsR $R B }B{RR Y RkR8 $t s bsk Ys sjjBbR B $It$Pk Y R BP s{$% ZjR b$Y Y$Y R}I qY$R {st A IBt $t bB }sRU 6 eJZsj$9s$Bt BP Y 88ARY$} PZt{$BtR stI Y 7tR$Aj VsR 6 yIt$h{s$Bt 8YBI BP Y R BP s{$% ZjR eJZsj$9s$Bt BP Y 8ARY$} 3Zt{$BtR stI Y 7tR$Aj VsR qY JZsj$9s$Bt BP Y 88ARY$} PZt{$BtR BP Y RkR8 sjjBbR B BAs$t $t st ^{$t bsk Y 7tR$Aj Vs $t bY${Y st $t}Z { $R $t{jZII stI B $It$Pk Y R BP s{$% ZjR qY JZsj$9s$Bt $R IBt b$Y Y 3Zt{$Bt ] 3Bs{Y
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