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Design of a rule-driven architecture for a genetic T-norm

Frías Martínez, Enrique,Gutiérrez Ríos, Julio,Fernández Hernández, Felipe

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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sYbs m 7BP ]B8}Z$t  w 1((( D n1nTnnx *R$t BP s iZjT*$%t V{Y${Z PB s pt${ qTtB8 e 3?sR F pZ$?9 stI 3 3t?stI9 =t$% _Bj$?{t${s I sI$I *} I q{tBjB?s 3B?Bt${s ]s8}ZR Btst{IB 1MEE( BsI$jjs Ij Bt sI$I 7}s$t P$sRoIPhZ}8R VARs{ iZjT*$%t }B{RR$t YsR At }B%I sR s bsk BP s{Y$%$t Y$Y R}I $t PZ99k YsIbs =} B tBb ZjTI$%t s{Y${ZR b IR$tI B bB, b$Y 8$t$8Z8 B }BIZ{ sR qTtB8 qY$R }s} }B}BRR bB tb ZjTI$%t 8BIjR IR$tI PB stk qTtB8 w }Bs88sAj qTtB8 D stI stk ,$tI BP 88ARY$} PZt{$Bt qY hR Bt $%R s %sj$I YBk PB ZjTI$%t }B{RR$t b$Y }Bs88sAj qTtB8 stI RsAj$RYR Y As{,BZtI PB Y R{BtI 8BIj qY R{BtI 8BIj YsR At IR$tI s,$t $tB s{{BZt $R $8}j8ts$Bt {Yss{$R${R stI PB tB8sj$9I 88ARY$} PZt{$BtR b$Y st B%js} Ps{B BP bB qY s{Y${Z }B}BRI {st A $8}j8tI $Y Ak YsIbs B RBPbs kbBIR U iZjT*$%t _B{RR$t qTtB8 _Bs88sAj 3Z99k _B{RRBR d ytBIZ{$Bt qY I%jB}8t BP PZ99k YsIbs $R IZ B Y t{RR$k BP }B{RR$t PZ99k ,tBbjI AsR RkR8R b$Y Y$Y R}I 7B8 bskR BP s{Y$%$t Y$Y R}I $R ZR$t }ssjj$R8 stI }$}j$t }B{RR$t {Bt{}R I%jB}I $t {B8}Z:R s{Y$T {Z Ys {st A sR$jk $8}j8tI $t s PZ99k YsIbs }jsPB8 !Y B}$Bt B {BtR$I $R ZjTI$%t }B{RR$t yt Ys {sR Btjk Y ZjR Ys s j%st B Y BZ}Z s -{ZI qY 8s$t &{ BP s ZjTI$%t s{Y${Z $R B $t{sR Y }B{RR$t R}I A{sZR Y R BP Y j%st ZjR $R Btjk s R8sjj }s BP Y {B8}j PZ99k ,tBbjI AsR y,Is >EH I%jB}I Bt BP Y hR ZjTI$%t s{Y${ZR !Y VZYBR >nH >dH >1H >;H >xH Ys% I%jB}I PZ99k ZjTI$%t s{Y${ZR AZ $t sjj BP Y8 Y IR$t bsR 8sI PB 8$t$8Z8 B }BIZ{ sR qTtB8 qY IR$t BP s ZjTI$%t s{Y${Z I}tIR Bt Y qTtB8 ZRI Ak Y RkR8 A{sZR $ I8$tR $P s Zj $R j%st B tB Ak {sj{Zjs$t Y I BP ZY BP Y st{It qY$R }s} }B}BRR bB tb ZjTI$%t 8BIjR IR$tI PB stk qTtB8 w }BT s88sAj qTtB8 D stI stk ,$tI BP 88ARY$} PZt{$Bt qY hR Bt $%R s n1n n1; e 3?sR F pZ$?9 m 3 3t?stI9 %sj$I YBk PB ZjTI$%t }B{RR$t b$Y }Bs88sAj qTtB8 stI RsAj$RYR Y As{,BZtI PB Y R{BtI 8BIj qY R{BtI 8BIj $R IR$tI s,$t $tB s{{BZt $R $8}j8ts$Bt {Ys{$R${R stI PB tB8sj$9I 88ARY$} PZt{$BtR b$Y st B%js} Ps{B BP bB qY$R 8BIj $R s hR R} BbsIR Y IR$t BP s PZjjT}Bs88sAj Y$YTR}I PZ99k }jsPB8 1 VI%stsR BP s iZjT*$%t V{Y${Z BC ) w x z ,x  ,-,h,\,;,p,-B,-B L ,{,5 D $R s %{B Ys IhtR s y7! PZ99k RkR8 b$Y x z Y qTtB8 x  Y qT{BtB8 - Y R BP 8BI$hR h Y }B}ss$Bt B}sB \ Y ss$Bt B}sB ; Y I&Z9$h{s$Bt sjB$Y8 p Y R BP iZjR -B Y 88ARY$} PZt{$BtR IhtI Bt Y $t}ZR -B L Y 88ARY$} PZt{$BtR IhtI Bt Y BZ}Z { ) w { d ,333,{ z D Y $t}Z stI 5 ) 5 d Y BZ}Z BP Y RkR8 p$%t E ) gyQ w p D  z ) gyQ w { D  stI t Y B%js} Ps{B BP Y $t}Z 88ARY$} PZt{$BtR p y  Y R BP s{$% ZjR %$hR YsU p y ) z t cc E n _Bs88sAj iZjT*$%t BIj qY s{Y${ZR I%jB}I Z} B tBb {st tB A ZRI PB s t${ qTtB8 A{sZR Yk RZ}}BR Ys $P Y R BP st{IR BP s Zj $R I$&t PB8 9B Y Zj b$jj A s{$% bY${Y $R Btjk Z PB }BIZ{ stI 8$t$8Z8 qY }B}BRRI 8BIj $R IR$tI B BAs$t PB8 st $t}Z Y R BP s{$% ZjR PB s t${ qTtB8 y $R I$%$II $t Y }sR Y hR Bt BAs$tR PB s $%t $t}Z Y 8s-$8Z8 R BP s{$% ZjR Y R{BtI Bt $tBIZ{R Y {Bt{} BP V{$% Vs BP s Zj stI Y Y$I Bt $%R s R$8}j$h{s$Bt 8YBI nd s-$8Z8 R BP V{$% iZjR 3B s{Y { 7 ; {  Y V{$%s$Bt yt%sjR BP { 7  \{ 7  s IhtI sR Y Zt$Bt BP Y R BP $t%sjR jPT{jBRI stI $YTB}t -{} Y jsR Bt bY${Y $R sjRB $YT {jBRI $%t Ak Y -8 }B$tR BP Y ,tj stI Y RZ}}B BP s{Y Bt BP Y 88ARY$} PZt{$BtR IhtI $t { 7  \{ 7 $R BAs$tI PB8 w -B 7, d ,333,-B 7, , -B 1 7, Ld ,333,-B 1 7, L > D b$Y  ) gyQ w -B 7 D stI -B 1 7,i b$Y i )  Ld ,333, L >  Y R BP > tb 88ARY$} PZt{$BtR BAs$tI PB8 s}}jk$t Y R BP 8BI$hR 3$ d }RtR st -s8}j BP V{$%s$Bt yt%sjR 3$Z dU e-s8}j BP V{$%s$Bt yt%sjR *R$t BP s iZjT*$%t V{Y${Z PB s pt${ qTtB8 n1x 3$Z 1U -B  \{ stI h 3B8sjjk Y V{$%s$Bt yt%sjR BP { 7 {st A BAs$tI sRU \{ 7 ) B 7 w B  w B L w  L >  E )d w C`  w -B 7,E D  zq  w -B 7,E D D D D D bY C`  stI zq  s PZt{$BtR Ys BAs$t Y -8 }B$tR Ys Iht Y ,tj stI Y RZ}}B BP s jsAj B L $R s PZt{$Bt Ys BIR s R BP }B$tR B  $R s PZt{$Bt Ys j$8$tsR Y }sI }B$tR BP s R stI B 7 BAs$tR Y $t%sjR $YT{jBRI stI jPTB}t Ys s IhtI Ak s R BP }B$tR p$%t \{ 7  7 )d 333gyQ w { D  stI C Y tTI$8tR$Btsj $t}Z R}s{ $%t Ak w { d ,333,{ z D  h $R IhtI sR s }s$$Bt BP C $%t Ak Y {sR$st }BIZ{ w  D BP \{ 7  7 )d 333gyQ w { D U h )  \{ 7 ,7 )d 333gyQ w { D p$%t w \{ d , 1 ,333,\{ z,> 1 D Y V{$%s$Bt yt%sjR Ys Iht Y {jj h i BP h  stI Y Zj p E IhtI sRU p E U {W { d 7X -B d , yzQ 333 yzQ { z 7X -B z,> x_z gLzXR`z y b$jj A Rs$I Ys p E $R $t{jZII $t Y {jj h i $P stI Btjk $PU p E ; h i hp  w 7,i,_ D ) w d ,, 1 D ,333, w z,>,> 1 D 87W7X -B 7,i  \{ 7,_ W ) ! VZj p E b$jj A $t{jZII $t s {jj h i $P stI Btjk $P %k 88ARY$} PZt{$Bt -B 7,i BP Y Zj YsR s tBt 8}k $tR{$Bt b$Y Y {BR}BtIt I$8tR$Bt \{ 7,i 1 Ys IhtR Y {jj h i  qY ]jsRR$h{s$Bt BP iZjR gp $R IhtI sR Y {jsRR$h{s$Bt BP Y R BP ZjR p $t h ZR$t Y }%$BZR {$$s gp $R -}RRI sR s %{B bY${Y {Bts$tR Y s{$% ZjR PB s{Y {jj BP h U gp ) w gp d ,333,gp > D j70_ > ) gyQ w h D ,gp 7 ) w p > 1 ,333,p i 1 D n1E e 3?sR F pZ$?9 m 3 3t?stI9 e-s8}jU p$%t BC ) w x z ,x  ,-,h,\,;,p,-B,-B L ,{,5 D s PZ99k RkR8 b$Y z )1 ,p ) w p d ,p 1 ,p n ,p ; D U p d U {W { d 7X \ d , d yzQ { 1 7X \ 1 , d x_z . 7X . d p 1 U {W { d 7X \ d , d yzQ { 1 7X \ 1 , 1 x_z . 7X . 1 p n U {W { d 7X \ d , 1 yzQ { 1 7X \ 1 , d x_z . 7X . n p ; U {W { d 7X \ d , 1 yzQ { 1 7X \ 1 , 1 x_z . 7X . ; qY 88ARY$} PZt{$BtR s w \ d , d ,\ d , 1 D stI w \ 1 , d ,\ 1 , 1 D  IhtI $t { d stI { 1 R}{$%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 ,; 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