Some classes of divergence measures between fuzzy subsets and between fuzzy partitions

sYbs m 7BP ]B8}Z$t x w dM D 1xnT1Ex 7B8 ]jsRRR BP *$%t{ sRZR bt 3Z99k 7ZARR stI bt 3Z99k _s$$BtR 7ZRsts BtR stI _IB p$j *}ss8tB I eRsI?R${s  y! k * =t$%R$k BP !%$IB ]\]sj%B 7BjB R\t nn(d !%$IB 7}s$t T8s$jU R8}IBo}$tBt{{ZZt$B%$R VARs{ qY s$8 BP Y$R }s} $R B }Rt stI RZIk Bt $8}Bst {jsRR BP I$%t{ 8sRZ Abt PZ99k RZARR stI Bt $8}Bst {jsRR BP I$%T t{ 8sRZ Abt PZ99k }s$$BtR s{Y BP Y8 Ys%$t RB8 R}{$h{ }B}$R yt Y hR {sR Y I$%t{ 8sRZ s8}R B JZst$Pk Y I BP I$&t{ Abt bB PZ99k RZARR  \ stI  4 Ak {B8}s$t Y PZ99$tRR BP ABY  \ stI  4 b$Y Y PZ99$tRR BP Y $t8I$s PZ99k RZAR yt Y R{BtI {sR b ZR Y$R I$%t{ Abt RZARR B 8sRZ Y I$%t{ Abt }s$$BtR kbBIRU I$%t{ 8sRZ jB{sj I$%t{ PZ99$tRR 8sRZ PZ99k }s$$Bt d ytBIZ{$Bt !Z bB, sIR Y RZIk BP Zt{s$tk sRRB{$sI b$Y RkR8R $t s PZ99k tT %$Bt8t qY Rs$t }B$t BP BZ Rs{Y YsR At Y s-$B8s${ $tPB8s$Bt YBk BP 3B stI Fs8}?I3r$ w >;H D  bY Zt{s$tk $R I${jk sRRB{$T sI b$Y s {Bjj{$Bt BP w {$R} D RZARR BP s R}s{  yt Y Ps8 BP Y$R YBk $ $R }BRR$Aj B ZRR Ys Y -$RR s Ps$jk RBt js$BtRY$} Abt Zt{s$tk w stI $tPB8s$Bt D stI PZ99$tRR stI Abt Zt{s$tk stI {jsRR${sj I$%t{ yt Y$R R}{ s PZtIs8tsj bB, YsR At I%jB}I Ak * NZ{sTq8$t$ >nH bYB $tBIZ{I s ,$tI BP 8sRZ BP PZ99$tRR w Y tBt}BAsA$j$R${ tB}k BP s PZ99k R D AsRI Bt s }BAsA$j$R${ Zt{s$tk 8sRZ yt BZ B}$t$Bt Y A$I Abt Y w {$R} D $tPB8s$Bt w b$Y B b$YBZ }BAsA$j$k D stI 8sRZR BP Zt{s$tk stI $8}{$R$Bt $t PZ99k t%$Bt8tR 8sk j$ $t bYs b P B sR I$%t{ A{sZR BP Y stsjBk b$Y Y {jsRR${sj 8st$t BP Y 8 ZRI Ak %s$BZR sZYBR w >H  D $t {B8}s$t bB }BAsA$j$k I$R$AZ$BtR !t{ b Ys% {Yss{$9I stI RZI$I Y 8sRZ BP Y I$&t{  G;R TR4RIT { Y $t Y$R }s} $R RZ}}BI $t }s A k *py]Oq pst  WB _ ;Tdn1M 1xn 1x; 7 BtR m _ p$j Abt bB w PZ99k B {$R} D RZARR Ys $R Y I$%t{ 8sRZ Abt PZ99k RZARR w R >MH D  BZ Zj$8s BA`{$% {BtR$RR $t ZR$t Y$R 8sRZ B %sjZs Y PZ99$tRR stI \ B Y Zt{s$tk qY RZIk BP Y bsk B 8sRZ Y I$&t{ Abt bB RZARR B bY${Y b b$jj P B sR I$%t{ Abt RZARR $R $%t $t 7{$Bt 1 stI b RZIk 8s$tjk Y {sR bYt Y I$%t{ $R BAs$tI PB8 PZ99$tRR 8sRZR *}sT $t PB8 Y$R b$I {jsRR BP I$%t{ 8sRZ b RZIk s jB BP }B}$R qY bsk B 8sRZ Y PZ99$tRR BP s PZ99k }s$$BtR stI Y Iht$$Bt BP I$%t{ Abt PZ99k }s$$BtR b$jj A $%t $t 7{$Bt n yt Y$R R{$Bt b RZIk sjRB s }s${Zjs {jsRR BP I$%t{ Abt }s$$BtR bY${Y $R Y {jsRR BP I$%t{R $tI}tIt BP Y 8sRZ 1 *$%t{ 8sRZ PB8 PZ99$tRR 8sRZ qY 8sRZ BP Y I$&t{ BP bB PZ99k RZARR $R IhtI s-$B8s${sjjk Bt Y AsR$R BP Y PBjjBb$t tsZsj }B}$RU T y $R s tBtts$% stI Rk88${ PZt{$Bt BP Y bB PZ99k RZARR B A {B8}sI T y A{B8R 9B bYt Y bB RR {B$t{$I T y I{sRR sR Y bB RZARR A{B8 X8B R$8$js" $t RB8 RtR GYsR $ $R sRk B stsjk${sjjk PB8Zjs Y hR st Y R{BtI {BtI$$Bt Y Y$I Bt I}tIR Bt Y PB8sj$9s$Bt BP Y {Bt{} BP X8B R$8$js" G AsR BZ s}}Bs{Y Bt Y Ps{ Ys $P b sII w $t Y RtR BP Zt$Bt D s RZAR " g B ABY PZ99k RZARR " \ stI " 4  b BAs$t bB RZARR bY${Y s {jBR B s{Y BY Y Rs8 Ys}}tR b$Y Y $tR{$Bt 7B b }B}BR Y PBjjBb$t *ht$$Bt 1d w >MH D N  A Y Zt$%R stI j " h w  D A Y Ps8$jk BP Y PZ99k RZAR BP   V 8s} ; U " h w  D  " h w  D  {p $R s I$%t{ 8sRZ $P stI Btjk $P  " \, " 4 ; " h w  D  Rs$RPk Y PBjjBb$t {BtI$$BtRU d ; w " \, " 4 D ) ; w " 4, " \ D  1 ; w " \, " \ D )(  n 8s- \ ; w " \  " g, " 4  " g D ,; w " \  " g, " 4  " g D i ; w " \, " 4 D ,  " g ; " h w  D   " g ; " h w  D  V Y A$tt$t BP Y$R R{$Bt b Ys% $tI${sI Ys $ $R tsZsj B sRRZ8 Ys Y I$%t{ $R tBtts$% Y$R {BtI$$Bt YsR tB At $t{jZII $t Y s-$B8R R$t{ $ {st A IIZ{I PB8 Y8 3B8 tBb Bt b b$jj {BtR$I Btjk Y {sR bY  ) \ ? @ ,?  ,333,? z i $R ht$ yt Y$R {sR $P b {BtR$I Y {BZ}jR w " \, " 4 D , w " \ \ ? 7 i , " 4 \ ? 7 i D bY${Y 7B8 ]jsRRR BP *$%t{ sRZR bt 3Z99k 7ZARR 1xx Btjk I$& $t Y $ 0_ j8t w $ YsR At {YstI PB8 w " \ w ? 7 D , " 4 w ? 7 D D B w d , d D D  $ R8R tsZsj B RZ}}BR Ys Y %s$s$Bt BP I$%t{ Btjk I}tIR Bt bYs YsR At {YstI qYZR b $tBIZ{ Y PBjjBb$t *ht$$Bt 11 w >MH D V I$%t{ 8sRZ YsR Y jB{sj }B}k w B A$4k X$R jB{sj" D $P  " \, " 4 ; " h w  D ,  ? 7 ;   b Ys% Ys ; w " \, " 4 D  ; w " \ \ ? 7 i , " 4 \ ? 7 i D ) _ w " \ w ? 7 D , " 4 w ? 7 D D 3 qY$R }B}k $R tsZsj $t tsj AZ tB sjj I$%t{ YsR Y jB{sj }B}k V bsk B {Yss{$9 Y jB{sj I$%t{R $R $t Y PBjjBb$t Rs8t _B}BR$$Bt 1n w >MH D V 8s}}$t ; U " h w  D  " h w  D  {p  bY  $R s ht$ Ps8 ) \ ? @ ,?  ,333,? z i $R s jB{sj I$%t{ $P stI Btjk $P Y -$RR s PZt{$Bt _ U>( , dH  >( , dH  {p RZ{Y Ys ; w " \, " 4 D ) z ! 7 @ _ w " \ w ? 7 D , " 4 w ? 7 D D stI $ D _ w ?,r D ) _ w r,? D ,  ?,r ; >( , dH  $$ D _ w ?,? D )( ,  ? ; >( , dH  $$$ D _ w ?,F D  8s- \ _ w ?,r D ,_ w r,F D i ,  ?,r,F ; >( , dH b$Y ?crcF  qY }{I$t }B}BR$$Bt sjjBbR ZR B {BtRZ{ jB{sj I$%t{ PB8 s bBT R$I PZt{$Bt _  7B8$8R RB8 I$ ^{Zj$R 8sk s$R $t %$Pk$t {BtI$$Bt $$$ D  7B b RsI Y PBjjBb$t ]BBjjsk 1; w >MH D ]BtI$$Bt $$$ D $t _B}BR$$Bt 1n {st A }js{I Ak $$$ 1 D _ w N ,r D $R s PZt{$Bt I{sR$t $t >( ,r H stI $t{sR$t $t > r, dH  qY hR bsk b {YBBR B {B8}s Y 88ARY$} %sjZR $R Ys BP {B8}s$t Y PZ99$tRR BP ABY " \ stI " 4 b$Y Y PZ99$tRR BP Y $t8I$s PZ99k RZAR qY$R jsIR B s b$I {jsRR BP 8sRZR yt Ps{ Y$R bsR Y Rs$t }B$t BP BZ Rs{Y N ZR {BtR$I Y {jsRR BP PZ99$tRR 8sRZR >xH w BP jB{sj k} D $%t Ak W w " \ D ) ! ? % ;  ` w " \ w ? 7 D D 1xE 7 BtR m _ p$j bY ` U>( , dH  {p L $R s {Bt{s% PZt{$Bt $t{sR$t $t >( , d b 1H Rk88${ b$Y R}{ B Y }B$t d b 1 b$Y ` w ( D ) ` w d D )( qY tsB BP Y PZ99$tRR w PZt{$Bt ` D {st sjRB ts s jB{sj I$%t{ yt Ps{ Ak }BR$t _ w ?,r D ) ` M ? L r 1 9  ` w ? D L ` w r D 1 ,  ?,r ; >( , dH b BAs$t s PZt{$Bt _ bY${Y YsR sjj Y }B}$R JZ$I $t _B}BR$$Bt 1n $P ` $R b${ I$&t$sAj RB Ys ; w " \, " 4 D ) z ! 7 )d _ w " \ w ? 7 D , " 4 w ? 7 D D $R s jB{sj I$%t{ 8sRZ qB }B% Y$R $ $R RZ^{$t B }B% Ys _ Rs$RhR Y {BtI$$BtR $ D v$$$ D $t ]BBjjsk 1; yP ?,r s $t >( , dH b Ys% YsU $ D _ w ?,r D ) ` w ? L r 1 D  ` w ? D L ` w r D 1 ) ` w r L ? 1 D  ` w r D L ` w ? D 1 ) _ w r,? D ,  ?,r ; >( , dH $$ D _ w ?,? D ) ` w ? L ? 1 D  ` w ? D L ` w ? D 1 ) ` w ? D  ` w ? D )( $$$ D G ItB Ak _ r Y PZt{$Bt _ w N ,r D PB s h-I r  7$t{ _ r $R s RZ8 BP I$&t$sAj PZt{$BtR $ $R sjRB I$&t$sAj stI Yt{ _ r w ? D ) ` w ? L r 1 D  ` w ? D L ` w r D 1) p ( (?_ r w ? D )d 1 ( (?` w ? L r 1 D  ( (? ` w ? D 1 7$t{ ` $R {Bt{s% b Ys% Ys ( ! (? ! ` w ? D c ( ,  ? ; >( , dH stI YPB Y PZt{$Bt ( (? ` w ? D $R $t{sR$t bYt{ F ?cr ) p 1 N ?c? L r ) p ( (? ` w ? L r 1 D c ( (? ` w ? D ?kr ) p 1 N ?k? L r ) p ( (? ` w ? L r 1 D k ( (? ` w ? D 3 qYZR ( (? _ r w ? D $R ts$% $P ?cr stI }BR$$% $P ?kr  Y$R $8}j$R Ys _ r w ? D Ys$R _ w N ,r D  $R I{sR$t $t >( ,r H stI $t{sR$t $t > r, dH V }s${Zjs $8}Bst {sR BP Y$R k} $R $%t Ak Y 8sRZ BAs$tI PB8 Y * NZ{sTq8$t$ tB}k w >nH D  3Zt{$Bt _ BAs$tI PB8 $R ` PZt{$Bt  ? jB ?  w d  ? D jB w d  ? D $R I}${I $t 3$Z d y R8R B A %$It PB8 Y hZ Ys _ $t{sRR sR / ?  r / $t{sRR ss$tR $R 8s-$8Z8 s Y }B$tR w ( , d D stI w d , ( D w _ w ( , d D ) _ w d , ( D ) ` w d 1 D stI $R 8$t$8Z8 s Y }B$tR ? ) r w _ w ?,? D )( D D  7B8 ]jsRRR BP *$%t{ sRZR bt 3Z99k 7ZARR 1x 3$Z dU ps}Y${ BP _ w ?,r D  VR st -s8}j j ZR {BtR$I Y RZARR 4 \, 4 4, 4 g w R qsAj AjBb D BP st Zt$%R  b$Y PBZ j8tR IhtI Ak w YR RR s I}${I $t 3$Z 1 D   ? d ? 1 ? n ? ; 4 \ ( 3 n ( 3  ( 3 E ( 3 1 4 4 ( 3 1x ( 3 M ( 3 E ( 3 d 4 g ( 3 (x ( 3 ; ( 3  ( 3 x 4 ; ( 3  ( 3 d ( 3 d ( 3  3$Z 1U ps}Y${ BP 4 \  4 4  4 g stI 4 ;  1xM 7 BtR m _ p$j 3B YR RR b BAs$t Ys ; w 4 \, 4 4 D )( 3 (n ,; w 4 \, 4 g D )( 3 ;E ,; w 4 \, 4 ; D )d 3 E( 3 qY I$%t{ 8sRZR RYBb Ys 4 \ $R %k R$8$js B 4 4 stI JZ$ I$&t PB8 4 ;  WB${ Ys Y sARBjZ 8s-$8Z8 ; {st sRRZ8 $t Y$R {sR $R $%t Ak ; Ey? ); qY I$%t{ AsRI Bt * NZ{sTq8$t$:R tB}k {st A tsj$9I yt Ps{ $t >1H $ bsR }B%t Ys s PZ99$tRR 8sRZ {st A BAs$tI PB8 stk Zt{s$tk 8sRZ I  }B%$II $ Rs$RhR Y _$t{$}j BP qstRP yt Y$R {sR b {st Iht ` w 0 D ) I w 0, d  0 D stI Y I$%t{ 8sRZ s,R Y PB8 ; w 4 \, 4 4 D ) 3 ? ;  ^ I XX 4 \ L 4 4 1 ~ w ? D , X4 \ L 4 4 1 ~  w ? D ~  I w 4 \ w ? D , 4 \  w ? D D L I w 4 4 w ? D , 4 4  w ? D D 1  3 y $R sRk B {Bt$9 Ys $P ; $R {BtRZ{I sR sAB% PB8 s PZ99$tRR 8sT RZ Yt $ {st A -}RRI $t 8R BP PZt{$Bt W sR PBjjBbRU ; w 4 \, 4 4 D ) W w E w 4 \, 4 4 D D  W w 4 \ D L W w 4 4 D 1 D bY E w 4 \, 4 4 D $R Y Xs%s" BP Y RZARR 4 \, 4 4  Ys $R Y PZ99k R IhtI Ak E w 4 \, 4 4 D w ? D ) 4 \ w ? D L 4 4 w ? D 1 ,  ? ;  3 yt Y PBjjBb$t }B}BR$$BtR b RsAj$RY RB8 $8}Bst }B}$R BP Y$R {jsRR BP I$%t{ 8sRZR bY${Y -}RR tsZsj {Yss{$R${R BP Y 8st$t BP BZ 8sRZ 3B8 tBb Bt $t Y$R R{$Bt b {BtR$I Ys ; w 4 \, 4 4 D ) W w E w 4 \, 4 4 D D  W w  \ D L W w  4 D 1  bY W $R stk jB{sj PZ99$tRR 8sRZ _B}BR$$Bt 1x N " \ stI " 4 A $t " h w  D yP " \ $R RYs} Yst " 4 w / " \ w ? D  d b 1 / / " 4 w ? D  d b 1 / ,  ? ;  D Yt ; w " \, " \  D $R s Yst B JZsj B ; w " 4, " 4  D  Ys $R $P " \ U " 4 Yt ; w " \, " \  D  ; w " 4, " 4  D 3 _BBP 7$t{ W w " \ D ) W w " \  D  W w " 4 D ) W w " 4  D stI  \ L  \  1 w ? D )  4 L  4  1 w ? D ) d 1 ,  ? ;  Yt ; w " \, " \  D  ; w " 4, " 4  D 3 qY$R 8stR sR bBZjI A tsZsj Ys sR Y PZ99$tRR I{sRR Y I$%t{ Abt s R stI $R {B8}j8t $t{sRR y s,R Y 8s-$8Z8 bYt " \ $R {$R} BB% 7B8 ]jsRRR BP *$%t{ sRZR bt 3Z99k 7ZARR 1x _B}BR$$Bt 1E N .,~ A bB {$R} RZARR BP   Yt ; w .,.  D ) ; w ~,~  D 3 _BBP y $R $%$sj R$t{ W w . D ) W w .  D ) W w ~ D ) W w ~  D )( _B}BR$$Bt 1 yP b {BtR$I Y PZt{$Bt W  U " h w  D  {p IhtI Ak W  w " \ D ) ; w .,.  D  ; w " \, " \  D ,  " \ ; " h w  D , Yt W  $R s PZ99$tRR 8sRZ _BBP y $R $%$sj R$t{ W  {B$t{$IR b$Y W  _B}BR$$Bt 1M N . A s {$R} RZAR BP  qYt  " \, " 4 ;  b Ys% ; w " \, " 4 D  ; w .,.  D _BBP y $R s {BtRJZt{ Ys W w  \ D L W w  4 D 1  ( W w . D ) W w .  D )(stI W w  \ L  4 1 D  W w " o D ) W w . L .  1 D  bY " o $R Y JZ$j$A$Z8 Ys $R Y PZ99k RZAR IhtI Ak " o w ? D )d b 1 ,  ? ;  _B}BR$$Bt 1 qY I$%t{ Abt s PZ99k RZARR stI Y JZ$j$A$Z8 $R JZsj B Y I$%t{ Abt $R {B8}j8tsk stI Y JZ$j$A$Z8 Ys $R ; w " \, " o D ) ; w " \  , " o D ,  " \, " h w  D 3 BB% $P " \ U " 4 Yt ; w " \, " o D  ; w " 4, " o D 3 _BBP 3$R sRR$Bt $R s {BtRJZt{ Ys ` w ? D ) ` w d  ? D stI YPB ` w ? Ld b 1 1 D ) ` w w d  ? D Ld b 1 1 D  qY R{BtI Bt $R s {BtRJZt{ Ys Y }B}T $R BP 8BtBBtk stI Rk88k b$Y R}{ B d b 1 BP Y PZt{$Bt _ w ?,r D ) ` , ? L r 1 E  ` w ? D L ` w r D 1 w Is$jR {st A PBZtI $t >H D  VjYBZY $%$sj Y PBjjBb$t }B}BR$$Bt sjjBbR ZR B {Yst Y R{sj Ps{B BP s I$%t{ s{{BI$t B BZ }s${Zjs JZ$8tR 1E( 7 Bt R m _ p$j _B}BR$$Bt 1d( N * U {p  {p A s tBt I{sR$t PZt{$Bt b$Y * w ( D )(  qY 8s}R ; * ,; * IhtI AjBb s sjRB I$%t{ 8sRZR ; * w " \, " 4 D ) 3 ? ;  * X ` X4 \ w ? D L 4 4 w ? D 1 ~  ` w 4 \ w ? D D L ` w 4 4 w ? D D 1 ~ ; * w 4 \, 4 4 D ) * w ; w 4 \, 4 4 D D _BBP 3B ; * $ $R Btjk t{RRsk B }B% Ys * p ` D ? L r 1 i  ` w ? D L ` w r D 1 Q Rs$RhR Y {BtI$$BtR $t _B}BR$$Bt 1n qY }BBP B ; * $R $%$sj R$t{ PB sjj 4 \, 4 4 stI 4 g $t 4 h w  D b Ys% Ys * w ; w 4 \, 4 4 D D ) * w ; w 4 4, 4 \ D D  * w ; w 4 \, 4 \ D D ) * w ( D )( * w ; w 4 \  4 g, 4 4  4 g D D  * w ; w 4 \, 4 4 D D stI * w ; w 4 \  4 g, 4 4  4 g D D  * w ; w 4 \, 4 4 D D A{sZR BP ; A$t s I$%t{ 8sRZ * w ( D )(stI * A$t tB I{sR$t < b Ys% }B%t Y$R }B}$R PB Y$R }s${Zjs {jsRR BP I$%t{ 8sT RZ BAs$tI PB8 s PZ99$tRR 8sRZ AZ b {st R w >H D Ys 8BR BP Y8 s Z $t tsj PB sjj I$%t{ 8sRZ bY${Y YsR Y jB{sj }B}k n *$%t{ Abt }s$$BtR $tI}tIt BP Y 8sRZ yt Y$R R{$Bt hRjk b RZIk Y {Bt{} BP I$%t{ 8sRZ Abt }s$T $BtR sP b -tI Y PZ99$tRR 8sRZ B {sj{Zjs Y PZ99$tRR BP s PZ99k }s$$Bt stI htsjjk b }Rt Y {jsRR BP I$%t{ Abt }s$$BtR $tIT }tIt BP Y 8sRZ nd *$%t{ 8sRZ Abt PZ99k }s$$BtR y R8R jB${sj B Y$t, Ys Y I$%t{ Abt bB }s$$BtR I}tIR Bt Y I$%t{ Abt Y RR $t Y8 sR bjj sR Bt Y 8sRZ BP YR RR qYZR b Ys% {BtR$II Ys s RZ$sAj bsk sIs}I BP 8sRZ$t Y I$%t{ Abt bB }s$$BtR bsR YBZY s PZt{$Bt Ys I}tIR Bt Y I$%t{ IhtI $t Y }%$BZR R{$Bt stI Bt s }B}jk {YBRt 8sRZ BP Y RR $t Y }s$$BtR 7$8$jsjk B Y {jsRR${sj }BAsA$j$R${ I$%t{R b s B$t B {BtR$I st sA$sk R stI B {B8}s bB }BRR$Aj bskR w Rsk Y bB }s$$BtR RsAj$RYI Ak bB -} Bt Y B}${ D BP }s$$Bt$t $ $tB  PZ99k RZARR Ak R$t $P YR bB bskR s %k R$8$js B %k I$&t G b$jj P sjbskR B I$%t{R Abt }s$$BtR R$t{ Y$R $R Y 8BR $tR$t {sR PB ZR AZ $t Ps{ b s B$t B $% Y Iht$$Bt BP I$%t{ Abt Ps8$j$R qYZR $tRsI BP bB,$t b$Y Y R PB8I Ak sjj }s$$Bt $t  b s B$t B bB, b$Y Y R PB8I PB Y RkR8R BP  RZARR BP  Ys b b$jj ItB Ak " B T  7B8 ]jsRRR BP *$%t{ sRZR bt 3Z99k 7ZARR 1Ed 3$Rjk b Ys% B IB RB8 }%$BZR {B88tR jsI B Y bsk B s{{B8}j$RY Y 8s{Y$t Abt Y RR BP ABY Ps8$j$R B 8sRZ Y I$%t{ Abt Y8 yP b {BtR$I PB $tRst{ Y Iht$$Bt BP Y RR XOBZt" stI XWB OBZt" BP s 1x ksRTBjI }RBt stI BP s xx ksRTBjI }RBt $ $R {js Ys YR }s$$BtR s tB %k R$8$js 7Z}}BR Ys Y RZj BP Y$R JZR$Bt $R BAR%I $t 3$Z n 3$Z nU *ht$$Bt BP Y RR XOBZt" stI $R {B8}j8tsk Ak bB I$&t }RBtR y $R {js Ys b Ys% B {B8}s Y R " \ @ b$Y Y R " 4 @ stI " \  b$Y " 4   GYt Y$R BI B {B8}s$t $R tB h-I b Ys% B s}}jk Y _$t{$}j BP $t$8Z8 *$%t{ *ht$$Bt nd _$t{$}j BP $t$8Z8 *$%t{ w >H D N "  @ stI "   A bB Ps8$j$R $t " B T  PB8I Ak Y RR \ " \ % i T % @ stI \ " 4 % i T % @  R}{$%jk N ; A s I$%t{ 8sRZ Abt RR G Rsk Ys YR Ps8$j$R s BII $t s{{BIst{ b$Y Y _$t{$}j BP $t$8Z8 *$%t{ w ; D  $P stI Btjk $P PB sjj }8Zs$Bt  BP \ d , 1 ,333, i b Ys% Ys T ! % )d ; w " \ % , " 4 % D  T ! % )d ; w " \ % , " 4  w % D D ,  7 ;\ d , 1 ,333, i 3