Generalized Choquet-like aggregation functions for handling bipolar scales

Texte intégral

(1)Generalized Choquet-like aggregation functions for handling bipolar scales Christophe Labreuche, Michel Grabisch. To cite this version: Christophe Labreuche, Michel Grabisch. Generalized Choquet-like aggregation functions for handling bipolar scales. European Journal of Operational Research, Elsevier, 2006, 172 (3), pp.931-955. �10.1016/j.ejor.2004.11.008�. �halshs-00186907�. HAL Id: halshs-00186907 https://halshs.archives-ouvertes.fr/halshs-00186907 Submitted on 12 Nov 2007. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(51)

(52) . 5{)+*@'(%@*2gJv)6#?!"*i#0`?' J ¼8L N - #?*% 2 h Jv-'G!A@*@)?B#0()+* 3PJ M¼ L c:j!)

(53) %@*)?!Au")+,ac)+@*%#?F*i#0!`+ N - '@BAAi#0 4[JLD #?*% L v)?!A"FJL'?r¨1(,($#0HuDR)?jgJv)6F|#?`+"")+'K)0D8'")+"' ¼ N ½ 0 h N J{j%*@)?!j>dHk3 ¼ :vAj)+,ac)?*%u`+""!)? N ½ 0 '@BA6!Ai#q 4 DR)+ #0*% DR)+ N r N. .

(54)

(55)

(56)

(57)

(58) " ( "!# " %$'&G ($ £_,C#|H Pºy('I_*D- <#-ai#?I!(#?,*d_)?&"`+"*) h #?(% XEUP¹yO\WFM?SS(UP]?UPSTh 'FBA !Ai#0D J, + -) h !A"*DJt('L)?*'%F%;#0'´F2?)y)1%· h JLA@((D:J/.0) h !A@*DJt('. )+*'F(%""%;#?'C´F>i#0%·GDR)+8!Aj79kr ÿ@BA}#u*"@!#?<(P`+"Pºy('I!'JLA*@"`+"nF(#0!)+*+C v")+F'Fac)+*@%'!)ugJ{))+ay ac)+'FG*)?!)+*'p)0Dv")+,,C)+*6$#?*2?i#?2+0rm§i)+&Pº@#?,a( h !A'p('_AG|#0'GJLA*;C ,C#?*'´F,)+G#q!#?"`?K!Ai#?*@· h ´F>cP!Ai#0*· h "?r h JLA)+'ai#?')?Dv)+aaZ)+'F! *)?!)+*'=#?F8"'aZP!`?H´#0F!!#0"!`+"*'F'Bo0Fa'`+*@''F· h #0*%k´F2+)1)y%¸oq>i#?%·r:hvH )+*d!#?'F h "$#0()+*@'_'@BAk#0' ´F,)+n#?()xJ{"%6!Ai#0*· h ´F>Z)+*2+'&,C)?n)|#q!2?)+FH !Ai#?*@·%@)C*)0L(#?HYº@A@(>#-*@@!#?b"`+"4r µ'F|#?8(''!#?%K!)p>Zj¬ [®i¢qSM?W D - i)+*d!#?(*''BAC#p*y!!#0(P`+lr ¹1Xi[®i¢qSM?W QxNM?S(U Ai#?'b*)L*"@!#?+"`+" h >@A#?'#(|#0'F(P`+" h 4rs?rt#?*"(,*d)+b"`?+%"*)?% #?('F)>dH e(/ * - e'BA!Ai#q J:C bDR)?L#?(` J N - 4r zA¬ [®i¢qSM?W *i#0)0D#8'F|#?(')?D^*9¤w<%">i#0B#0>( h "'aZ"$#?H&(*j;5879kr £g*;5879 h AK"F$#CA#x`?K!Am,C#?*(*@2.)?D='F)+,Cn/w(*%;)0D='!#0('FD\#0"!)+*r&zA s ¼ *@(aZ)+$#?t"a"'*d!#0!)+*C)0Dc"!F$#_"$#?'F'|#?Hj'"%C*;5879 Ai#?'<A(*y !FaPB#0()+*n)?D¸#'!#0('FD\#0"!)+*j%2+F0r<zAvgJv)p>Z)+*%@'<)?DA('e'#?(%a@("´F*)? '!#0('F%#q{#0((·p#?*%©Íac"FDRP!HG'!#0('Ii%·9`0#?(@'="'aZ"`?H?r=&)xJv"`+" h `?#0("' #?)+@*%.j#?F"(#?H´F>i#0%· h JLAF|#?'`0#?("'#?)+@*% #?F"(#?H´F2+)1)1%·rezA s ¼ E@*(aZ)+$#0'F|#?p|#0*.!Aw'>Z_'F*#?'{#m>ac)+(#?='#?( h JLA.DR)+v(*'IB#?*"_!A@ *@!#?=`0#?(@ . ru£g*}§¸@"H²ÿP!'mzA@)+IH h @*(*)?,'3R,C º@*2# *)+, )?*k!A@ (( g'#0!'Fi"%K'!i#0()+*@'<#?*%C# g")+*)+F, )+*GA8J{"( g'!#q!('Ii%-'F!#0!)+*'Ls¡ $:<#?F Pº@#?,a("'&)?D>(aZ)+(#?8)+aZ#0!)+F'#?aa(%u)AjDR@"H*wI`?#0s h lr{zA NPW!¢xQBQ ¢q]?UPW aZ)+(*dv(*@*(*)?,'{)?"'aZ)+*%'8)K!A_*@!#?c(P`+c(*>@(aZ)+$#?'#?("'rze) ',Gga h 'F|#?'j'"%k*k;5879 #?*k>ZG`1("Jv%}#?'9!A"*(aZ)+(#?p)+>ac)?$#? %G!)AGai#?I!("$#0_,|#?**2u#?()?%!)u!A"'G'F|#?'rKÿ) h AGBA)+G)?D=!A@ gHyaZ9)?De'#?(p%@aZ*%'L,)+_)+*!ABA@)+(")?D!AF"DRF*"9ac)+*d!'8'F% )+*u!A@ #0(>@@!"'&!A#?*6!A@m!FK,|#?**2)?D!AK#0(>@@!"'r ,kK#0%@`+)1|#0m!A@K'm)?D >(aZ)+$#0<'#?("'DcA79 >c"Ai#|`+'v%cF*d!HKJLA"*CD\#?"%-!)J{"( g'!#q!('Ii%-")+,- ai#?"%)C( g'!#q!('Ii%C`?#0("'r=7p!)-")+,C,*@'#0!"*'F'&>Z"gJv"*;F!"(# h )+*@ 'A)+@(%.@'&A'!#?,L'|#0(m3l#?*%!Aw'!A'!#?,LPDR"*_("`?'B:<)+*#0(iF(#@r zA('<'F2+2+"'F'=Ai#0D¸)+*8#0(>@@!v¤w"'=#_>(aZ)+(#?t'F|#? h #0(y#0(>@@!"'*"% !) >cG|#q!%#?'9>ac)?$#?"> r ,k-#?''F,A@*""DR)+I!A!Ai#0j#0('F|#?'j#?FG>(aZ)+$#0r ,}9,C#?/?!A@n#0''@,Ca@()+*uAi#0!A@j*@@!#?b"(,*d' ePºy'F)+*#?(E'|#0('"r. 1. 2). 3. 0). . . ³. ).

(59)

(60) . . . ! #. %$'&G *$. $ " "$ . "$ . £g*65{)1)+aZ#0!`+ 9#?,C&zA)?FH h #G2d#0,Cp)?* 2('8%Pi*"%;#?'#G'F"DR*P!)+*!Ai#q `?#0*('FA'K)?*}!AC,a@gHk'"r b"

(61) . 3 26:j>ZC!A@.'PG)?D#? bdM .UBQ 3l#0(')|#?("% [ _ZWB¢BiUP_W bdM .UBQ :s¡ c 3. . 3 26:4 3w¡BH £ ¼ E 3w:4 . _*¯(*d"'F(*2²'F>Z$#0'')?Dp2d#?,'.'CA;)+*"'CAi#0u#0;*)?*yg%"F|#?'F(*2©#0*% *)+,C#?("%f3 . . 3 26:4. N. . . . 3 2;: ¼ Z. . 2 ¼ 3 :3 :L#0*%E3 2;:4. . . . d=,*d!'e)?D . 3 2;:#?=|#0(("% NMP@M1NP[Ôl[4UBQ xy)?e"¤w`0#?*d!H TY¹

(62) .UMqQP¹yW!UBQ 04r. . g£ * 65879 h 3 :.('*d!FaP!"% #0'!A

(63) )x`+"!#?#?'F''F',*d)?D9!Af´F>@(*i#?IH1· `+P!)+)?D&'")+"'C)+*"F$#3 ¼ E:Yrÿ(*"u!Au'#?,C 'F|#?u('-'"%¦DR)?-#?( !"$##?*%¦DR)+G!A)+@a@.#?''F''F,C"*d h )+*Ai#?' 3w: 4 k#?*@%!3 2;: 4 r )+")x`+ h '*A('G")+,,C"*'#0!u'F|#?u('-#;'#0!'FD\#?P!()?*©'|#0(3\A@*"Ai#0' !A;DR)+()xJL(*@2},|#?**2 3 ´ O iU

(64) SM?W b1UPW6O iU ¬ UPOlOgUPW ·w: h µ('*)?*yg%"F|#?'F(*2r ÿP DR*"()+*@'&")+*'%F%;*;65879 #?A1@'_|#0ai#?!'r8&)xJ{P`+" h #?'LJvjJL(b'" $#0 h > g#?ai#?"!'#?FnF$#q!%!)C2d#?,'!Ai#qp#?Fm*"A*)+*y%"#?'*2.*)? *)+,C#?("%r . .

(65).

(66).

(67). zA.5{A)1¤w"m(*d!"2+!#?=)?D 43 . ¼ | | ¼ 0+: N ½ 0 %@"i*"%²J9r "rsru#2+#?,C N . 3 2;:8Ai#?'ADR)+()JL*2KYº@a@'F')+*© q3. 1 3

(68).

(69) . j3 6 3 : ¼ ?A?A? ¼ 3 7 : 9 : ¼ 34¡+: JLAF

(70) U3 4 -#?*%

(71) . %

(72) 3 ?A?A? %

(73) 0 Ir 0 ,kp'!#|H!Ai#q

(74) ¼$N ½ #0 NB¢ .¢qXE¢qOg¢qXEU D(

(75)

(76) LDR)+{6 #?*dH F¼ ^0 N 2krm£g*)?ApJv)+F%' h

(77) ¼ #?G")+,C)?*)?!)?*KDA"H;>c"()+*2C!) 34

(78) N ½

(79) .

(80) 3 ?A?A?

(81) 0 9 DR)+pA-'!#?,GaZ,m@B#0()+* rzAw' h ('9|#? DR)+,~3l¡+:v!A#0LDR)+)+,)+*)0!)+*9#0"!'

(82) ¼ JvnA#x`? 1 3

(83) :4 1 3

(84) : 1 3 :Pr ".

(85). 0. . ¼ | | ¼ 0d:4. (*)32 +. #. %$I.'&. (*) +4.

(86). . (*) ,+. ». (*) +5. (-). 6. +/. . 10. 0. (*) 7+. 98. ;:=<. 9. :. ?>. A@ (. (*) +D. (*) +D. 4. CB. 0. (*) 1+. FE. HG. FE. IG. FE. zA('=aF)+ac"FgH h #?(% NB¢ .¢qXE¢qOg¢qXi[4N&M R R [Ô\[^]x[Ô

(87) qh ('BAi#0!#?P!F('I!()0DcA&5{A)y¤wP (*d!"2+!#? h #?'_'FA)xJL*>dH6ÿBA,%("G lrp*"m!A@G5{A)1¤w"*d!2?!#?t#?"'_(/? #-Jv2+Ad!%'@, (*u|#0B A @ ( 3RDR)+L#G@ºy% 0 :Yr. b".'*)xJ. +2 `+;#0*¯#qºy()+,C#0(nF'I!|#0()+*)?D!A

(88) 5{A)y¤wPu(*d2+#?L)+* (*d!"F`0#?'F|#?'3R4rs?rj'|#0('_%"i*@%a

(89) !) #'A@D^9#?*@%

(90) %((#0!)+*¸:(*6AG)+*dPº1 )?D65879krbzA,.#?*;"'j)+,'pDRF)+, 6#0(BA#?Ls¡+³qlrG£9BAi#?!#0"!"'9!A@ 5{A)y¤wP.*d!2?!#?L#?'#?*#?2+2?2+#0!)+*²DR*P!()?**¦£ 0 rzA@('-"'CA#?'->c"*. .

(91) (,a)x`+"%©>dH²'F(*2#6Jv|#?/0-#qºy)+, s¡?4rf,kua"'*dGA('KBA#?!#?P!"(#0!)+*r ÿ(*"9LAi#?'L>Z"*%)?*9(*u!An;5879 )?*wPº1 h L)+*"F*'&)?*H.|#?ai#0("'r 5{)+*@'(%@K#DR*"()++ * V " 3t£ 0 H £ 3\(*@%Pºy%©>dH}#6|#0ai#?gH N . 3 2;:F: %%|#0%-!)!A@L#?2+2+F2d#0()+*G)0Dc"!F$#p)+*-*wI`?#0'#?("'r=ÿ) h V " 'A#?('#0!'FD^H ')+,9|#0')+*i#0>(")+*%!()?*'r.

(92) ' "!#$&%A3L§¸)? #?*dH ¼ . ¼ | | ¼ ' N . 3; 2 :'BA²Ai#0

(93) #4)( ,$I. * h JLA * . ¼ | | ¼ * ' N £ h jA)?(%' DR)+L#? N £ 0 ' V " 3 p:4 # * V ",+ 3 p: ,$I.. -

(94).

(95).

(96). !#$-%L('v¤w`?#0(*dv!)mAp(*|#0gH#0 º@)+, 2+`+*u*s¡+³lrzA('{$#0F!'F!#0!"' !Ai#0C!A";Yºy('F' ¡ 0 DR*P!()?*'aV L 3 £ H £ 3RDR)+C#? 2;:C'FBAµ!Ai#q V " 4 ( /. E3 :WV rv6#?F(BAi#0b,C)?`0#0'8A'#qºy()+,'!#|H1(*2-!Ai#q h *)+F%) /?"a²!A.#?2+2+F2d#q!()?*,)1%#?'n'(,a-#?'maZ)+''F(> h V " 3 :-3\P`+"*²!A)+@2+A}*)0. .

(97). *. *.

(98). . ((*@|#?{J9rsr|r p:{('L#?'F',%!)->c9(*#?{J9rsr|r cr !#$-%|#?*>ZuPºya(#?(*"%(*²!A@DR)+()JL*2J{#|H+r²£-'K'Fi#?(*¦65879 ) JLj#-#?ai#?"gA H #?'#G((*@|#?8")+,K>*i#0()+*u)?Dt,*dB#0FHu#?ai#?"!' grvÿBA (",C"*dB#?IH-|#?ai#0("')+F'Fac)?*%C)jgH1a|#?¸%"('F()+*-'I!!#q!2?('"r§i)+=(*'IB#?*@ h #gJv)0V#?%@%`+-#?ai#?"gH 0|#?*k>c-`1(PJ{"%©#?'n#)?*w`?Pº})+,m>(*i#q!()?*

(99) )?D8!A@ DR)+()JL*2G!AFmgH1aZ'p)0D<gH1a(#?t%@')+*;'F!#02+' 3Pº1!F,m(*d)+("!#?*"m#0*% !)+!#0*G>Z"gJv"*kgJv)"F$#3\|#?%@(*2.)u!A-,(*,K, #?*%

(100) !A@,C#qºy(,m, )?Db!AgJ{)m!"$#9'")+"'8"'aZP!`?H: h #?*%.%(PB#0)+'FA(a-J9r "rsr=#mF)+*rt |#?ai#0gHC|#0*#0(')m>c_JLFF!*.(*!",'{)?DAp*i#0*(,gH2d#?,'p 0 h '*2K!A@ )+0 >'m!#?*'IDR)+,r_!A"K%")+,ac)+'F()+*'n#?Fu#?('F);aZ)+''F(>

(101) 0lrÿ(*".!A@ 1 (",C"*dB#?IH%"('F()+*u'I!#0!"2+("'L#?_`?IH (*d!!`+&DR)?#-79 h )+*@pJ{)+@(% (/?_) %"i*@8!A#02+2+"2d#0()+*jDR*"()+* V ",+ DR)+tA'F'F!#02+'#?*@%G%%@8!A@8)x`+#?( DR*"()+B * V " >dH©#?aa@H1(*2!A'#?,%")+,ac)+'F()+*})6!A@ V ",+ s'rzA('KH1("(%' !#2-%ry£g*u!AYº#0,Cap)?D!A@p%")+,ac)+'F()+*.J9rsr|rAp*i#0*(,gH2d#?,' h !A@ )1"*d!'&,.#|Hu>Z9*2d#q!`? h JLABA6Pºya(#?(*@'8JLAwH)+*@nAi#0' * . ¼ | ¼ * ' N £ * !#2-%r. 3"454 64/ 78 9:;< =!#3>-% 3e§¸)?9#?*dH 0 #?*%aZ ¼ $N £ h.

(102) .

(103) Q ¼ Z N. 2. . <.

(104). . V " 3 p: Q@V " 3 : . . N . . 3 2;:.

(105) g£ *"#?'*2+*"'')?DAK#?2?2+"2d#0!)+*DR@*"()+*;'_#*#0!#?e¤w",C"*wG 04r £g*}65879 h #?e"!F$##0K2+`+"*

(106) )+*;!AG'#?,m)?,C,*'F!#q!K'F|#? h #?*@%A(' $#0F!_%a"'9AG'!#q!('ID\#?"()+*6%2+F-)?D=!A@-79krb&"* h Dv#?*#?F*i#0!`+ Ai#?'<>Z"F!ai#?F$#?w'F)+F'<!A#?*-#?*)?At)+* h !A"* ¥('taPDRF%G) )`?<#?BA !"()?*r*" h ¦('#0|#?'I#?'t2+)1)y%m#?' DR)+e!A{79 h ')_Ai#0 V " 3 p: Q@V " 3 :Pr zA('p' t#?P!)0)+a@(,C#?(gH+r ,kKAi#|`+G#0(#?%@H'"*;Ai#0p*@)+*yg%@F|#?'F(*2?*'F')?D #m2d#?,&'{#0(')F'Fi"%>dHCA_'#?,_#?F2+,*d|r£g*@#?'*2+*"''8)0 D V " #?*)+*@H >c9)+>@!#?(*@%uJLA* '*)+*y%"#?'*2r.

(107). .

(108). .

(109).

(110) . . : 4 5 6 -:;< !

(111) -% 3@§¸)?L#?*dH N . 3 2;: V " 3 ¼ c:4 E3 : Z 2r h h 0 §i)+b#{Jv2+Ad!"%n'F, V " 3 p:4 ( ,$I. 3 6 9 : h )+*|#?FH&Ai#?'Ai#0V " 3 ¼ 3 6 9 :K#0*%,)+Fu2+*"!#?H+V " 3 ¼ E:S4 ( 3 6 9 :S4 3 : h *%|#0(*2. . .

(112).

(113). . )?DEF!"(#p('=%"*%u#0'=A)`?#?(iP`?#0(i#0()+* . !Ai#0=AJv2+Ad{)0D#9)d#0(()+* )?D{A->(*i#0FH;`?")+.3 ¼ c:Pr-zAC#?'F'(2?*,C"*dn)0D8(,aZ)+F!#?*m)?D8")d#?(!)+*' )?DF(#'!(2?AwH

(114) (*/0%!)A.P`0#?(i#q!()?*DR@*"()+*a r ,k.)?>@B#?9 * ! &% *i#0!@!#?H+r. . < 4/ 6/ ; ; 4/ ! 4/<" 4 $# 6 1 % ; 6 ; 8! :$&%A3{§i)+.#?*dH! N . 3 26: h RD )+#0( 2 h ' * & h #0*%)( N £ h. . V " I3 3 *. ( c :4. t: ¼. G*(. ¼ c: *(. * V " 3. G. z AG(*d!"F`0#?'#?(K#?''F)y"$#0%6)u#.F)+* ('&2+`?*;a!)u#.aZ)+'F!`+n((*@|#? !!#0*'FDR)+F,.#q!()?*,+V3 $:4.- 1G0/ h JL!A1- & m#?*%,/ N £ ¡+¡4r§iF)+, #n,|#q 'F,*d'F!#?*%aZ)+*w h Ap#?2?2+"2d#0!)+*CDR@*"()+*C'Ai#?c>Z_'IB#?>@(_@*%{ac)+'F`+ ((*@|#?e!!#0*'FDR)+F,.#q!()?*' 3 V " 3 - . . G)/ . ¼ | ¼ -0 0 G)/0+: 42-`V " 3 . ¼ | | ¼ 0+: G)/ h JLAF+43 3E : 4.-53 G6/9'v!A@_!#?*'FDR)?,C#0!)+*#?a@a(%.)m!A_)`?#?(c"`0#?(#0!)+*r ÿ(*"_#0(i'#?("'{#0)+,,C"*'@!#0 h )+*,.#|HG)+*@H-#?a@aHGA&'#?,!#?*'IDR)+,C#q !()?* )#?('F|#?'ns¡+³ h (#?%(*@2K!) 3.

(115). V " 73 -.

(116). ..

(117). G8/. ¼ | ¼ -.

(118).

(119).

(120).

(121).

(122).

(123). 0=G8/:4.- V " 3 . ¼ | | ¼ 0d:. G9/. .

(124). ,

(125)

(126). 3ld:. zA-)+2+(*i#0#qºy)+, DRF)+, 6#0(BA#?*%(#0!"'p!Ai#qC3ld:_A)?(%'_DR)?9#?( 4 3 . h 0 | | h 0d: N £ h - & 6#0*%'/ N £ nruºy)+, ! $-%K'9Jv|#0/?m(*kA'*@' !Ai#0m3\d:{('F¤w(F%)+*H)+* !A9>*i#?IHu#?P!'r.

(127). ,k9Ai#|`+9!ADR)+()xJL(*2n"'Ks¡?0lr «. :4.

(128) 4. !. 6V "9. . M?X R ¢qXiS

(129) [ TT|¢qWnM?X

(130). ". . N. ). % M?X R ! :2-% [ T M?O\[(Q8UBQ ! 2-% !#3>&% !

(131) . Q3 2; :

(132) U @?M ]?U V " 3 :U4 " 3 p: T|q¢ WnM?S^S N £ 0 ª. 1

(133).

(134). + .

(135). ,kL*)xJ¯2+`?#9BA#?!#?P!"(#0!)+*)?DcA_5{A)y¤wP{*d!2?!#?@DR)?2+#?,C"'(*'I!#?%. )?D>Z(*@2."'F(P!"%6!)#?ai#?"('"r)+F)x`+"_J{m)+*'F(%"_)+*@H aZ)+'!`?n'F)+F'"r zA('n'FjJL(>c'F"DRDR)+n>@g#?ai#?"('"S r ,k.*w)1%"ACDR)+()xJL(*@2 #qºw ()+,'r9zA"'#?G'I!#?(2+AdFDR)+FJ{#?%

(136) ,)1%i#0!)+*')?Dv#qºy()+,' ! 2-% h !#3>&%n#0*% ! :$&%xr ,}9Yºy*%)+*H.!A@j(*#?gH#º@)+,)?*2d#0,C"'r.

(137) ' ! #! % 3 §i)+t#?*dH

(138) ¼ . ¼ | | ¼ ' N . 3 2;: 'BA²Ai#0

(139) +4)( ,$I. * h L J A * . ¼ | | ¼ * ' N £ h nA)+%'jDR)?n#0( 0 N £.

(140). .

(141). '. V " 3 p:4 #.

(142). * V ," + 3 p: . ,$I.. 3"454 64/ 7 :;< 0 1 4/ 4/ 5 ; !#3> . §i)+L#?*dHA N 3 2; : #?*%aZ ¼ $N £ h .

(143) .

(144) Q ¼ Z N. 2.

(145). %3 . . V " 3 p: Q@V " 3 : <. * 4/ 51< ; 6 < 4 ! 64/< 4/ # 6/= 4 ; ; 6 ! $ % 3i§ )+ #?*dH 3 . 3 6 2 : h DR+) L#0( 2 h * & h ?# *% ( N £ h . *(t: ¼ ( c:4. V " I3 3 * 6 V " 9 " [ TnM?X R ¢qXiS

(146) C[ TT|¢qWjM?X

(147) 4. !. . ?) . . G. ¼ c: *(. * V " 3. G. % ?M X R ! :$ QM?. O\[(Q8UBQ ! % #! 3> % ! & N 3 26 : :V " 3 p:4 " 3 : T|q¢ WmM?S^S N £ 0 ª +. 1

(148).

(149).

(150). . %. *-)+>'FI`+'n!Ai#0n#BAi#?!#0"!"|#0()+*)?Dv!A.5{A)1¤1@"n(*d!"2+!#?*k£ 0 DR)+ p 2d#?,'"'!'L>dHu"a$#0(*@2 !#$-%(* zA")+", ¡KJL!Au(*#?gHCJ9rsr|r#G2d#?,?r zAna@)1)?D'>i#?'F%)+*ADR)+()xJL(*2KF'Fr. !. T V 3d£ 0 H £ Q M?O\[(Q8UBQ 0 [ V [(QjXE¢qX R UBNPWBUMqQP[^Xgb-[^X £ [^[ µ V 3F3 * G*(t: ¼ ( : 4 * µ V 3 ¼ E:4G ( N £ !. . . (. T|¢qWM?X

(151). . 2 * &. M?X R.

(152) . V 3 ¼ c: N 6 ¼ 9 |T ¢qWnM?S^S [^[^[ . [^] V.3\ : 4 ?M X R VC3 : 4 : 4 3 : T|¢qWGM?S^S N £ 0 O iUPX V.3 V 3 ¼ c: T|¢qWnM?S^S . 2 ª . 1

(153).

(154). . .

(155). 2. iUPW!U}[(QGM

(156) NMP@M1NP[Ô

(157) 1b?[^]?UPX ¬

(158)

(159). . 3 : 4. zA'(",C,C#K('L#G'(2+AdL,)y%@i#0!)+*.)?Dt!ADR)+()xJL(*@2m)+*0r. !. !. . . U Mu[^X

(160) T V 3d£ 0 H £ QM?Ol[(Q8UBQ . V ([ QjXE¢qX R UBNPWBUMqQP[^Xgb-[^X £ 0 ^[ [ µ V 3F3 * G*(t: ¼ ( : 4 * µ V 3 ¼ E:4G ( N £ [^[^[ V.3 2 ¼ c: N 6 ¼ 9 T|¢qWnM?S^S [ . . . . (. T|¢qWM?X

(161). . 2 * &. M?X R. ^[ ] V.3\ :4 ?M X R VC3 :4 0 O iUPX V.3 :F4 3 : T|q¢ WGM?S^S N £

(162) iUPW!U²[(QM;NMP@M1NP[Ô

(163) b?[^]?UPX ¬

(164) 3 :F4 V 3 ¼ c: T|¢qWnM?S^S . 2 ª : 4 4 4 !6! 0 pzAK)?*H%E"*@K>Z"gJv"* b",C,C#?' #?*%¡Pºy"a@ !A&'I!F("()+*C)?D£ ('=!A&'(2?*.)?D (

(165) (* [^[ : r ,¶A*.Jv_F'I!"{)+'FD!)m#?"' 0 (*

(166) £ h ")+*%!)+* [^[ (* b",C,C#u¡('p@'%)+*@HJL!A

(167) aZ)+'F!`+m`0#?')0D (=r &*@"DR)? F!A h ")+*%!()?* [^[ * b,,.# ¡|#0*>ZG"a$#0%>dH

(168) )?*%()+* [^[ * ",C,C# r .

(169) 1

(170) . .

(171).

(172). 4 ! <zA@a@)1)?D1('b',C$#?¸!)8Ai#0)?DyzA")+", (*s¡?0+JLABA ("'j)?* b",C,C#¡yr",C,C#¡('9"a$#?"%AFC>dH b",C,C# rC)+")x`+ h Jv 'pA_%")+,aZ)+'!()?*.)?De#m2+#?,C(*C!F,C'v)?Db!A@p*i#?*@(,gH-2d#?,'"r§i*P!()?* V " JLAF

(173) u('L#G*#?*(,gHC2d#?,'!#q!('Ii'&#?E)?*%()+*@')?D b",C,C# r. : 4 4 4. b";';)?*%}A(''P!)+* >dH %"'"(>@(*2µA6#?">cP!A±#?a@a)d#0BA )+* *(aZ)+(#?='|#0('_s¡?0lr<zAp*wI`?#0i'|#0(_)?*.F)+* 'v2+`+"*.a.)K#jac)+'F`+ ((*@|#?m!#?*@'FDR)+F,.#0()+**+V 3

(174) R :4 - 0

(175) G / h 3RJLA- & #?*%8/ N £ &:n!Ai#q. *)+,C#?("'{!A@j'F|#??r=zA9*)+*1g*)+F,.#0(("%*d!I`0#?b'#?("'&#0)?*'FP!%(*y %aZ*%@*d!H¶3 [^XiO\WFM NPWY[ÔVUPWY[4¢qX ")+*'FP!)+*¸:Pr£g*²)+F%j!)yº}ACgJv)

(176) %2?"' )?DvDRF"%)+, - v#?*@6 % / )+*|#0BAk'F|#? h gJ{)PDRF*"C"`+"('!A#09Ai#|`+-!AG'#?, ,C#?*(*@2A)?2+A)+yG!AF!"(#

(177) #? (*d)1%"%r£('-#?'F',%¦!Ai#0GAF Pºy('I!'n#?*(",C"*dn%@*)?%>dH =JLABAk')+*@'(%@"%}#0'j")+,a(P!H;*@'!#0('I D\#?")+FHGDR)+=!A@_79 h #?*@%#?*,*d{%@*)?%>dH cAi#0(')?*'%F%#0'v2+)1)1% #?*%;")+,Ca@("H '!#0('FD\#0"!)?FH h "`?*

(178) D<,C)+Fm#q!#?"`?m,*d!'&)+@(%;Yº@'F_)+*. ). .

(179) !A'pac)?(*dp)?D=`1(PJ ¡?q4r9zAG'F|#?'9#?FK*)+F,.#?("%6>dH6'*2!AK#?aaF)+a(#0! !!#0*'FDR)+F,.#q!()?* ' + &')²#0'C!)k*@DR)?)?,C,*'F!#q!*@''.>cPgJ{"*µ!A@6(P`+"(' h !Ai#09' W."3 `.F: 4 ?A?A?`4 03 0+:_#?*% W."3 ._ : 4 ?A?A?`4 03 0+:PrmzA@('p,Ca("'&!A@ )`?#?(b")+,C,*@'#0!"*'F'&>Z"gJv"*6!A9"F$#@r ,knJL('m%cF*dpF"DRF*"G(P`+'&DR)+&>(aZ)+(#?'#?("'p>@&!AG#0aa)+#?BA JL((E>c'F(,($#0r. ).

(180) . . ). . #. $ " "$. %$'&G *$. "$ . z A.aF"`1()?'m'F"()+*kAi#?'j'A)xJL*#?*k(,ac)?FB#0*w9a@)+aZIgH)?D8!A@5{A)1¤w"m(*y !2?!#? h *i#?,H A ! -%a)+aZIgH h '#xH1*2¯!Ai#0

(181) DR)?#?*dH¬ [^XZM?W

(182) `+"")+ 3 ¼ c: h mA)+%'K!Ai#q " 3 ¼ 1 : 4 E3 :Yr²zA'G'A)xJL'G!Ai#q->(*i#0FH`+Y !)+F'u#?6a)?)?gH1ac;`?P!)+F'DR)+*ac)?$#?'#?("' h '(*@6A

(183) ,C)1%"&'.*d("H %",(*@% DR)+,!A9)x`+"!#?b')?j#?''F(2+*@% !)G!A"'9`+""!)?'r ze*@(*2!)j>ac)+(#?<'F|#?' h AL¤1@'F()+*.#?'"')?*CA)xJ!)j')?&#?*#0!`+' Ai#|`y*2 #©´F*@2d#0`?·3\lr 0rp>Z()xJ±!A@K*y!!#0(P`+"^:'F)+FG)+*;'F)+,Cm!"$# h * ai#?F("$#? OgUPWYXZM?W

(184) G]?UBNPOg¢qW!Q 3 ¼ » <¼ ) +l: h JLA)+'Fp)?,CaZ)+*"*w'v!#?/?`?#0("' )+* h » )+* h #?*%G'"JLA@0r8¨1"`+"!#?'F)+(@()+*@'#?9aZ)+''F(>?r zAiF'F)+*(')/0a !A

(185) DR)+F,K$#²)0D-5{A)1¤w"(*d!"2+!#034¡+:#?' 'r ÿ(*"A;5{A@)y¤wP(*d2+#?L)+,,K@'-JL!Aac)?'`?#qC*@!#?*'IDR)+,C#0!)+*' 3\4rs?rK#qºy()+, ! :$&%jYº1!*@%%!)#?*dH;`+"")+9)?D{'F)+F'!: h *) ai#?I!("$#0_`0#?( )?DtA9'#?(9|#0*a@$#|H #Gai#?I!("$#0{)?( h #?*%')G!A9>ac)?$#?FgH)?De!A9'#?(pJL( >c9(2?*)+"%r zA¦'")+*@% ')?(@()+* ') #02+2+"2d#0©'a#?!#0H ac)?'`?#0*% *@2d#0`? ')?'"r9_''F,(*2u#C'FH1,C,"FH(*!AK,)1%e>cPgJ{"*

(186) !A@Kac)?'`?K#?*%

(187) *@2d#q !`?&a#?F'v)?Dc!A&'#?( h Jvp#0(%-!)9!A@&'F)0g#?(% Q

(188) .UPO\WY[4N i ¢ ¹iUPO[^XiOgcU b?WFM?S s«0)? ÿ (aZ) '. (*d2+#?= 3. . .

(189). . 1 . .

(190)

(191).

(192) I. ".

(193) .

(194). 3 p: 354. . 1 3

(195). :» . ". 1 3

(196) : ¼ ". /

(197). JLAF #?*% #?FnF'Fac""!`+"H!Ajac)?'`?m#?*@%6*"2d#0!`+nai#?F'_)?D h 4rs?r 3 : 354 ,C#qºE3 ¼ d: h 3 : 3 4 ,.#ºE3I» ¼ d:YrfzA@;a)?ac"F!')?D!A@ ÿ ac) '. (*d!"2+!#?E(*u!An;5879DR!#0,CPJ{)+F/u#?Fj2?`+"* (*k h ³qlr zAm'FH1,C,"FH)?DAK#?>Z)x`+K,)1%e,.#|H>Zm*)?_'B#?>@(j(*;"F!#?(*'!i#q !()?*'_)?D%"'()?*;,.#0/1*2

(198) 3R?rs2r%"('F()+*6*%"('F/ )+_*@IB#?*dgH h JLA"K!A@ >c"Ai#|`y)+_)0D=(*%`1(%i#0('('D\#?(FHu%@c"*d_DR)+&2d#?(*@'_#?*@%;()+'F'"'B:Pr&z8`+"'/dH#0*% j#0A*,C#?**

(199) A#x`?KaF)+ac)?'%

(200) 'FBA#.2+"*#?(|#0()+*}s q h /w*)xJL*k#0'&!A@ ¹ G¹ SM?Ol[^]? U vW!¢xQgiUBNPO iUB¢q W

(201) ,C)1% 3.

(202). 1. .

(203).

(204). 3 :$3 4. 1 3

(205) ". . . :». 1 3

(206) : ¼ ". 3w:.

(207) 3. JLAF .&#?*% #0mgJv)u|#?a#?!("'r9§i)+&a)+aZI!'#?*@%

(208) BAi#?!#0"!"|#0()+*'_)?D !An5z,)y%" h J{jPDR!A9F|#?%"!)G!A9F"DRF*"'Ks h +« h h lr &'_#'(,aPº@#?,a(9JLA!A@jF(#-JL('FA)xJ h %"'a!n!'L2+"*#?(gH h !AK5=z ,)1%b,C#|HD\#?()CFaF'F*daF"DRF*"'p)0D<!An79 h JLA"*;)+,aPº (*d!"!#?P!()?*>Z"gJv"*k#q!F(>y!'L)1"rLze).2+`+9!An(*d!!)+*DR)+L!A' h J{n()1)+/ #0!AJ{#|Hu!F*i#?IH`+""!)?'&#?'F)+F%>wHuAn5z ,)y%"4r<&aaHy*23 d:v!)# !F*i#?IHu`+P!)+n3 ¼ » <¼ ) + : h Jv92+"3 3 : 4 " 3 ¼ :» " 3 ¼ : 4 ."3 :<» 3 : ¼ » =¼ ) + . 1. . . . . 1. . 1. . 3. *@8!A@vJ{#xHm#&*#?FH9`+"")+<('t'")+"%G('e)+,a(P!"H9%P!F,C*%m>wHj!A@vJ{#xH & ac)+'F`+#?*@%}*"2d#0!`+>(*#?FH;`?P!)+F'K#?FC'F)+F% h >@n)+*,.#|H;JL'Ak)A#x`? ,C)+FvDRF%@)+D , 3e')?,Cv(*d!"!#?P!()?*maA"*)+,*i#p")+%K)y"t>cPgJ{"*-!A{ac)+'F`+ #?*%}A.*"2d#0`+ai#?I!' h JLA(BA},.#|H

(209) `1()+(#0!GA.#0>c)x`+DR)+,m$#@a r hvHk#?*i#?)+2?H JL!Af*ac)?$#?'F|#?' h J{,C#xHµ'!#|H¯!Ai#qF*i#?FH¯`?P!)+F'6#?F

(210) !Aa)0!)?gH1aZ `+P!)+F'&)0DtA9>(aZ)+$#0{|#0' h #0*%'F)G!A9,)y%"'A@)+(% >Z9>i#?'"%)?* A9)x`+#?( ')?#?''F(2+*@%

(211) !)A,rnzA@('9#?,)+*d!'&!)u%Pi*#DR*"()+ * ²JLA@(BA#?''F(2+*@' !).#?BA;ai#0(j3 ¼ :)?D<%@('RF)?(*d'>'F"' ¼ 2 #*w,m>c"_(*}T» +¼ h JLABA ('nA'F)+Fu#?''F(2+*@%²!)!AC!F*i#?IHk`?")+ 3 ¼ » ¼ ) +l:Pr6£g * 3 ¼ : h !A9#0F!F(>@'* "DR"8!)G,|#?'F"% '!#0('FD\#0"!)+*u#?*@% A9#0F!>@'(* ) ,C#?'F% %''!#q!('ID\#?"()+*C!AF)+2+AAp(*@%`1(%@i#?Z@!(("' r _#0!#?c)+*@%()+*' #?=3 2 ¼ wU : 4 h =3 ¼ 2; : 4 » #?*@ % =/3 ¼ w : 4 h '*!A"{'*i#?*,CgH)+*m#?( !"$#y r &)xJ%@!)-%)+,(*i#0*")+*%!()?*' h L('L#0(')G*#0!#?E),CaZ)+'F_!Ai#q D h A*

(212) =3 ¼ : =3 ¼ :G3\,)+FG!"$#A#x`?.#u2+)1)1%

(213) ')?x: h #0*% =3 ¼ : Q3 ¼ :L3\,)+F!"$#pA#x`?_#9>i#?%'")+|:Pr<¯DR*@"!)+* '#0!'FD^H1(*@2 #?(EA'Fn")+*%!)+*'8'|#?(%#¬ [ NMP@M1NP[Ô

(214) r b"'L'IB#09A(',)+FpDR)+,C#?(H+r b". . . . . . . . . . . . . . . 3 2;: 4 6 3 ¼ : N 3 26:F=. . 3 2;: B. . 4 . 9 . . zAn2?*"!#?(|#q!()?*)?Dt2d#?,'(#?%'!)GA9*)?!)+* )?D8¬ [ bdM .U 3. 3 2;: 4 6 3 3 26: H £ ¼ =/3 ¼ wU : 4 9 >@g#?ai#?"gH

(215) ('L#G*)+F,.#0(("% #?*@%*)?*yg%"F|#?'F(*2-> g2d#?,. 3. 3 3 26: 4 N 3 3 26: ¼ =3 ¼ : 3 ¼ : ¼ 3 ¼ : Q=3 ¼ : ¼ =3 2 ¼ w: 4 #?*%=3 ¼ 26:4 » 9 _''!#0(%u|#0( h =3 ¼ :v)+F"'aZ)+*%'!)KA)x`+"!#?#?'F''F',*d&)?D!Ap*#?FH `+P!)+u3 ¼ » ¼ :Yr6zA"Yº@'F'n!Aw'K#?*²('F)+,)+aA@(', 3 3 26: H 6 » +¼ ¼ 9 h %Pi*%>dH 3 ¼ :4 3 ¼ » ¼ : 34³+: . . . . . <. . <. . F . . . . ) +. . . ¡. . . ) +.

(216) . .

(217).

(218) .

(219) . . . ¸§ )? 2 h (" f354 6 N £ 0 ¼ fQ¶ ¼ 8¯ 9 #0*% :3 4 6 » +¼ ¼ 9 r zAu5{A)1¤w"n(*d2+#?<J9r "rsr# >|#?a#?gHa@)+aZ)+'"%k*µ ='9*)xJ 2+ `?*r §¸)?L#?*dH 2 h N h. .

(220). . 1 3

(221) : 3 4 1 1 :Yr C3 1 ¼

(222).

(223) ¼ »

(224) : JLAF 3 1 : 354 zA=#º@)+,C#0!tDR)+*@%i#0!)+*p)?D1!A@Pºya"''F()+*j)?D 1 .

(225) E. FE. . ". 3. . J (q>c2+`+"*j*jÿP!)+* L rzA9#?'IHy,,"!F(_5{A)1¤1@"L(*d2+#? h !A ÿ (aZ) '{ *d!2?!#?c#?*%A95z ,)1% #?ai#?I!("$#0#?'"'{)?DE!A_5{A)1¤1@"*w2+#?J9rsr|r=#n>@g#?ai#?"gH?rzA'JL(i>Z 'A)xJL*6* zA)+F,' h ³G#?*% F'Fac""!`+"H+r ,k=*%9!A''P!)+*n>dH'F)+,>@(>()+2+#?aA|#?F,C#?/w'rt£g*n")y)?ac"!#0`+2+#?,C !A")+FH h "¤w`0#?*d)+*"a@'&A#x`?m>Z"*6aF)+ac)?'%ErvzA9iF'F&#0,a@'",') >c%!)7KrL§i('F*d!A#?j#?*% kr&6#?BA)x`+" h JLA)a)+aZ)+'F% OgUPWYXZM? W

(226) ]?¢qO\[^gX b bdM .UBQ #?'_#G2+"*#?(|#0()+*u)0D>*i#?IH`+)?(*2-2d#0,C"'m 0lr=zt"*i#?IHu`+)?(*22d#?,' #?DR*P!)+*'DR)+, 3 2;:8!) 6 » +¼ 9 '!#q!('ID^H1(*2#?)+*@%()+*')0D> g#?ai#?"!' Pºy"a@ =3 ¼ w: 4 @r hv(*i#?IH`+)?(*2

(227) 2d#0,C"'m,)y%"Au"'K)?D&#`?)?!JLA@* ')+,`?)?!"'.#?(*¦D\#x`?)+)?Dp!A@>(#0*%¥!A@)?A-`+)0!F'#?F6#02d#?(*@'F6s?04r zA,C#?*©((,!#0!)+*})0D_'FBA¥2d#0,C"''K!Ai#qA"H#?**)0CFaF'F*d%"'()?* 'G(*²JLA@(BA M ¬ QPOVUPXiO\[4¢qX ('-#?*#0!"*i#q!`?)+a@()+*²);!A 'Fi#?

(228) dUBQ #?*% XE¢ )+a(*@()+*'"rnzA@('(#?%"%k7KrE§i('F*d!A#?#?*%kkrb6#?BA)x`+"j)u(*d!F)y%@ OgUPWYXZM?W

(229) ]?¢qOl[^gX b bdM .UBQ qlr=zA'F9`?)?!*2G2d#?,'#?*u>Za@'F*d!"%6>dH #mDR*@"!)+*uJLA gJ{)6#?2+@,C"*w' h )+*-DR)+pA

(230) wUBQ `+)?'n#?*%!A@C)?A9)+*@-DR)?p!A XE¢ `?)?!"'"r zA('p")+*"a@J{#?'(,C!"%>dH!AKD\#?P_Ai#0pAK)+@a@p`0#?m>Z)+*2+'&)+*H) !A!#?*@2+ 6 » ?¼ 9 rzA('-Ai#0'>Z"*2?*"!#?("%>w] H j@r®kr h{(>i#?) UPOKM?S (* s³q h Hy%(*2GAn%@"i*!)+*)0DL¬ [ NB¢x¢BiUPWFM?Ol[^]?_ U bdM .UBQ r h{ g")y)+aZ#0!`+2d#0,C"''#0!'FD^H #?(")+*%!)+*'8)?D>|#?a#?!("'r zA2+"*#?(|#0()+*¥)?Dj|#?ai#0("'u(*f;5879 !)©>ac)?$#?C'|#0(' Ai#0'u>c"* |#?F("%)+@{(*%@aZ*%"*d!HC(*; #0*% 0lr<zAp")+*"a@L)?D¬ [®i¢qSM?W9NMP@M1NP[Ô

(231) (' %"i*@% (*; q#?'{#m)?a(&)?D|#0ai#?!' h )+*DR)+=!ApaZ)+'F!`+ai#?I#?*%.)+*_DR)+ !AG*"2d#0`+mai#?Fr h{(aZ)+(#?&#?ai#?"('_#?m'F!F(P!H¤w`0#?("*w&!)u> g#?ai#?"!' JLA*!An5{A)1¤w"&(*d!"2+!#0(''F%!)-(*d!"aZ)+$#q!_A'FjJv2+Ad!'n «04r. F

(232) . . . G>j|. *$ & " <" . * G. D. K . . FE. f. . . zAp%P!)+=)?Db#m&*@`+"'FgH%"(%"'{)+*C'F%*d'{JLA)G#?F_#0aaH1*2jDR)?v2+#?%y #0!n'F!@%("'_(*")+*)+,("'JLA@m')+,na@F¤w''DR)+, 'FBA)y)?#?FmF¤w(F%r ¨1!%@*d!'j#?FK(*%@%

(233) P`0#?(i#q!%#0)?%*2.!).,.#0A,C#0('K34;: h 'IB#0('F("'G34¨@: .

(234) ?# *%-$#?*@2+i#?2+v'/w(('L3e:Pr?zA@'A"!"$#&'I`+&#?'#p>i#0'('<DR)?#pa"'"(P!)+* )?DvAG|#0*%(%#0!"'rGzA->Z'Fj#?*%%i#0!"'p!A"*kA#x`?#?*(*d!"F`1(PJ JL!A#nFFH )+,ac)?'%m)?D¸,C",K>Z't)?DA&*@`+"'FgHj!)p#0''"''<A,)?!`?#q!()?*j*m'I!%@H1*2 )?*)+,('"r zAa@'F"()+*9F('@ac)+*9'F)+F(*28A|#?*@%(%i#q!'b)?*9A<!A@#0F!F(>@'"r zA'F.'")+"'m#0-)+,a@%DR)+, !A-,C#?/w'!A@"H)+>@!#?(*@%%F(*2u!A@((#?'F #?|#?%@,(6H?|#?"r zA|#0'("'FuJ{#|Hµ!)©aF'F(""uA

(235) |#?*@%(%i#q!'Jv)+%¶>c;) ¤wAi#0mAu,C#?/w'K#0u#?>Z)x`+u'F)+,CC!AF'A@)+(%'m)+*²!AA"u#0F!>@'r &)xJ{P`+" h )?*'A@)+(%©*@)?G'Fu'BA>i#?'F(F(C'* h DR)?m(*@'FB#0* h #;'I!%@*d !Ai#0Ai#0'v#Jv|#?/w*"''8*)?*L)+F'>@('`?FH-2?)y)1%-(*G!A)?A=)+*"'=%'FF`?' >c"(*2 aF'"(""!"%r-zA-`?#0("'pJ{-PDRF%!)#?'pA"'A)+%'j#?G*

(236) D\#?"j#?'Fa !#0()+*(P`+'r8ÿ)+F'_#?>c)x`?jA'Fm(P`+"('#?9!Aw')?*'%F%

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