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(2) Conjunction of conditions of DRs obtained from different DTs Candidate conditions. (3) Select candidate conditions having no conflict with any DR inferring the negative conclusion. (4) Construct common DRs using selected conditions.1=B <  f"'5ffMffP98xi,Previous Approaches (merging decision rules)-"Extension of Decision Matrix Methods (Inuiguchi 2004) - Extension of Decision Matrices Logic Function - Many approaches6M$ff'!b*byjPrevious Approaches zkPlanBackground and Aim Brief Review of Rough Set Analysis Previous approaches Merging decision rules Extension of decision matrix Proposed Approach Rough sets under multiple decision tables Rule Induction Conclusions and Future TopicJ49J38   bR Our Approach>Definition of rough set under multiple DTs Introduction of VPRS Permit the inconsistencies in each DT Agreement ratio: how many DTs support Permit the inconsistencies among DTs Unevaluated objects (objects doesn t appear in some DT but others) Discard such DTs in calculation of agreement ratio Use upper estimation of rough membership Definitions of rough sets A Numerical Example+&(%N\.+&($N  \  .  `Q-DTs described by condition attribute patterns.%   YJVariable Precision Rough Sets&Classical Rough Set Variable Precision Rough Set Large DT often includes noise RS analysis  weak 000000VPRS (Ziarko, 1993) is useful. 43,,2nlVariable precision rough set Under a large decision table: Lower Approximation small RS Analysis becomes weak. (1) Noise, (2) Absence of influential condition attribute(s) Variable Precision Rough Set Model: Accept some errors b [0, 0.5) Lower approximation Upper approximation Boundary region 0x 0x 7xTx%0x<"FF33$33E"FFB3FG FF%F.   PARough Sets under Multiple DTs l[Rough Sets under Multiple DTs m\Rough Sets under Multiple DTs n]Rough Sets under Multiple DTs o^Rough Sets under Multiple DTs ZKAgreement Ratio hWXAgreement Ratio (Discard DTs with  no data )"-"C [L^Agreement Ratio (Estimate values for  no data )"0" C UF  iX^Agreement Ratio (Estimate values for  no data )"0" C VGRough Sets under Multiple DTs _PdRS under Multiple DTs (Discard DTs with  no data )(3 " nRule inductiontDirect application of decision matrix The obtained conditions are not sufficient conditions of the conclusion part of DR. Modified decision matrix The obtained conditions are sufficient conditions but minimality is not guaranteed. Usual decision matrix The obtained conditions are sufficient and minimal.&@T`#`ZT`#`Z :`&SfT 8 hpRule inductionADirect application of decision matrix Modified decision matrixb& x&  fjYdRS under Multiple DTs (Discard DTs with  no data )(3 "rdRS under Multiple DTs (Discard DTs with  no data )(3 "sdRS under Multiple DTs (Discard DTs with  no data )(3 "D7Conclusions and Future Topics0Definitions of Rough Set under Multiple DTs Level of classification error and agreement ratio are parameters. Treatments of  no data : Discard the DT with  no data and Use the upper estimation of rough membership value Based on the rough set, we may induce decision rules common among DTs. Future Topics More study of rule induction based on the proposed rough sets Dominance-based approach: Group Decision LG@2h#ht+Thank you very much for your kind attention,,%E-mail: inuiguti@sys.es.osaka-u.ac.jp/gP   0` !3̙` Q.<ffff3` 3333fff` 3K=̙fff` 3fffff` ff3ff3` aNR>ff` 3fY33` 3f3f>?" dd@&3~?od3d(@n<)o6=n+7%', n?" dd@   @@``PR   = 7 ,`(p>>   t(    < #" `wTN  N000 0000n0f_-[ |  0L "e  Z000 0000n0f_-[ ,{ 2 000 ,{ 3 000 ,{ 4 000 ,{ 5 000ZbB  # BCE6FGIIQU*VWX @`@$ G"T 4 0C`B  s *Dg "<<P  s *޽h ?"` 3f3f___PPT10i. "+D=' $= @B +,___PPT9RpRR Profile-  0 D< (    <s  #" `p   N000 0000n0f_-[   0  "p`    R000 000000n0f_-[   0  "YFy   .  0  "`    F*   0В  "Y y   F* bB  # $ BCE6FGjIQU*VWX @`@$ G") 4 0CP  s *޽h ?"` 3f3f___PPT10i. "+D=' $= @B +z 0  D(  D D 0@  /7    Z*  D 0P  c 7   \* d D c $ ?8\   n D 0   u   Z000 0000n0f_-[ ,{ 2 000 ,{ 3 000 ,{ 4 000 ,{ 5 000Z D 6  /F    Z*  D 6  c F   \* H D 0af ? 3380___PPT10.86@=d  \8(  \ \ 0  /7    >*  \ 0  c 7   @*  \ 6  /F    >*  \ 6  c F   @* H \ 0af ? 3380___PPT10.;` 7 0L0  n(  x  c $    x  c $| S    R  C *Aj02055824 -7R  C *Aj0205466 Ro  Z 333 ?"6@ NNN?N O  dGraduate School of Engineering Science Osaka University, Japan E-mail: inuiguti@sys.es.osaka-u.ac.jpee"GH  0޽h ? 33___PPT10i.q5 +D=' $= @B +}  0 `$(  `r ` S  wTN   r ` S  M   H ` 0޽h ? 3f3f___PPT10i.Ty+D=' $= @B +  0 0(  x  c $<wTN  < x  c $<M < H  0޽h ? 3f3f___PPT10i.Ty+D=' $= @B +:  0 Q5I5B4(    6 "`}j  Questionnaire 1. How do you feel the design ? modern, classic 2. How is the functionality ? multiple, simple 3. How do you feel the size ? normal, compact 4. Do you accept it ? yes, no xA AA#AA!AA&AA   0 AS" e    R < CSet of ObjectsAr  S  wTN   #| DCC  #"."CDC  6  ?"`  C  Uyes  @@``  6D  ?"`   Xnormal  @@``  6(  ?"`   Xsimple  @@``  6,!  ?"`   Yclassic  @@``   69  ?"`D   Y3F3n  @@``   6B  ?"`  C  Uyes  @@``   6K  ?"`   Ycompact  @@``   6T  ?"`   Xsimple  @@``   6]  ?"`   Xmodern  @@``  6f  ?"`D   Y2F3n  @@``  6o  ? C Tno  @@``  6x  ?  Ycompact  @@``  6  ? Zmultiple    @@``  6  ? Yclassic  @@``  6  ?D Y6F3n  @@``  6  ? C Tno  @@``  6  ?  Xnormal  @@``  6$  ?  Xsimple  @@``  6,  ?  Xmodern  @@``  64  ?D  Y5F3n  @@``  6<  ?  C  Tno  @@``  6D  ?  Ycompact  @@``  6L  ?   Xsimple  @@``  6T  ?   Xmodern  @@``  6\  ?D   Y4F3n  @@``  6d  ? # C  Uyes  @@``  6  ?#   Xnormal  @@``   6  ?#   Zmultiple    @@`` ! 6|  ?#   Xmodern  @@`` " 6   ?D#   Y1F3n  @@`` # 6%  ? CC#  ^AcceptF  @@`` $ 6.  ?C #  \SizeF3  @@`` % 67  ?C#  a Function   F3  @@`` & 6<@  ?C#  _Design F3  @@`` ' 6I  ?DC#  XObject  @@``fB ( 6o ?DCCC`B ) 01 ?D# C# `B * 01 ?D C `B + 01 ?D C fB , 6o ?DCfB - 6o ?DCD`B . 01 ?C`B / 01 ?C`B 0 01 ?C`B 1 01 ? C fB 2 6o ?CCC`B 3 01 ?DC`B 4 01 ?D C `B 5 01 ?D C  6 BO vvv"  7Decision Table: Customer Evaluation of Audio EquipmentsF80G EE L ts~G GA# `, A B CDEXFbV53! [ @)c+} vhpV.0@`i m  B BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx  C lBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G $ D BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) d E 4B,CDEtF~S ^(;Nai|ADP,<@@` {G| F LBCDEF 3[33*U{-uea~a{rek# kBD@` ~   H X  ?"6@ NNN?NY@ IInformation TableEff  H[  ?"6@ NNN?NY @,$ 0 |$ Decision Table<fE  Hb  ?"6@ NNN?N]D ?OpinionEH  0޽h ? 3f3f& TIMING |45.6___PPT10.4ЖM+RZDB' $= @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =A@BBB B0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*+8+0+0 +S  0 NNP\!N(  r  S \<wTN  < r  S  <e < ( L ts~G # }d2  B CDEXFbV53! [ @)c+} vhpV.0@`i m   BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx   rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G *  BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j   :B,CDEtF~S ^(;Nai|ADP,<@@` {G   RBCDEF 3[33*U{-uea~a{rek# kBD@` ~    <8<  > Equipments  A  <<3"`c   :Quest.A   <\<3"`}g :Quest.A( L ts~G # F 2  B CDEXFbV53! [ @)c+} vhpV.0@`i m   BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx   rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G *  BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j  :B,CDEtF~S ^(;Nai|ADP,<@@` {G  RBCDEF 3[33*U{-uea~a{rek# kBD@` ~  ' 6$<"` 6DTA ( 6)<"` G  6DTA  <,<   IMany decision tables C $ B0<vq0 a-Getting opinions common among many consumers..Cd2  <f t)I  <(6< _ i7To know what kinds of Audio Equipments are successful 88A  6T2<"`M   Questionnaire 1. How do you feel the design ? modern, classic 2. How is the functionality ? multiple, simple 3. How do you feel the size ? normal, compact 4. Do you accept it ? yes, no xA AA#AA!AA&AA& 6<  #"2&6< * 68M<?, < Ky)=7, + 6V<?"` , Kc)=7, , 6`<?"`  Km)=7, - 6ti<?"`  Kc)=7, . 6r<?"`6  K7)=7, / 64|<?"`6   K6)=7, 0 6<?"`6   K5)=7, 1 6<?"`64   K4)=7, 2 6<?"`6a 4  K3)=7, 3 6d<?"`6 a  K2)=7, 4 6Ī<?"`6  K1)=7, 5 6<?"`6 hObj.)=7, 6 6<?"`   Kc)=7, 7 6<?"`   Kc)=7, 8 6D<?"`4   Kc)=7, 9 6t<?"`a 4  Km)=7, : 6|<?"` a  Km)=7, ; 6<?"`  Km)=7, < 6<?"` LDe)=7, = 6<?"`   Ks)=7, > 68??"`   Km)=7, ? 6??"`4   Km)=7, @ 6??"`a 4  Ks)=7, A 6"??"` a  Km)=7, B 6+??"`  Km)=7, C 64??"` LFu)=7, D 6=??"` ,  Kn)=7, E 6F??"` ,  Kc)=7, F 6P??"`4 ,  Kc)=7, G 6Y??"`a ,4  Kc)=7, H 6b??"` ,a  Kc)=7, I 6k??"`,  Kn)=7, J 6t??"`, fSi)=7, K 6t}??, <  Kn)=7, L 6|??, <  Ky)=7, M 6??,4 <  Kn)=7, N 6??,a <4  Kn)=7, O 6??, <a  Kn)=7, P 6??,<  Ky)=7, Q 6??,< LAc)=7,`B R 0o ?6<ZB S s *1 ?6<ZB T s *1 ?6 < ZB U s *1 ?6a <a ZB V s *1 ?64 <4 ZB W s *1 ?6 < ZB X s *1 ?6 < `B Y 0o ?6<`B Z 0o ?66`B [ 0o ?<<ZB \ s *1 ?,,ZB ] s *1 ?ZB ^ s *1 ?ZB _ s *1 ?ZB ` s *1 ?6 < ( L ts~G A# 6 2  B CDEXFbV53! [ @)c+} vhpV.0@`i m   BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx   rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G *  BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j  :B,CDEtF~S ^(;Nai|ADP,<@@` {G  RBCDEF 3[33*U{-uea~a{rek# kBD@` ~ XB @ 0D>@ P ]  N?1?"6@ NNN?NQ ,$D 0 Group Opinion Decision Rule If De= m and Fu= s then Ac= y N= G3333=G33H  0޽h ? 3f3f& TIMING |11.3___PPT10v.aw8+RwD' $= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*+8+0+0 +  0 0(  x  c $?wTN  ? x  c $?M ? H  0޽h ? 3f3f___PPT10i.Ty+D=' $= @B +`  0 `_?K_(  r  S lb wTN  b  YF  7   <B  3 |Y B  3 W 3B   3   B   3  B   3  Y B   3  B   3 P +| B  3  |B  3 | WB  3  Y  B  3 S  B  3  | B  3 | W B  3 SZ / B  3 |U W B  3   Y B  3  Y    X B CDEF >> Y o P 1 C    Hz Q '  j Q 8   n V = z m      ' > 0V Km g       V; _   b   > Y= %   t a P ? .v \ B ( hM0|uoiefaH^*\ YXX0Pp   &*.I6g?IT_lx 5 Q n  + .E B` Wz m= XX{ZQ^(diq{]5uP,3Ke{Y83Uw}`C6dV>v rCUh8&Mu|iYID;o/$ IvXC(  3[x2b`M8%NL"|Yunhc9`r^[[ n2 "K,6AMmZ5hxb/i9' ?XpW,C[ [j _ b iG q z  b - o . .k M | iD X G 9r ,+  O   l [ .k H e #])7Oju%PFxs8c5X/k4sR2K  .k @`@`@`@`@`@`=    BCDE F& 5 ~ y h Va H : . q ( N   .E #  + x  ccYY [} _1 c j rQ z .c ~ 7%3IBSgR{TM!Be=#l-ZC ONPaQ/ ;yN%_y*rS57:7~,riwb\YcYc.Bi{ _O%i2Z;a 9F R g z3   % w   r  k it f" ` X M0 A 2 !E   _  r8Q-cbU5Wm7l4P  n  f zYgR9F *uZP2"fO+l{B"^PW7mp35wb6m(-QrT w+!F2AM[X ` fj i k  N ;oC1l^#=%IMjTR$8IIXf7qz~ cc32/w*",7:7qV9*y_f<; Q[*Pc H  z q2 f X} I# 8 $t   q  xj'I%;Y^1=o;w7v3*u[B<ffM9= V q 6   7   ?   "N * /2c3c7^"Jl+uEf"lPF"u*Ft_KY: +f n  [ \ `j f n x[F+w5 TTu(m 6b6w#3Yp:Wv7 t X ^\ \v [ [ [ @`@`@`@`@`@`@`@`@` `   BBC9DEF B"9 @`-  BBC9DEF"B 9 @`-  XBCDEFTgv)=Rek#Z5HI6\&o !&+18=KW[`cgkortwxyyyxvrmixgpgkgghai[kOrB|6( $?U"d'm-s1w7y<zDyNuXpchn^xUJ>3& /DYlp]J@6+"oR.uV8&Kj|pdXMF=6.'  zu q lha$[0Y<XBXIYO[V]ddsp|w|}ztlaTE"/GXegZ:PG@:530+'!{qiaZTPKHECA@@@@AA$T@`C@B  3  S  B  3 t P B  3      B CDEF((   // --             Y\@`@`@`@`@`@`@`@` U  ! B CDEF((   // --             Y\@`@`@`@`@`@`@`@`RU 7  " B CDEF((   // --             Y\@`@`@`@`@`@`@`@`wU [  # B CDEF((----        Y\@`@`@`@`@`@`@`@`U   $ B CDEF((   // --             Y\@`@`@`@`@`@`@`@` U   % B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`  ^  & B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`R7^  ' B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`w[^  ( B CDEF((--,,        Y\@`@`@`@`@`@`@`@`^  ) B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@` ^  * B CDEF((   // --             Y\@`@`@`@`@`@`@`@`   + B CDEF((   // --             Y\@`@`@`@`@`@`@`@`R7 , B CDEF((   // --             Y\@`@`@`@`@`@`@`@`w[ - B CDEF((----        Y\@`@`@`@`@`@`@`@` . B CDEF((   // --             Y\@`@`@`@`@`@`@`@`  / B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`   0 B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`R 7 1 B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`w [ 2 B CDEF((--,,        Y\@`@`@`@`@`@`@`@`  3 B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`   4 B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`  5 B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`R 7  6 B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`w [  7 B CDEF((--,,        Y\@`@`@`@`@`@`@`@`   8 B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`  2 9 Z?? 8 :  ` b  ?? + AX$0GB ;  `Do??f  I~F `  `  <  b 9 B =  `Do??`  p B >  `Do??` ` F  ,Y  ?  1T B @  fDo?? 9 A  B CDEFo((   // ,,             Y\@`@`@`@`@`@`@`@`S" G,Y  K <<b  $ b  H  0޽h ? 3f3f___PPT10i.ü+D=' $= @B +(  0 2*F(  x  c $7b wTN  b   A # |A  ??txp_figM,$ SOURCE\documentclass{slides}\pagestyle{empty} \usepackage{color,ascmac} \begin{document} \definecolor{Blue1}{rgb}{0,0,0.3} \color{Blue1} \centerline{ \begin{tabular}{@{\ }c@{\ }|@{\ }|c@{\ }|c@{\ }|@{\ }c@{\ }|@{\ }c@{\ }|@{\ }c@{\ }} \hline \ Patient & Headache & Sneeze & Temperature & Muscle-pain & Flu \\ \hline p1 & no & no & very high & yes & yes \\ p2 & no & yes & high & yes & yes \\ p3 & yes & no & high & no & no \\ p4 & yes & yes & high & no & yes \\ p5 & no & no & very high & yes & no \\ p6 & yes & no & normal & no & no \\ \hline \end{tabular} } \end{document} 6EXTERNALNAMEtxp_fig" BLENDTrue0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600"TIMEOUT15&BOXWIDTH348(BOXHEIGHT576"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG False4BITMAPFORMAT png16m8 DEBUGINTERACTIVETrue0ORIGWIDTH628.8758PICTUREFILESIZE 69370  E  pA ?txp_fig"6@ NNN?N I-  N SOURCE2\documentclass{slides}\pagestyle{empty} \usepackage{color,ascmac} \begin{document} \definecolor{Blue1}{rgb}{0,0,0.3} \definecolor{Green1}{rgb}{0,0.5,0.3} \color{Blue1} \small \noindent $\mbox{Partition by Headache, Sneeze, Temperature, Muscle-pain}$ \vspace{0.1ex} \centerline{ $ \{\{p1,p5\}, \{p2\}, \{p3\}, \{p4\} \{p6\} \} $ } \vspace{-1ex} \noindent A Set of Flu=yes :\ $ X=\{p1,p2,p4\} $ \vspace{-2ex} \begin{screen} \noindent \begin{itemize} \item (\textcolor{Green1}Lower Approximation of "Flu=yes") $$ C_*(X)=\{x \in U \mid [x]_C \subseteq X \}=\{p2,p4\} $$ \item (\textcolor{Green1}Upper Approximation of "Flu=yes") $$ C^*(X)=\{ x \in U \mid [x]_C \cap X \neq \emptyset \}=\{p1,p2,p4,p5\} $$ \end{itemize} \end{screen} \end{document} 6EXTERNALNAMEtxp_fig" BLENDTrue0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600*TIMEOUT (none)&BOXWIDTH348(BOXHEIGHT551"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False4BITMAPFORMAT png16m0ORIGWIDTH490.8758PICTUREFILESIZE 76413l F NLb 331?"6@ NNN?NC6] ,$D 0 |Treatment of inconsistent dataB G f G G fH  0޽h ? 3f3f___PPT10v.ü+CD' $= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*F%(D' =-6B'blinds(horizontal)*<3<*F+8+0+F0 +F  0L0 ;;KV<;(  < O< 0$[b  e 8Rough Set (Pawlak/1982) Induce important attributes & rules 00from a Single Decision Table. bZ$Z ZZ$  x < c $0bb wTN  b  "| `^  V< #"."`G  < 6lb  ?"` 8 ^ 1  Sy  @@`` < 6ub  ?"`8 1  Sn  @@`` < 6}b  ?"`8 1  Ss  @@``  < 6b  ?"`h8 1  Sc  @@``  < 6xb  ?"`8 h1  Y3F3n  @@``  < 6b f ?"` ? ^ 8  Sy  @@``  < 6db f ?"`? 8  Sc  @@``  < 6b f ?"`? 8  Ss  @@`` < 6b f ?"`h? 8  Sm  @@`` < 6hb f ?"`? h8  Y2F3n  @@`` < 6b  ? # ^  Sn  @@`` < 6b  ?#  Sc  @@`` < 6b  ?#  Sm  @@`` < 6b  ?h#  Sc  @@`` < 6b  ?# h Y6F3n  @@`` < 6b  ? * ^ #  Sn  @@`` < 6b  ?* #  Sn  @@`` < 6j  ?* #  Ss  @@`` < 6 j  ?h* #  Sm  @@`` < 6j  ?* h#  Y5F3n  @@`` < 6!j f ? 1 ^ *  Sn  @@`` < 6+j f ?1 *  Sc  @@`` < 64j f ?1 *  Ss  @@`` < 6=j f ?h1 *  Sm  @@`` < 6Fj f ?1 h*  Y4F3n  @@`` < 6 Oj  ? F^ ?  Sy  @@``  < 6(Xj  ?F ?  Sn  @@`` !< 60aj  ?F?  Sm  @@`` "< 68jj  ?hF?  Sm  @@`` #< 6@sj  ?Fh?  Y1F3n  @@`` $< 6H|j  ? `^ F ZAcF  @@`` %< 6ąj  ?` F tSiF3  @@`` &< 6j  ?`F ZFuF3  @@`` '< 6j  ?h`F ZDeF3  @@`` (< 6(j  ?`hF pObj.  @@``fB )< 6o ?`^ ``B *< 01 ?F^ F`B +< 01 ?? ^ ? `B ,< 01 ?* ^ * fB -< 6o ?^ fB .< 6o ?``B /< 01 ?h`h`B 0< 01 ?``B 1< 01 ?``B 2< 01 ? ` fB 3< 6o ?^ `^ `B 4< 01 ?# ^ # `B 5< 01 ?8 ^ 8 `B 6< 01 ?1 ^ 1  7< 0Dj }Gs d \Decision Table20EE( L ts~G 8<A# `2 9< B CDEXFbV53! [ @)c+} vhpV.0@`i m  :< BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx  ;< rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G * << BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j =< :B,CDEtF~S ^(;Nai|ADP,<@@` {G >< RBCDEF 3[33*U{-uea~a{rek# kBD@` ~ ` ?< s *"`I" @< <j %!  b: lower approx. of a set of objects s.t. Ac= yes 22A$ ` A< s *f"`YA~" B< <j 5 b: upper approx. of a set of objects s.t. Ac= yes 22A$ ` C< s *"`Y D< <xj '! 4 A_l    T<  ,$D 0" F< 6j "`~   ,A G< 0j # I ODecision rule inductionE H< <j P   L - De= modern & Fu= multiple Ac= yes . - Fu= multiple & Si= normal Ac= yes & & & J_!A !A A"? I< H`j G(H  # E  ,Ah L< <j x5 ,$ 0 6Reducts {De, Fu} {Fu, Si}BG GG, S< <j  FSet of EquipmentsA7 U< Hj ?"6@ NNN?N ^j ,$D 0 M= (key) opinion of DMEH < 0޽h ? 3f3f & TIMING |45.6 ___PPT10} .4ЖM+nD ' $= @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L<%(D' =-o6Bdissolve*<3<*L<D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*T<%(D' =-o6Bdissolve*<3<*T<D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*U<%(D' =-o6Bdissolve*<3<*U<+p+0+L<0 ++0+U<0 +   0 $(  r  S 5j wTN  j  r  S +j T j    # |A  ??txp_fig/ ,$ SOURCE\documentclass{slides}\pagestyle{empty} \usepackage{color,ascmac} \begin{document} \definecolor{Blue1}{rgb}{0,0,0.3} \color{Blue1} \centerline{ \begin{tabular}{@{\ }c@{\ }|@{\ }|c@{\ }|c@{\ }|@{\ }c@{\ }|@{\ }c@{\ }|@{\ }c@{\ }} \hline \ Patient & Headache & Sneeze & Temperature & Muscle-pain & Flu \\ \hline p1 & no & no & very high & yes & yes \\ p2 & no & yes & high & yes & yes \\ p3 & yes & no & high & no & no \\ p4 & yes & yes & high & no & yes \\ p5 & no & no & very high & yes & no \\ p6 & yes & no & normal & no & no \\ \hline \end{tabular} } \end{document} 6EXTERNALNAMEtxp_fig" BLENDTrue0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600"TIMEOUT15&BOXWIDTH348(BOXHEIGHT576"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG False4BITMAPFORMAT png16m8 DEBUGINTERACTIVETrue0ORIGWIDTH628.8758PICTUREFILESIZE 69370   # |A& ??txp_fig Y(   SOURCE\documentclass{slides}\pagestyle{empty} \usepackage{color,ascmac} \newcommand{\ds}{\displaystyle} \begin{document} \definecolor{Blue1}{rgb}{0,0,0.3} \definecolor{Green1}{rgb}{0,0.5,0.3} \color{Blue1} \small %\centerline{\textcolor{red}{zl[LRk000el}} \centerline{\tiny \begin{tabular}{c|ccc|c} & p3 & p5 & p6 & $\wedge$\\ \hline & & & & \\[-1ex] & [H=no]$\vee$[S=yes] & & [H=no]$\vee$[S=yes] & \\ \raisebox{1.5ex}[0pt]{p2} & $\vee$[M=yes] & \raisebox{1.5ex}[0pt]{[S=yes]$\vee$[T=high]} & $\vee$[T=high]$\vee$[M=yes] & \raisebox{1.5ex}[0pt]{$\beta_1^{\rm Y}$}\\[1ex] & & [H=yes]$\vee$[S=yes] & & \\ \raisebox{1.5ex}[0pt]{p4}& \raisebox{1.5ex}[0pt]{[S=yes]} & $\vee$[T=high]$\vee$[M=no] & \raisebox{1.5ex}[0pt]{[S=yes]$\vee$[T=high]} & \raisebox{1.5ex}[0pt]{$\beta_2^{\rm Y}$}\\ \end{tabular} } \end{document} 6EXTERNALNAMEtxp_fig" BLENDTrue0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600"TIMEOUT15&BOXWIDTH348(BOXHEIGHT710"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG False4BITMAPFORMAT png16m8 DEBUGINTERACTIVETrue0ORIGWIDTH532.8758PICTUREFILESIZE 37155   pA ?txp_fig"6@ NNN?N q# n SOURCER\documentclass{slides}\pagestyle{empty} \usepackage{color,ascmac} \newcommand{\ds}{\displaystyle} \begin{document} \definecolor{Blue1}{rgb}{0,0,0.3} \definecolor{Green1}{rgb}{0,0.5,0.3} \color{Blue1} \small \textcolor{Green1} {\bf "F=yes"} $\qquad$ $C_*(X)=\{ p2,p4\}$ \end{document} 6EXTERNALNAMEtxp_fig" BLENDTrue0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600*TIMEOUT (none)&BOXWIDTH348(BOXHEIGHT551"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False4BITMAPFORMAT png16m(ORIGWIDTH2776PICTUREFILESIZE7169H  0޽h ? 3f3f___PPT10i.Ǽqq+D=' $= @B +O  0 f^(  x  c $j wTN  j  x  c $,j T j     # |A& ??txp_fig/p(   SOURCE\documentclass{slides}\pagestyle{empty} \usepackage{color,ascmac} \newcommand{\ds}{\displaystyle} \begin{document} \definecolor{Blue1}{rgb}{0,0,0.3} \definecolor{Green1}{rgb}{0,0.5,0.3} \color{Blue1} \small %\centerline{\textcolor{red}{zl[LRk000el}} \centerline{\tiny \begin{tabular}{c|ccc|c} & p3 & p5 & p6 & $\wedge$\\ \hline & & & & \\[-1ex] & [H=no]$\vee$[S=yes] & & [H=no]$\vee$[S=yes] & \\ \raisebox{1.5ex}[0pt]{p2} & $\vee$[M=yes] & \raisebox{1.5ex}[0pt]{[S=yes]$\vee$[T=high]} & $\vee$[T=high]$\vee$[M=yes] & \raisebox{1.5ex}[0pt]{$\beta_1^{\rm Y}$}\\[1ex] & & [H=yes]$\vee$[S=yes] & & \\ \raisebox{1.5ex}[0pt]{p4}& \raisebox{1.5ex}[0pt]{[S=yes]} & $\vee$[T=high]$\vee$[M=no] & \raisebox{1.5ex}[0pt]{[S=yes]$\vee$[T=high]} & \raisebox{1.5ex}[0pt]{$\beta_2^{\rm Y}$}\\ \end{tabular} } \end{document} 6EXTERNALNAMEtxp_fig" BLENDTrue0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600"TIMEOUT15&BOXWIDTH348(BOXHEIGHT710"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG False4BITMAPFORMAT png16m8 DEBUGINTERACTIVETrue0ORIGWIDTH532.8758PICTUREFILESIZE 37155.  # |A ??txp_fig% C< z SOURCE\documentclass{slides}\pagestyle{empty} \usepackage{color,ascmac} \newcommand{\ds}{\displaystyle} \begin{document} \definecolor{Blue1}{rgb}{0,0,0.3} \definecolor{Green1}{rgb}{0,0.5,0.3} \color{Blue1} \small \begin{eqnarray*} \beta_1^{\rm Y}&=&(\mbox{[H=no]$\vee$[S=yes]$\vee$[M=yes]}) \wedge(\mbox{[S=yes]$\vee$[T=high]})\\ & = & \mbox{[S=yes]}\vee(\mbox{[H=no]$\wedge$[T=high]})\vee (\mbox{[T=high]$\wedge$[M=yes]}) \\[0.5ex] \beta_2^{\rm Y}&=& \mbox{[S=yes]} \end{eqnarray*} \end{document} 6EXTERNALNAMEtxp_fig" BLENDTrue0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600"TIMEOUT15&BOXWIDTH348(BOXHEIGHT710"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG False4BITMAPFORMAT png16m8 DEBUGINTERACTIVETrue(ORIGWIDTH5168PICTUREFILESIZE 29923  # |A ??txp_fig m SOURCEv\documentclass{slides}\pagestyle{empty} \usepackage{color,ascmac} \newcommand{\ds}{\displaystyle} \begin{document} \definecolor{Blue1}{rgb}{0,0,0.3} \definecolor{Green1}{rgb}{0,0.5,0.3} \color{Blue1} \begin{screen} \begin{itemize} \item If [S=yes] then [F=yes] %\vspace{-2ex} \item If [H=no] and [T=high] then [F=yes] %\vspace{-2ex} \item If [T=high] and [M=yes] then [F=yes] \end{itemize} \end{screen} \end{document} 6EXTERNALNAMEtxp_fig" BLENDTrue0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600"TIMEOUT15&BOXWIDTH348(BOXHEIGHT710"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG False4BITMAPFORMAT png16m8 DEBUGINTERACTIVETrue(ORIGWIDTH4698PICTUREFILESIZE 29733H  0޽h ? 3f3f___PPT10i.Ǽqq+D=' $= @B +}  0 $(  r  S PBk wTN  k  r  S Bk e k  H  0޽h ? 3f3f___PPT10i.x#+D=' $= @B +  0 0(  x  c $Tk wTN  k  x  c $HUk M k  H  0޽h ? 3f3f___PPT10i.Ty+D=' $= @B +l  0 vvu(  r  S Zk wTN  k    6t\k "`/ m 6DTA  6dck "`  6DTA v <gk ' KMerge all decision tablesA( L ts~G w# A $ 2 x B CDEXFbV53! [ @)c+} vhpV.0@`i m  y BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx  z rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G * { BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j | :B,CDEtF~S ^(;Nai|ADP,<@@` {G } RBCDEF 3[33*U{-uea~a{rek# kBD@` ~  ~ <xmk P  > Equipments  A( L ts~G A# 32  B CDEXFbV53! [ @)c+} vhpV.0@`i m   BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx   rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G *  BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j  :B,CDEtF~S ^(;Nai|ADP,<@@` {G  RBCDEF 3[33*U{-uea~a{rek# kBD@` ~ ( L ts~G # 3 2  B CDEXFbV53! [ @)c+} vhpV.0@`i m   BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx   rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G *  BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j  :B,CDEtF~S ^(;Nai|ADP,<@@` {G  RBCDEF 3[33*U{-uea~a{rek# kBD@` ~   <uk  & R Analyze all DTs without mergence!!ALB  c $D v  <zk . % |<- We do not know how many consumers support each opinion.$=;CA/  <̀k < *  gHow many consumers support each opinion ? We may analyze the similarity and conflict among consumers.@ - -"--hA"  6@k ̙"`f 0 ,$D  0 Z"Rough Set Analysis of multiple DTs##G L 6Tk "` 6DTA}3 ]<n   #">2 ]jn   6k ? <  Kn)=7,  6Pk ?"`   Kn)=7,  6Xk ?"`   Ks)=7,  6`k ?"`^   Kc)=7,  6hk ?"` ^  K9)=7,  6pk ? <  Ky)=7,  6xk ?"`   Kc)=7,  6k ?"`   Km)=7,  6k ?"`^   Kc)=7,  6k ?"` ^  K8)=7,  6k ?" <  Ky)=7,  6k ?"`"   Kn)=7,  6q ?"`"   Km)=7,  6q ?"`^"   Kc)=7,  6q ?"`" ^  K7)=7,  6 !q ?O <"  Kn)=7,  6<*q ?"`O "  Kc)=7,  6D3q ?"`O "  Ks)=7,  6L +Ke>~k+mPT@`sx   rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G *  BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j   :B,CDEtF~S ^(;Nai|ADP,<@@` {G   RBCDEF 3[33*U{-uea~a{rek# kBD@` ~    <dr   > Equipments  A( L ts~G A#  2  B CDEXFbV53! [ @)c+} vhpV.0@`i m   BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx   rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G *  BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j  :B,CDEtF~S ^(;Nai|ADP,<@@` {G  RBCDEF 3[33*U{-uea~a{rek# kBD@` ~ ( L ts~G #  ) 2  B CDEXFbV53! [ @)c+} vhpV.0@`i m   BCDEF''-)V3p^+i qx^QD> +Ke>~k+mPT@`sx   rBCDEF$$xGG>d g *'Tu{Z`*Rkax.X `MqZ*Kta,JL@`t G *  BC_DETF^X0o!@ b3r3 :2uR__K^X,0@` z ) j  :B,CDEtF~S ^(;Nai|ADP,<@@` {G  RBCDEF 3[33*U{-uea~a{rek# kBD@` ~   <Xr   i)- Decision rules (opinions) are obtained.$*(CA  <@r  ,$  0 N Group Decision MakingAH  0޽h ? 3f3f & TIMING |43.8 ___PPT10 .w m+,D ' r = @B D ' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+p+0+0 ++0+0 +?   0 V N  (  r  S q wN  r    S r 'i q   8haQ  H  f?"6@ NNN?N@ 4 |DT1: If De=m & Si=s then Pre=y & & If De=c & Fu=m then Pre=n??A-  H  f?"6@ NNN?N@~ 94 |DTk: If Fu=s & Si=s then Pre=y & & If De=m & Fu=s then Pre=n0?AA<A$ -  Hr  ?"6@ NNN?N]  8& C(   HTr  ?"6@ NNN?Nc J  81st in DT1 + 1st in DTk: If De=m, Fu=s & Si=s then Pre=yf9AIAAAA A,   HHr  ?"6@ NNN?Nf  f In some DT, if De=m & Fu=s then Pre=n In any Dt, there is no rule inferring the negative conclusiond'@'="/5H  0޽h ? 3f3f___PPT10i.?+D=' $= @B ++  0   "(  x  c $r wN  r    c $r '  r   8haQr  B f?"6@ NNN?N7   Ht ?"6@ NNN?Nm;T B In each DT  E  Nr  ?"6@ NNN?NP  TPositive elements in the DTEf     pA  ?txp_fig"6@ NNN?Nd   p SOURCET\documentclass{slides}\pagestyle{empty} \usepackage{color,ascmac} \newcommand{\ds}{\displaystyle} \begin{document} \definecolor{Blue1}{rgb}{0,0,0.3} \definecolor{Green1}{rgb}{0,0.5,0.3} \color{Blue1} \small %\centerline{\textcolor{red}{zl[LRk000el}} \centerline{\tiny \begin{tabular}{c|ccc|c} & p3 & p5 & p6 & $\wedge$\\ \hline & & & & \\[-1ex] & [H=n]$\vee$[S=y] & & [H=n]$\vee$[S=y] & \\ \raisebox{1.5ex}[0pt]{p2} & $\vee$[M=y] & \raisebox{1.5ex}[0pt]{[S=y]$\vee$[T=h]} & $\vee$[T=h]$\vee$[M=y] & \raisebox{1.5ex}[0pt]{$\beta_1^{\rm Y}$}\\[1ex] & & [H=y]$\vee$[S=y] & & \\ \raisebox{1.5ex}[0pt]{p4}& \raisebox{1.5ex}[0pt]{[S=y]} & $\vee$[T=h]$\vee$[M=n] & \raisebox{1.5ex}[0pt]{[S=y]$\vee$[T=h]} & \raisebox{1.5ex}[0pt]{$\beta_2^{\rm Y}$}\\ \end{tabular} } \end{document} 6EXTERNALNAMEtxp_fig" BLENDTrue0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600*TIMEOUT (none)&BOXWIDTH348(BOXHEIGHT551"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False4BITMAPFORMAT png16m0ORIGWIDTH445.8758PICTUREFILESIZE 28345   ZDt  f?"6@ NNN?N ` ,A    Ht  ?"6@ NNN?N SNegative elements in the DTEf l &@F  @&F ,$D 0I@ &@F  &@F @ SPF  SPF    H t ?"6@ NNN?NPF  ,AB  BD?"0@NNN?NSCCB  BD?"0@NNN?Nw`w    Hl ?"6@ NNN?NS`:4 Mq1 q3 q4 q5Gd  H|t  ?"6@ NNN?Npqv  L[H=n]v& & & & .& [T=h] [H=y] & & & & & . [M=n]''G !  H ?"6@ NNN?NS`  Ht  ?"6@ NNN?N&@t XNegative elements in other DTG"  Ht  ?"6@ NNN?NwpwW  db1D"  Htt  ?"6@ NNN?Nw w  db2D]  H@%t  ?"6@ NNN?NF - ,$ 0 s?After we obtain decision rules in all DTs, we take conjunction @@A&l -c  "-c ,$D 0.  H)t  ?"6@ NNN?N-   pDRs inferring negative resultsEB   NDԔ?"0@NNN?N  B ! NDԔ?"0@NNN?N c H  0޽h ? 3f3f  ___PPT10t .?+ dD ' $= @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-6B'blinds(horizontal)*<3<*"+8+0+0 +  0  6(  x  c $ht wTN  t  x  c $|Mt M t  H  0޽h ? 3f3f___PPT10i.Ty+D=' $= @B +  0 @,t(  ,r , S St wTN  t   , s *St  "6 ? t   , <hYt Id  ` Once we obtain lower and upper approximations, we may induce decision rules describing them.,1-0-aGr , H 3o?"6@ NNN?NP6 ,$D 0H , 0޽h ? 3f3fE=___PPT10. J+iD' $= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-o6Bdissolve*<3<*,+ p  0  oo #n(  " ! dAtxp_figIHu SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} \centerline{ $ \mu_C(w_3,yes)=\displaystyle\frac{}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }=\frac{1}{3} $ } \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATbmpmono0ORIGWIDTH578.8758PICTUREFILESIZE 55694r  S vt wTN  t  E#| P /   #"."4 |    64t ?"`P ! d  Lw6)=7,   64t ?"`P Nd!  Lw5)=7,   6đt ?"`P {dN Lw4)=7,   6`t ?"`P d{ Lw3)=7,  6̌t ?"`P d Lw2)=7,  6Xt ?"`P d Lw1)=7,  60t ?"`P /d Qpattern)=7,  6t ?"`d!   Km)=7,  6Ȱt ?"`dN!  Km)=7,  64t ?"`d{N Km)=7,  6dt ?"`d{ Kc)=7,  6lt ?"`d Kc)=7,  6tt ?"`d Kc)=7,  6|t ?"`d/ LDe)=7,  6Dv ?"`!   Km)=7,  6, v ?"`N!  Ks)=7,  6v ?"`{N Ks)=7,  6|v ?"`{ Km)=7,  6$v ?"` Km)=7,  6<.v ?"` Ks)=7,  67v ?"`/ LFu)=7,  6@v ?"`! )  Kc)=7,   6\Jv ?"`N)!  Kn)=7, ! 6Sv ?"`{)N Kc)=7, " 6]v ?"`){ Kn)=7, # 6|fv ?"`) Kc)=7, $ 6ov ?"`) Kc)=7, % 6 kv ?"`/) fSi)=7, & 6Ѕv ?)!   (0,1)H)=7, ' 6ԑv ?)N!  (1,2)H)=7, ( 6Dv ?){N (0,2)H)=7, ) 6v ?){ (1,2)H)=7, * 6v ?) (6,0)H)=7, + 6,v ?) (6,1)H)=7, , 6v ?)/ LAc)=7,`B - 0o ?P //ZB . s *1 ?P ZB / s *1 ?P ZB 0 s *1 ?P ZB 1 s *1 ?P {{ZB 2 s *1 ?P NNZB 3 s *1 ?P ! ! `B 4 0o ?P  `B 5 0o ?P /P `B 6 0o ?/ ZB 7 s *1 ?)/) ZB 8 s *1 ?/ ZB 9 s *1 ?/ ZB : s *1 ?d/d  < <v  @ k9Decision table described by condition attribute patterns::A = <v  T FUsual Decision TableAi3 7j   #">2 7j   6Lv ?"`Zl j?  Ky)=7,  6v ?"`Jl Z?  Kn)=7,  6v ?"`:l J?  Ks)=7,  6v ?"`l :?  Km)=7,  6!w ?"`7l ?  K7)=7,  6+w ?Z j  @)=7,  6D-w ?"`J Z  @)=7,  6=w ?"`: J  @)=7,  6HFw ?"` :  @)=7,  6Ow ?"`7   J& )=7,  6Ww ?Z j  Ky)=7,  6`w ?"`J Z  Kc)=7,  6iw ?"`: J  Km)=7,  6rw ?"` :  Kc)=7,  6|w ?"`7   K9)=7,  6w ?Z? j  Ky)=7,  6w ?"`J? Z  Kc)=7, ~ 6w ?"`:? J  Ks)=7, | 6w ?"`? :  Kc)=7, z 6w ?"`7?   K8)=7, D 6w ?"`7l  K6)=7, E 6w ?"`7 K5)=7, F 6w ?"`7 K4)=7, G 6w ?"`7  K3)=7, H 6,w ?"`7M  K2)=7, I 64w ?"`7zM K1)=7, J 6I4AAAA  ^A4txp_figP f (  SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ w_3 $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue&ORIGWIDTH754PICTUREFILESIZE990  ^Atxp_figg9 / `X SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ X=\{ yes\} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATbmpmono.ORIGWIDTH 99.8756PICTUREFILESIZE4586RB  s *Dj3 RB  s *D j3 f  0"`M P o  <z  VNumber of object in pattern w3 taking  yes ,,C " <z   SNumber of objects in pattern w3 CXr # 0V wYH  0޽h ? 3f3f___PPT10i.PHX+D=' $= @B +  0  l(  r  S T2z wTN  z  r  S 2z  z  f" 0 03"` 1 <4z ] qn X Classical RS defined by patterns!!E 2 dAtxp_fig2c SOURCEt\documentclass{slides}\pagestyle{empty} \begin{document} $ \underline{C}(X)=\{ w_i\in V_C|\mu_C (X|w_i)= 1 \}\\ \overline{C}(X)=\{ w_i\in V_C|\mu_C (X|w_i)> 0 \} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue0ORIGWIDTH320.8758PICTUREFILESIZE 34334` 3 s *"`c  " 4 <HAz 3"`(  ,A 5 <x?z  *  PVPRS defined by patternsE" 6 <Hz u be1: admissible level of classification error820Aj   vA ?txp_fig"6@ NNN?N C~ SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \underline{C}_{\varepsilon_1}(X)=\{ w_i\in V_C|\mu_C (X|w_i)\ge 1-\varepsilon_1 \}\\ \overline{C}_{\varepsilon_1}(X)=\{ w_i\in V_C|\mu_C (X|w_i)> \varepsilon_1 \} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG False6BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue.ORIGWIDTH 382.758PICTUREFILESIZE 41662H  0޽h ? 3f3f___PPT10i.{+D=' $= @B +f{  0L0 uzmz@::z(  :  3  c>:  3 s c :  3  c>p x  c $dnz   z  x  c $> Y o P 1 C    Hz Q '  j Q 8   n V = z m      ' > 0V Km g       V; _   b   > Y= %   t a P ? .v \ B ( hM0|uoiefaH^*\ YXX0Pp   &*.I6g?IT_lx 5 Q n  + .E B` Wz m= XX{ZQ^(diq{]5uP,3Ke{Y83Uw}`C6dV>v rCUh8&Mu|iYID;o/$ IvXC(  3[x2b`M8%NL"|Yunhc9`r^[[ n2 "K,6AMmZ5hxb/i9' ?XpW,C[ [j _ b iG q z  b - o . .k M | iD X G 9r ,+  O   l [ .k H e #])7Oju%PFxs8c5X/k4sR2K  .k @`@`@`@`@`@` /   BCDE F& 5 ~ y h Va H : . q ( N   .E #  + x  ccYY [} _1 c j rQ z .c ~ 7%3IBSgR{TM!Be=#l-ZC ONPaQ/ ;yN%_y*rS57:7~,riwb\YcYc.Bi{ _O%i2Z;a 9F R g z3   % w   r  k it f" ` X M0 A 2 !E   _  r8Q-cbU5Wm7l4P  n  f zYgR9F *uZP2"fO+l{B"^PW7mp35wb6m(-QrT w+!F2AM[X ` fj i k  N ;oC1l^#=%IMjTR$8IIXf7qz~ cc32/w*",7:7qV9*y_f<; Q[*Pc H  z q2 f X} I# 8 $t   q  xj'I%;Y^1=o;w7v3*u[B<ffM9= V q 6   7   ?   "N * /2c3c7^"Jl+uEf"lPF"u*Ft_KY: +f n  [ \ `j f n x[F+w5 TTu(m 6b6w#3Yp:Wv7 t X ^\ \v [ [ [ @`@`@`@`@`@`@`@`@`   BBC9DEF B"9 @` U   BBC9DEF"B 9 @` U   XBCDEFTgv)=Rek#Z5HI6\&o !&+18=KW[`cgkortwxyyyxvrmixgpgkgghai[kOrB|6( $?U"d'm-s1w7y<zDyNuXpchn^xUJ>3& /DYlp]J@6+"oR.uV8&Kj|pdXMF=6.'  zu q lha$[0Y<XBXIYO[V]ddsp|w|}ztlaTE"/GXegZ:PG@:530+'!{qiaZTPKHECA@@@@AA$T@` G :  3  kj :  3 n = :  3 r qL   B CDEF((   // --             Y\@`@`@`@`@`@`@`@` u   B CDEF((   // --             Y\@`@`@`@`@`@`@`@` u   B CDEF((   // --             Y\@`@`@`@`@`@`@`@` @$u   B CDEF((----        Y\@`@`@`@`@`@`@`@` dIu   B CDEF((   // --             Y\@`@`@`@`@`@`@`@` mu   B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`C    B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`C    B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`C@$  ! B CDEF((--,,        Y\@`@`@`@`@`@`@`@`CdI  " B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`Cm  # B CDEF((   // --             Y\@`@`@`@`@`@`@`@` 4 $ B CDEF((   // --             Y\@`@`@`@`@`@`@`@`4 % B CDEF((   // --             Y\@`@`@`@`@`@`@`@`@$4 & B CDEF((----        Y\@`@`@`@`@`@`@`@`dI4 ' B CDEF((   // --             Y\@`@`@`@`@`@`@`@`m4 ( B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`  ) B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`  * B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@` @$ + B CDEF((--,,        Y\@`@`@`@`@`@`@`@` dI , B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@` m - B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`m   . B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`m   / B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`m @$  0 B CDEF((--,,        Y\@`@`@`@`@`@`@`@`m dI  1 B CDEF((   // ,,             Y\@`@`@`@`@`@`@`@`m m 2 2 Z??  3  `zz  ??g  DjN0GOG 4 S Ad ?txp_fig"S  X SOURCE<\documentclass{slides}\pagestyle{empty} \begin{document} $$ \underline{A}_{\beta}(D_j)=\{ x \in U \mid \mu_{D_j}(x|A)\geq 1-\beta \} $$ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600*TIMEOUT (none)&BOXWIDTH348(BOXHEIGHT554"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono0ORIGWIDTH361.8756PICTUREFILESIZE7923 5 S Ad ?txp_fig"2 ^ SOURCEB\documentclass{slides}\pagestyle{empty} \begin{document} \begin{eqnarray*} \mu_{D_j}(x|A)=|[x]_A \cap D_j|\ \Big/\ |[x]_A|, \end{eqnarray*} \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600*TIMEOUT (none)&BOXWIDTH348(BOXHEIGHT554"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono(ORIGWIDTH3046PICTUREFILESIZE6459 6 S A"d ?txp_fig" L SOURCE0\documentclass{slides}\pagestyle{empty} \begin{document} $$ \overline{A}_{\beta}(D_j)=\{ x \in U \mid \mu_{D_j}(x|A)> \beta \} $$ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600*TIMEOUT (none)&BOXWIDTH348(BOXHEIGHT554"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono(ORIGWIDTH3246PICTUREFILESIZE7706N 7 S A)d ?txp_fig"  z SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $$ \underline{A}_{\beta}(D_j) $$ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600*TIMEOUT (none)&BOXWIDTH348(BOXHEIGHT554"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono.ORIGWIDTH 70.8756PICTUREFILESIZE2107: 8 # |A* ?txp_fig"p&Y7 x SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $$ \overline{A}_{\beta}(D_j) $$ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600*TIMEOUT (none)&BOXWIDTH348(BOXHEIGHT554"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono.ORIGWIDTH 70.8756PICTUREFILESIZE2122 9 S A,d ?txp_fig"v dV SOURCE:\documentclass{slides}\pagestyle{empty} \begin{document} $$ BN_A^{\beta}(D_j)= \overline{A}_{\beta}(D_j)-\underline{A}_{\beta}(D_j) $$ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION600*TIMEOUT (none)&BOXWIDTH348(BOXHEIGHT554"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono(ORIGWIDTH2916PICTUREFILESIZE7383 : # lLz d ?" iallowable error ratio80 Gf GfH  0޽h ? 3f3f3fy___PPT10Y+D=' $= @B + K  0 #JJ `I(  r  S lz wTN  z  ? `   #"2&#O  | 6 z ?   (3,0)H)=7, z 6 s *1 ?YY` ZB N s *1 ?II` ZB ^ s *1 ?  ` ZB o s *1 ?    <p   KAggregated Decision TableA  <莅 w N no data : No evaluation on the pattern((A^B  6 8   < %'  l:Example: DTs obtained from 4 consumers of Audio Equipments;;A  <  f44 Decision Tables aggregate them into a table55AX  0/j  6 "` _O  ~Condition attributes: Design (De): classic, modern Function (Fu): simple, multiple Size (Si): compact, normal Decision attribute Acceptance (Ac): yes, no!AA AA AA"AAEAEaH^  <,    @number of  yes number of  no !A E33AE33EA EAEA8 D"  "D   B?"6@ NNN?ND =   B?"6@ NNN?N=" H  0޽h ? 3f3f___PPT10i.RPFN+D=' $= @B +K  0 JJ`bd#J(  dx d c $ wTN   ? `  d# #"2& #O  d 6 ?   (3,0)H)=7, d 6H# ?"`^  (8,0)H)=7, d 6L҅ ?"` ^  (6,0)H)=7, d 6  ?"`Z   (8,0)H)=7, d 6P ?"`Y Z  Kn)=7,  d 6 ?"`I Y  Km)=7,  d 6T ?"`  I  Km)=7,  d 6# ?"`   Jw6)=7,  d 6 - ?"` `  Jw7)=7,  d 6(6 ?"`   Jw5)=7, d 60? ?"`   Jw4)=7, d 68H ?"`A   Jw3)=7, d 6@Q ?"`n A Jw2)=7, d 6HZ ?"` n Jw1)=7, d 6Pc ?"`  Opattern )=7, d 6Xl ?"`  I`  Kc)=7, d 6`u ?"`  I  Km)=7, d 6h~ ?"`  I  Km)=7, d 6p ?"` AI  Km)=7, d 6x ?"` nIA Kc)=7, d 6 ?"` In Kc)=7, d 6䢆 ?"` I LDe)=7, d 6` ?"`I Y`  Ks)=7, d 6 ?"`I Y  Km)=7, d 6 ?"`I Y  Ks)=7, d 6Ȇ ?"`IAY  Ks)=7, d 6ц ?"`InYA Km)=7, d 6@ۆ ?"`IYn Ks)=7,  d 6 ?"`IY LFu)=7, !d 6 ?"`Y Z`  Kn)=7, "d 6` ?"`Y Z  Kc)=7, #d 6 ?"`Y Z  Kn)=7, $d 6 ?"`YAZ  Kc)=7, %d 6 ?"`YnZA Kc)=7, &d 6 ?"`YZn Kc)=7, 'd 6 ?"`YZ fSi)=7, (d 6/ ?"`Z `  Qno data)=7, )d 6; ?"`Z   (0,1)H)=7, *d 6H ?"`Z   (1,2)H)=7, +d 6S ?"`ZA  (0,2)H)=7, ,d 6`_ ?"`ZnA (6,0)H)=7, -d 6dk ?"`Zn (6,1)H)=7, .d 6t ?"`Z MDT1)=7, /d 6 ? `  (6,0)H)=7, 0d 6 ?"`^ `  (2,0)H)=7, 1d 6@y ?"` ^ `  (9,1)H)=7, 2d 6L ?   (0,3)H)=7, 3d 6D ?"`^  (1,0)H)=7, 4d 6 ?"` ^  (1,4)H)=7, 5d 6@ȇ ?    (1,5)H)=7, 6d 64ч ?^   Qno data)=7, 7d 6܇ ?"` ^  (1,3)H)=7, 8d 6d ? A  Qno data)=7, 9d 6 ?"`^ A   (0,3)H)=7, :d 6H ?A^   Qno data)=7, ;d 6 ? nA (1,3)H)=7, d 6, ? n (1,4)H)=7, ?d 68 ?"`^  n (3,0)H)=7, @d 6D ?"`^ n (5,0)H)=7, Ad 6dM ?  MDT4)=7, Bd 6U ?^   MDT3)=7, Cd 6$_ ?^  MDT2)=7,`B Dd 0o ?ZB Ed s *1 ?ZB Fd s *1 ?nnZB Gd s *1 ?AAZB Hd s *1 ?  ZB Id s *1 ?  ZB Jd s *1 ?  `B Kd 0o ?` ` `B Ld 0o ?` ZB Md s *1 ?^ ^ ` ZB Nd s *1 ?  ` `B Od 0o ?` ZB Pd s *1 ?` ZB Qd s *1 ?ZZ` ZB Rd s *1 ?YY` ZB Sd s *1 ?II` ZB Td s *1 ?  ` ZB Ud s *1 ?   Vd <e   KAggregated Decision TableA Wd <k w N no data : No evaluation on the pattern((A^B Xd 6 8  Yd <i %'  l:Example: DTs obtained from 4 consumers of Audio Equipments;;A Zd <0t  f44 Decision Tables aggregate them into a table55AX [d 0/j \d 6r "` _O  ~Condition attributes: Design (De): classic, modern Function (Fu): simple, multiple Size (Si): compact, normal Decision attribute Acceptance (Ac): yes, no!AA AA AA"AAEAEaH^ ]d <T    @number of  yes number of  no !A E33AE33EA EAEA _d H?"6@ NNN?ND  `d H?"6@ NNN?N   bd B?"6@ NNN?N" H d 0޽h ? 3f3f___PPT10i.RPFN+D=' $= @B +pK  0 JJ ``hJ(  hx h c $H wTN   ? `  h# #"2& #O  h 6 ?   (3,0)H)=7, h 6T ?"`^  (8,0)H)=7, h 6ӈ ?"` ^  (6,0)H)=7, h 6ވ ?"`Z   (8,0)H)=7, h 6 ?"`Y Z  Kn)=7,  h 6| ?"`I Y  Km)=7,  h 6 ?"`  I  Km)=7,  h 6 ?"`   Jw6)=7,  h 6 ?"` `  Jw7)=7,  h 6@ ?"`   Jw5)=7, h 6 ?"`   Jw4)=7, h 6h( ?"`A   Jw3)=7, h 6 ?"`n A Jw2)=7, h 6: ?"` n Jw1)=7, h 6LC ?"`  Opattern )=7, h 6TL ?"`  I`  Kc)=7, h 6\U ?"`  I  Km)=7, h 6d^ ?"`  I  Km)=7, h 6lg ?"` AI  Km)=7, h 6tp ?"` nIA Kc)=7, h 6|y ?"` In Kc)=7, h 6 ?"` I LDe)=7, h 6 ?"`I Y`  Ks)=7, h 6 ?"`I Y  Km)=7, h 6 ?"`I Y  Ks)=7, h 6 ?"`IAY  Ks)=7, h 6 ?"`InYA Km)=7, h 6 ?"`IYn Ks)=7,  h 6 ?"`IY LFu)=7, !h 6ʉ ?"`Y Z`  Kn)=7, "h 6Ӊ ?"`Y Z  Kc)=7, #h 6܉ ?"`Y Z  Kn)=7, $h 6 ?"`YAZ  Kc)=7, %h 6 ?"`YnZA Kc)=7, &h 6 ?"`YZn Kc)=7, 'h 6 ?"`YZ fSi)=7, (h 63 ?"`Z `  Qno data)=7, )h 6h 6 ? n (1,4)H)=7, ?h 6 ?"`^  n (3,0)H)=7, @h 6G ?"`^ n (5,0)H)=7, Ah 65 ?  MDT4)=7, Bh 6pY ?^   MDT3)=7, Ch 6b ?^  MDT2)=7,`B Dh 0o ?ZB Eh s *1 ?ZB Fh s *1 ?nnZB Gh s *1 ?AAZB Hh s *1 ?  ZB Ih s *1 ?  ZB Jh s *1 ?  `B Kh 0o ?` ` `B Lh 0o ?` ZB Mh s *1 ?^ ^ ` ZB Nh s *1 ?  ` `B Oh 0o ?` ZB Ph s *1 ?` ZB Qh s *1 ?ZZ` ZB Rh s *1 ?YY` ZB Sh s *1 ?II` ZB Th s *1 ?  ` ZB Uh s *1 ?   Vh <i   KAggregated Decision TableA Wh <n w N no data : No evaluation on the pattern((A^B Xh 6 8  Yh <Pm %'  l:Example: DTs obtained from 4 consumers of Audio Equipments;;A Zh <w  f44 Decision Tables aggregate them into a table55AX [h 0/j \h 6Xv "` _O  ~Condition attributes: Design (De): classic, modern Function (Fu): simple, multiple Size (Si): compact, normal Decision attribute Acceptance (Ac): yes, no!AA AA AA"AAEAEaH^ ]h <܈    @number of  yes number of  no !A E33AE33EA EAEA ^h B?"6@ NNN?N D 6  _h B?"6@ NNN?N"   `h B?"6@ NNN?N" H h 0޽h ? 3f3f___PPT10i.RPFN+D=' $= @B +J  0 II0_`lgI(  lx l c $X wTN   ? `  l# #"2& #O  l 6 ?   (3,0)H)=7, l 6䗄 ?"`^  (8,0)H)=7, l 6Є ?"` ^  (6,0)H)=7, l 6@ ?"`Z   (8,0)H)=7, l 6 ?"`Y Z  Kn)=7,  l 6 ?"`I Y  Km)=7,  l 6 ?"`  I  Km)=7,  l 6D ?"`   Jw6)=7,  l 6, ?"` `  Jw7)=7,  l 6 ?"`   Jw5)=7, l 6| ?"`   Jw4)=7, l 6$ ?"`A   Jw3)=7, l 6<. ?"`n A Jw2)=7, l 67 ?"` n Jw1)=7, l 6@ ?"`  Opattern )=7, l 6\J ?"`  I`  Kc)=7, l 6S ?"`  I  Km)=7, l 6] ?"`  I  Km)=7, l 6|f ?"` AI  Km)=7, l 6o ?"` nIA Kc)=7, l 6l 6 ? n (1,4)H)=7, ?l 6 ?"`^  n (3,0)H)=7, @l 64% ?"`^ n (5,0)H)=7, Al 6 ?  MDT4)=7, Bl 67 ?^   MDT3)=7, Cl 6 @ ?^  MDT2)=7,`B Dl 0o ?ZB El s *1 ?ZB Fl s *1 ?nnZB Gl s *1 ?AAZB Hl s *1 ?  ZB Il s *1 ?  ZB Jl s *1 ?  `B Kl 0o ?` ` `B Ll 0o ?` ZB Ml s *1 ?^ ^ ` ZB Nl s *1 ?  ` `B Ol 0o ?` ZB Pl s *1 ?` ZB Ql s *1 ?ZZ` ZB Rl s *1 ?YY` ZB Sl s *1 ?II` ZB Tl s *1 ?  ` ZB Ul s *1 ?   Vl <DG   KAggregated Decision TableA Wl <lL w N no data : No evaluation on the pattern((A^B Xl 6 8  Yl <Q %'  l:Example: DTs obtained from 4 consumers of Audio Equipments;;A Zl <V  f44 Decision Tables aggregate them into a table55AX [l 0/j \l 6lU "` _O  ~Condition attributes: Design (De): classic, modern Function (Fu): simple, multiple Size (Si): compact, normal Decision attribute Acceptance (Ac): yes, no!AA AA AA"AAEAEaH^ ]l <h    @number of  yes number of  no !A E33AE33EA EAEA ^l B?"6@ NNN?ND  `l B?"6@ NNN?N" H l 0޽h ? 3f3f___PPT10i.RPFN+D=' $= @B +`I  0 wHoH@]_pH(  px p c $ؒ wTN   ? `  p# #"2& #O  p 6 ?   (3,0)H)=7, p 6 ?"`^  (8,0)H)=7, p 6 ?"` ^  (6,0)H)=7, p 6 ?"`Z   (8,0)H)=7, p 6(ɏ ?"`Y Z  Kn)=7,  p 6я ?"`I Y  Km)=7,  p 68ۏ ?"`  I  Km)=7,  p 6@ ?"`   Jw6)=7,  p 6H ?"` `  Jw7)=7,  p 6P ?"`   Jw5)=7, p 6D ?"`   Jw4)=7, p 6, ?"`A   Jw3)=7, p 6 ?"`n A Jw2)=7, p 6| ?"` n Jw1)=7, p 6$ ?"`  Opattern )=7, p 6<. ?"`  I`  Kc)=7, p 69 ?"`  I  Km)=7, p 6C ?"`  I  Km)=7, p 6 L ?"` AI  Km)=7, p 6U ?"` nIA Kc)=7, p 6^ ?"` In Kc)=7, p 6g ?"` I LDe)=7, p 6p ?"`I Y`  Ks)=7, p 6y ?"`I Y  Km)=7, p 6肐 ?"`I Y  Ks)=7, p 6 ?"`IAY  Ks)=7, p 6 ?"`InYA Km)=7, p 6 ?"`IYn Ks)=7,  p 6ঐ ?"`IY LFu)=7, !p 6诐 ?"`Y Z`  Kn)=7, "p 6 ?"`Y Z  Kc)=7, #p 6 ?"`Y Z  Kn)=7, $p 6ː ?"`YAZ  Kc)=7, %p 6Ԑ ?"`YnZA Kc)=7, &p 6ݐ ?"`YZn Kc)=7, 'p 6 ?"`YZ fSi)=7, (p 6l ?"`Z `  Qno data)=7, )p 6D ?"`Z   (0,1)H)=7, *p 68 ?"`Z   (1,2)H)=7, +p 6 ?"`ZA  (0,2)H)=7, ,p 6 ?"`ZnA (6,0)H)=7, -p 6, ?"`Zn (6,1)H)=7, .p 646 ?"`Z MDT1)=7, /p 6A ? `  (6,0)H)=7, 0p 6 N ?"`^ `  (2,0)H)=7, 1p 6Z ?"` ^ `  (9,1)H)=7, 2p 6|e ?   (0,3)H)=7, 3p 6q ?"`^  (1,0)H)=7, 4p 6\} ?"` ^  (1,4)H)=7, 5p 6 ?    (1,5)H)=7, 6p 6 ?^   Qno data)=7, 7p 6 ?"` ^  (1,3)H)=7, 8p 6` ? A  Qno data)=7, 9p 6 ?"`^ A   (0,3)H)=7, :p 6D ?A^   Qno data)=7, ;p 6lǒ ? nA (1,3)H)=7, p 6T ? n (1,4)H)=7, ?p 60 ?"`^  n (3,0)H)=7, @p 6 ?"`^ n (5,0)H)=7, Ap 6$ ?  MDT4)=7, Bp 6 ?^   MDT3)=7, Cp 6 ! ?^  MDT2)=7,`B Dp 0o ?ZB Ep s *1 ?ZB Fp s *1 ?nnZB Gp s *1 ?AAZB Hp s *1 ?  ZB Ip s *1 ?  ZB Jp s *1 ?  `B Kp 0o ?` ` `B Lp 0o ?` ZB Mp s *1 ?^ ^ ` ZB Np s *1 ?  ` `B Op 0o ?` ZB Pp s *1 ?` ZB Qp s *1 ?ZZ` ZB Rp s *1 ?YY` ZB Sp s *1 ?II` ZB Tp s *1 ?  ` ZB Up s *1 ?   Vp <4'   KAggregated Decision TableA Wp <, w N no data : No evaluation on the pattern((A^B Xp 6 8  Yp <t+ %'  l:Example: DTs obtained from 4 consumers of Audio Equipments;;A Zp <5  f44 Decision Tables aggregate them into a table55AX [p 0/j \p 6|4 "` _O  ~Condition attributes: Design (De): classic, modern Function (Fu): simple, multiple Size (Si): compact, normal Decision attribute Acceptance (Ac): yes, no!AA AA AA"AAEAEaH^ ]p <G    @number of  yes number of  no !A E33AE33EA EAEAH p 0޽h ? 3f3f___PPT10i.RPFN+D=' $= @B +f  0 Y~Y}Y(  x  c $  wTN   l  -   - ,$D 0n u 0"`tF   v <~  -  |Given e1=1/7, we obtain VPRS in each Decision Table. : Elements of lower approximation of a set of  yes p5C (AI-ABA? V  # #"2&F   6f ?Q   (3,0)H)=7,  6 ?"` Q  (8,0)H)=7,  6 ?"`[  (6,0)H)=7,  6ਓ ?"` [  (8,0)H)=7,  6 ?"`   Kn)=7,  6 ?"`   Km)=7,  6(ē ?"`   Km)=7,  6͓ ?"`   Jw6)=7,  64֓ ?"` V  Jw7)=7,  6<ߓ ?"`   Jw5)=7,  6D ?"`   Jw4)=7,  6L ?"`7  Jw3)=7,  6T ?"`d7 Jw2)=7,  6 ?"`d Jw1)=7,  6 ?"` Opattern )=7,  6 ?"` V  Kc)=7,  6| ?"`   Km)=7,  6( ?"`   Km)=7,  6H1 ?"`7  Km)=7,  6P: ?"`d7 Kc)=7,  6XC ?"`d Kc)=7,  6`L ?"` LDe)=7,  6hU ?"` V  Ks)=7,  6p^ ?"`   Km)=7,  6xg ?"`   Ks)=7,  6p ?"`7  Ks)=7,  6y ?"`d7 Km)=7,  6 ?"`d Ks)=7,  6 ?"` LFu)=7,  6 ?"` V  Kn)=7,  6 ?"`   Kc)=7,  6 ?"`   Kn)=7,  6 ?"`7  Kc)=7,  6 ?"`d7 Kc)=7,  6 ?"`d Kc)=7,  6D˔ ?"` fSi)=7,  6$Ԕ ?"` [V  Qno data)=7,  6ߔ ?"` [  (0,1)H)=7,  6` ?"` [  (1,2)H)=7,  60 ?"`7[  (0,2)H)=7,  6 ?"`d[7 (6,0)H)=7,  6 ?"`[d (6,1)H)=7,  6 ?"`[ MDT1)=7,  6 ?Q V  (6,0)H)=7,  63 ?"` Q V  (2,0)H)=7,  6@ ?"`[ V  (9,1)H)=7,  6DK ?Q   (0,3)H)=7,  6W ?"` Q  (1,0)H)=7,  6c ?"`[  (1,4)H)=7,  68o ?Q   (1,5)H)=7,  6Xy ? Q  Qno data)=7,  6̄ ?"`[  (1,3)H)=7,  6i ?Q 7  Qno data)=7,  6D ?"` 7Q  (0,3)H)=7,  6h ?[7  Qno data)=7,  6X ?Q d7 (1,3)H)=7,  6 ?"` dQ 7 (1,3)H)=7,  6ƕ ?"`[d 7 (0,1)H)=7,  6ѕ ?Q d (1,4)H)=7,  6ݕ ?"` Q d (3,0)H)=7,  6 ?"`[ d (5,0)H)=7,  6d ?Q  MDT4)=7,  6 ? Q  MDT3)=7,  6 ?[  MDT2)=7,`B  0o ?ZB  s *1 ?ZB  s *1 ?ddZB  s *1 ?77ZB  s *1 ?  ZB  s *1 ?  ZB  s *1 ?  `B  0o ?V V `B  0o ?V ZB  s *1 ?  V ZB  s *1 ?Q Q V `B  0o ?V ZB  s *1 ?[[V ZB  s *1 ?V ZB  s *1 ?V ZB  s *1 ?V ZB  s *1 ?V ZB  s *1 ?  l X  X ,$D  0n g 0"`Xx ln h 0"`Xx n i 0"`Xx n l 0"`  n m 0"`  n n 0"`  n o 0"`N nn p 0"`N `nn q 0"`N nn r 0"`N n n s 0"`n t 0"` ~  r   #"2&r ,$D 0  < ?r  RYes/no ?  )=7,  <! ?r RYes/no ?  )=7,  <* ?r> RYes/no ?  )=7,  <3 ?rk> RYes/no ?  )=7,  < % ?rk RYes/no ?  )=7,  <E ?r RYes/no ?  )=7,  <N ?r RYes/no ?  )=7,  <DW ?r V Lower approx  )=7,`B  0o ?rZB  s *1 ?rZB  s *1 ?rZB  s *1 ?rZB  s *1 ?rkkZB  s *1 ?r>>ZB  s *1 ?rZB  s *1 ?r`B  0o ?r  `B  0o ?rr `B  0o ? &l  )  ) ,$D 0` k 0j9 ` } 0d  <\  )  fWhich patterns should be in lower approximation of the rough set under multiple DTs? How may DTs support the membership ? We introduce Agreement Ratio. There is  no data . How can we define it ? (Discard vs. Estimate)tA AE A EA0AH  0޽h ? 3f3f  ___PPT10 .Y+TFcD ' $= @B Dq ' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+j  0 McEcPb(  Px P c $P 6 ?Q 7  Qno data)=7, ?P 6( ?"` 7Q  (0,3)H)=7, @P 6䭙 ?[7  Qno data)=7, AP 6 ?Q d7 (1,3)H)=7, BP 6 ?"` dQ 7 (1,3)H)=7, CP 6hљ ?"`[d 7 (0,1)H)=7, DP 6ܙ ?Q d (1,4)H)=7, EP 6X ?"` Q d (3,0)H)=7, FP 6 ?"`[ d (5,0)H)=7, GP 6H ?Q  MDT4)=7, HP 6 ? Q  MDT3)=7, IP 6 ?[  MDT2)=7,`B JP 0o ?ZB KP s *1 ?ZB LP s *1 ?ddZB MP s *1 ?77ZB NP s *1 ?  ZB OP s *1 ?  ZB PP s *1 ?  `B QP 0o ?V V `B RP 0o ?V ZB SP s *1 ?  V ZB TP s *1 ?Q Q V `B UP 0o ?V ZB VP s *1 ?[[V ZB WP s *1 ?V ZB XP s *1 ?V ZB YP s *1 ?V ZB ZP s *1 ?V ZB [P s *1 ?  f \P 0"`,L lf ]P 0"`,L f ^P 0"`Xx f _P 0"` f `P 0"` f aP 0"` f bP 0"`" Bf cP 0"``" Bf dP 0"`N nf eP 0"`N n f fP 0"`f gP 0"` \  rY  P #"2&rY ,$@ 0 jP <# ?rY  O3/3=1)=7, kP <, ?rY O4/4=1)=7, lP <t5 ?r>Y M1/4)=7, mP <? ?rkY> K0)=7, nP <|0 ?rYk K0)=7, oP <Q ?rY M1/4)=7, pP <Y ?rY M3/4)=7, qP <b ?rY W Lower approx.)=7,`B rP 0o ?rYZB sP s *1 ?rYZB tP s *1 ?rYZB uP s *1 ?rYZB vP s *1 ?rkYkZB wP s *1 ?r>Y>ZB xP s *1 ?rYZB yP s *1 ?rY`B zP 0o ?r Y `B {P 0o ?rr `B |P 0o ?YY  }P <Pg <#,$ 0 Bagreement ratio A0 P dA txp_fig   SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \underline{\tau}_{\varepsilon_1}(w_i,X)= $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATbmpmono0ORIGWIDTH122.8756PICTUREFILESIZE5886. P dAtxp_fig s SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \overline{\tau}_{\varepsilon_1}(w_i,X)= $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATbmpmono0ORIGWIDTH122.8756PICTUREFILESIZE58868 s =  Ps =   P <x wV =  %Number of DTs having evaluation on wi4&#AAI# P <z s Z  ,Number of DTs whose lower approx. include wi4-*AAI*TB P c $DV V F s =  P 9   P <؉ wV =  %Number of DTs having evaluation on wi4&#AAI# P < s Z  ,Number of DTs whose upper approx. include wi4-*AAI*TB P c $DV V H P 0޽h ? 3f3f___PPT10.Y+"D]' $= @B D' = @BA?%,( < +O%,( < +DO' =%(D' =%(DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B%slide(fromBottom)*<3<*PDR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*}P%(D' =-6B%slide(fromBottom)*<3<*}P+8+0+}P0 +G  0L0 BxBVB(  r  S dQ wTN   ? m   #"2&z  @ 6P ?  (3,0)H)=7, A 6е ?"`  (8,0)H)=7, B 6 ߚ ?"``   (6,0)H)=7, C 6 ?"`3 `  (8,0)H)=7, D 6ؚ ?"`2 3  Kn)=7, E 6 ?"`" 2  Km)=7, F 6 ?"`"  Km)=7, G 6D ?"`  Jw6)=7, H 6| ?"` m  Jw7)=7, I 6" ?"` Jw5)=7, J 6+ ?"`! Jw4)=7, K 64 ?"`N! Jw3)=7, L 6= ?"`{N Jw2)=7, M 6F ?"`{ Jw1)=7, N 6O ?"` Opattern )=7, O 6X ?"` " m  Kc)=7, P 6a ?"`"  Km)=7, Q 6j ?"`!"  Km)=7, R 6s ?"`N" ! Km)=7, S 6| ?"`{" N Kc)=7, T 6( ?"`" { Kc)=7, U 60 ?"`"  LDe)=7, V 68 ?"`" 2 m  Ks)=7, W 6@ ?"`" 2  Km)=7, X 6H ?"`" !2  Ks)=7, Y 6P ?"`" N2 ! Ks)=7, Z 6X ?"`" {2 N Km)=7, [ 6`ś ?"`" 2 { Ks)=7, \ 6hΛ ?"`" 2  LFu)=7, ] 6pכ ?"`2 3 m  Kn)=7, ^ 6x ?"`2 3  Kc)=7, _ 6 ?"`2 !3  Kn)=7, ` 6 ?"`2 N3 ! Kc)=7, a 6` ?"`2 {3 N Kc)=7, b 6 ?"`2 3 { Kc)=7, c 6 ?"`2 3  fSi)=7, d 6T ?"`3 ` m  Uno data)=7, e 6H% ?"`3 `  (0,1)H)=7, f 61 ?"`3 !`  (1,2)H)=7, g 6= ?"`3 N` ! (0,2)H)=7, h 6I ?"`3 {` N (6,0)H)=7, i 6U ?"`3 ` { (6,1)H)=7, j 6^ ?"`3 `  MDT1)=7, k 6i ? m  (6,0)H)=7, l 6Dv ?"` m  (2,0)H)=7, m 6b ?"`` m  (9,1)H)=7, n 6 ? (0,3)H)=7, o 6 ?"` (1,0)H)=7, p 6\ ?"``  (1,4)H)=7, q 6 ?! (1,5)H)=7, r 6躜 ?! Uno data)=7, s 6Ɯ ?"`` ! (1,3)H)=7, t 6М ?N! Uno data)=7, u 6@ۜ ?"`N! (0,3)H)=7, v 6 ?` N! Uno data)=7, w 6$ ?{N (1,3)H)=7, x 6( ?"`{N (1,3)H)=7, y 6\ ?"`` {N (0,1)H)=7, z 6 ?{ (1,4)H)=7, { 60" ?"`{ (3,0)H)=7, | 6 . ?"`` { (5,0)H)=7, } 6 ? MDT4)=7, ~ 6' ? MDT3)=7,  6DI ?`  MDT2)=7,`B  0o ?ZB  s *1 ?ZB  s *1 ?{{ZB  s *1 ?NNZB  s *1 ?!!ZB  s *1 ?ZB  s *1 ?`B  0o ?m m `B  0o ?m ZB  s *1 ?m ZB  s *1 ?m `B  0o ?m ZB  s *1 ?` ` m ZB  s *1 ?3 3 m ZB  s *1 ?2 2 m ZB  s *1 ?" " m ZB  s *1 ?m ZB  s *1 ?    <O   ,$ 0 How to estimate values of  no data  ? Use other data in the same DT.B'# 'C"CH  0޽h ? 3f3f& TIMING |14.6___PPT10b.p:$ +dD' $= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+0 +?Y  0L0 HHp[ FH(  fl 7 |7,$D 0` y 07t t <ʜ   w1-w8: De= c and Fu= s only w1 shares this part of pattern. upp. estim. of  yes = 6/7 upp. estim. of  no = 1/7&-h-AXG` { 0thl 7  7 ,$D 0` } 07t w B "  4 w2-w8: De= c w1, w2, w3 share this part of pattern. upp. estim. of  yes =(6+6+1)/(7+6+3)=13/16 upp. estim. of  no  =(1+0+2)/(7+6+3)= 3/16Z--TAC"ACAX>'! ~ 67t},$D 0.& Z  z #"2&Z   6 ?Z  M(8,0))=7,  60  ?"`  In)=7,  68  ?"`t  Im)=7,  6@  ?"`)t  Im)=7,   6H  ?"`)  Jw7)=7,   6P  ?"`) Jw6)=7,   6Xǝ  ?"`>) Jw5)=7,   6`Н  ?"`k)> Jw4)=7,   6hٝ  ?"`)k Jw3)=7,  6p  ?"`) Jw2)=7,  6x  ?"`) Jw1)=7,  6  ?"`) @)=7,  6  ?"`)t Im)=7,  6  ?"`)>t Im)=7,  6  ?"`)kt> Im)=7,  6H  ?"`)tk Ic)=7,  6(#  ?"`)t Ic)=7,  60,  ?"`)t Ic)=7,  685  ?"`)t JDe)=7,  6@>  ?"`t Im)=7,  6HG  ?"`t> Is)=7,  6PP  ?"`tk> Is)=7,  6XY  ?"`tk Im)=7,  6`b  ?"`t Im)=7,  6hk  ?"`t Is)=7,  6pt  ?"`t JFu)=7,  6x}  ?"` Ic)=7,   6  ?"`> In)=7, ! 6  ?"`k> Ic)=7, " 6  ?"`k In)=7, # 6  ?"` Ic)=7, $ 6  ?"` Ic)=7, % 6  ?"` dSi)=7, & 6 ?Z M(0,1))=7, ' 6(Ɵ ?>Z M(1,2))=7, ( 60ϟ ?kZ> M(0,2))=7, ) 68؟ ?Zk M(1,2))=7, * 6@ ?Z M(6,0))=7, + 6H ?Z M(6,1))=7, , 6P ?Z JAc)=7,`B - 0o ?ZZB . s *1 ?ZZB / s *1 ?ZZB 0 s *1 ?ZZB 1 s *1 ?kZkZB 2 s *1 ?>Z>ZB 3 s *1 ?Z`B 4 0o ? Z `B 5 0o ? `B 6 0o ?ZZ ZB 7 s *1 ? ZB 8 s *1 ? ZB 9 s *1 ?tt ZB : s *1 ?)) ZB ; s *1 ?Z u <  "`wTN ^Agreement Ratio (Estimate values for  no data )"0" C < ^A1txp_figL'.& SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ T_1 $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue,ORIGWIDTH 68.254PICTUREFILESIZE962kj 6 Z  =# #" 6 Z  > < ?6 Z  @)=7, ? < ?6   In)=7, @ < ?t6   Is)=7, A <8# ?-6 t  Ic)=7, B <@, ?6 -  Jw8)=7,`B C 0o ?6 Z6 `B D 0o ? Z `B E 0o ?6 ZB F s *1 ?-6 - ZB G s *1 ?t6 t ZB H s *1 ?6  ZB I s *1 ?6  `B J 0o ?Z6 Z  n </ F q ; &&Compare all patterns wi with w8 Take the common part in patterns. Count objects of  yes / no sharing the common part of pattern. !.EM EEKE}(l    ,$D 0  <5 5  r@& (Do the same for w3, w4, & , w7)!!A  BC =   D. w6-w8: No common part. use marginal distri. all wi share this part of pattern. upp. estim. of  yes =22/30 upp. estim. of  no  = 8/30v/-i-AAIXACA|&$Al    ,$D 0 g BhS G!&HL "`) 9  EThe sum is not 1.A e ^A@txp_figXP SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ (\frac{6}{7},\frac{5}{12}) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue&ORIGWIDTH616PICTUREFILESIZE3646 f <Z   UUpper estimation of w8:"AAf2  6   <`  9 Q  GTake maximum to each:AH  0޽h ?g 3f3f___PPT10.\"+pD' $= @B DX' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-o6Bdissolve*<3<*|D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*~%(D' =-o6Bdissolve*<3<*~D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+^  0L0 T(  Tx T c $ wTN   ; Zc  T# #"2&?  T 6p ?}  O(1,0))=7, T 6{ ?"`/}  O(1,0))=7, T 6t ?"`/  O(1,0))=7, T 6, ?"`   O(1,0))=7, T 64 ?"`   Kn)=7,  T 6< ?"`   Km)=7,  T 6D ?"`{   Km)=7,  T 6L ?"`Z{  Jw6)=7,  T 6T ?"`Z { c  Jw7)=7,  T 6\ ?"`Z{  Jw5)=7, T 6dʠ ?"`Z{  Jw4)=7, T 6lӠ ?"`ZD{  Jw3)=7, T 6tܠ ?"`Zq{ D Jw2)=7, T 6| ?"`Z{ q Jw1)=7, T 6 ?"`Z{  Opattern)=7, T 6 ?"`{ c  Kc)=7, T 6 ?"`{   Km)=7, T 6 ?"`{   Km)=7, T 6 ?"`{ D  Km)=7, T 6 ?"`{ q D Kc)=7, T 6@& ?"`{  q Kc)=7, T 6D/ ?"`{   LDe)=7, T 6T8 ?"` c  Ks)=7, T 6pA ?"`   Km)=7, T 6HJ ?"`   Ks)=7, T 6S ?"` D  Ks)=7, T 6D ?"` q D Km)=7, T 6Le ?"`  q Ks)=7,  T 6|n ?"`   LFu)=7, !T 6w ?"` c  Kn)=7, "T 6 ?"`   Kc)=7, #T 6 ?"`   Kn)=7, $T 6 ?"` D  Kc)=7, %T 6 ?"` q D Kc)=7, &T 6 ?"`  q Kc)=7, 'T 6( ?"`   fSi)=7, (T 6趡 ?"` c  B)=7, )T 64 ?"`  O(0,1))=7, *T 6ȡ ?"`  Q( 1, ))=7, +T 6(ҡ ?"` D O(0,1))=7, ,T 6`ۡ ?"` qD O(1,0))=7, -T 6 ?"` q O(6,1))=7, .T 6 ?"`  MDT1)=7, /T 6 ?} c  O(1,0))=7, 0T 6 ?"`/ }c  O(1,0))=7, 1T 6 ?"` /c  Q( 9,1 ))=7, 2T 6 ?} O(0,1))=7, 3T 6 ?"`/} O(1,0))=7, 4T 6 ?"`/ O(1,4))=7, 5T 6d/ ?} P( 1,5))=7, 6T 6t8 ?/} B)=7, 7T 6A ?"`/ P(1, ))=7, 8T 6J ?}D B)=7, 9T 6S ?"`/D} O(0,3))=7, :T 6\ ?D/ B)=7, ;T 6e ?}qD O(1,3))=7, T 6| ?}q O(1,4))=7, ?T 6܊ ?"`/}q O(1,0))=7, @T 6< ?"`/q O(1,0))=7, AT 6 ?} MDT4)=7, BT 6 ?/} MDT3)=7, CT 6\ ?/ MDT2)=7,`B DT 0o ?ZZB ET s *1 ?ZZB FT s *1 ?ZqqZB GT s *1 ?ZDDZB HT s *1 ?ZZB IT s *1 ?ZZB JT s *1 ?Z`B KT 0o ?Zc c `B LT 0o ?ZZc ZB MT s *1 ?//c ZB NT s *1 ?}}c `B OT 0o ?c ZB PT s *1 ?c ZB QT s *1 ?  c ZB RT s *1 ?  c ZB ST s *1 ?  c ZB TT s *1 ?{ { c ZB UT s *1 ?Z  l ("-  T"(- ,$D  0 VT XADtxp_figS"`?z " JB SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ (1,\frac{4}{5}) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue.ORIGWIDTH 49.8756PICTUREFILESIZE3310 WT XAEtxp_figS"`? 7 6. SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ (1,1) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue.ORIGWIDTH 49.8756PICTUREFILESIZE2386 XT ^AGtxp_figS"`? /D< SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ (\frac{8}{17},1) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue&ORIGWIDTH616PICTUREFILESIZE3646 cT XAtxp_figS"`?(s - ZR SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ (\frac{12}{13},\frac{2}{3}) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue&ORIGWIDTH616PICTUREFILESIZE3774 dT <ʢ G V$Insertion of upper estimation values%%A eT ^A!txp_figjItl SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \frac{6}{7},\frac{1}{7} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False,RESOLUTION1200*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono&ORIGWIDTH346PICTUREFILESIZE2196 fT ^A#txp_figktl SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \frac{1}{3},\frac{2}{3} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False,RESOLUTION1200*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono&ORIGWIDTH346PICTUREFILESIZE2598 gT ^A$txp_fig  tl SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \frac{1}{4},\frac{3}{4} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False,RESOLUTION1200*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono&ORIGWIDTH346PICTUREFILESIZE2208  hT XA'txp_fig"` tl SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \frac{1}{5},\frac{4}{5} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False,RESOLUTION1200*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono&ORIGWIDTH346PICTUREFILESIZE1952  iT XA$txp_fig"`` tl SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \frac{1}{4},\frac{3}{4} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False,RESOLUTION1200*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono&ORIGWIDTH346PICTUREFILESIZE2208  jT XA$txp_fig"``Z=tl SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \frac{1}{4},\frac{3}{4} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False,RESOLUTION1200*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono&ORIGWIDTH346PICTUREFILESIZE2208  kT XA'txp_fig"`Z>Etl SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \frac{1}{5},\frac{4}{5} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False,RESOLUTION1200*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono&ORIGWIDTH346PICTUREFILESIZE1952 lT ^A(txp_figpStl SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \frac{1}{6},\frac{5}{6} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False,RESOLUTION1200*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono&ORIGWIDTH346PICTUREFILESIZE2440 mT ^A+txp_fig 4 xp SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \frac{9}{10},\frac{1}{10} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False0TRANSPARENT False,KEEPFILES False.DEBUGPAUSE False,RESOLUTION1200*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATpngmono&ORIGWIDTH546PICTUREFILESIZE3027\  rY  T# #"2&? ,$@ 0 T < ?rY  M3/4)=7, T < ?rY K1)=7, T <`$ ?r>Y M1/4)=7, T <- ?rkY> K0)=7, T <h ?rYk K0)=7, T <? ?rY M1/4)=7, T <H ?rY M3/4)=7, T <Q ?rY W Lower approx.)=7,`B T 0o ?rYZB T s *1 ?rYZB T s *1 ?rYZB T s *1 ?rYZB T s *1 ?rkYkZB T s *1 ?r>Y>ZB T s *1 ?rYZB T s *1 ?rY`B T 0o ?r Y `B T 0o ?rr `B T 0o ?YY  T <AACn" ZT 03"`s  \T <g  {  sVPRS using upper. estima.En ]T 0"` D  aT dA txp_fig  SOURCE~\documentclass{slides}\pagestyle{empty} \begin{document} $ \underline{\tau}_{\varepsilon_1,\varepsilon_2}(w_i,X),\ \overline{\tau}_{\varepsilon_1,\varepsilon_2}(w_i,X) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue.ORIGWIDTH 256.758PICTUREFILESIZE 12438 bT <q 3  CAgreement Ratios can be defined in the same way as discarding case:&DE4A T dAtxp_fig 9 | SOURCE`\documentclass{slides}\pagestyle{empty} \begin{document} \begin{eqnarray*} \underline{C}_{\epsilon_1 ,\epsilon_2}^{T_i}(X)&=&\{ w_i\in V_C|\hat{\mu}_C^{T_i} (X|w_i)\ge 1-\epsilon_1,\\ &&\ \ \hat{\mu}_C^{T_i} (U-X|w_i)\le \epsilon_2\}\\ \overline{C}_{\epsilon_1 ,\epsilon_2}^{T_i}(X)&=&\{ w_i\in V_C|\hat{\mu}_C^{T_i} (X|w_i)> \epsilon_1\ or\\ &&\ \ \hat{\mu}_C^{T_i} (U-X|w_i)< 1-\epsilon_2\} \end{eqnarray*} \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATbmpmono.ORIGWIDTH 418.75:PICTUREFILESIZE 119962H T 0޽h ? 3f3f& TIMING |14.6___PPT10.p:$ +d8BD&' $= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-s6Bwipe(left)*<3<*TD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-o6Bdissolve*<3<*TD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-s6Bwipe(left)*<3<*TDO' =%(D' =%(DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-6B%slide(fromBottom)*<3<*TDR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-6B%slide(fromBottom)*<3<*T+8+0+T0 +'  0L0 &%/%(  f"  03"` r  S L& w'N      <J 33o"`% ^Agreement ratios in each treatment of  no data 00A  < /V  D1. Discard the DTsA  <8 53  K2. Using upper estimationA`  s *"` "`   s *"`Q "z   dAHtxp_fig@~  SOURCEf\documentclass{slides}\pagestyle{empty} \begin{document} $ \underline{\tau}_{\epsilon_1,\epsilon_2}(w_i,X),\ \overline{\tau}_{\epsilon_1,\epsilon_2}(w_i,X) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue(ORIGWIDTH2538PICTUREFILESIZE 12074N  dAJtxp_fig@ V SOURCE:\documentclass{slides}\pagestyle{empty} \begin{document} $ \underline{\tau}_{\epsilon_1}(w_i,X),\ \overline{\tau}_{\epsilon_1}(w_i,X) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue(ORIGWIDTH2118PICTUREFILESIZE 10254  < 3"`  RRequirements to be a member of the Lower Approximation: (1) High ratio of DTs whose Lower Approximations of X include it, (2) Low ratio of DTs whose Lower Approximations of U-X include it = High ratio of DTs whose Upper Approximations of X include it. &6EA  <    TRough Set under Multiple DTsE 8    .}*1h$  <H    rLet be agreement ratios, where or . "?4 2sAD & dAtxp_fig7 D > SOURCE"\documentclass{slides}\pagestyle{empty} \begin{document} $ \underline{\tau}_{\chi}(w_i,X),\ \overline{\tau}_{\chi}(w_i,X) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue0ORIGWIDTH199.8756PICTUREFILESIZE9890 ' dA txp_figG ;} NF SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \chi=\{\epsilon_1\} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue,ORIGWIDTH 82.756PICTUREFILESIZE3890 ( dA%txp_fig } h` SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ \chi=\{\epsilon_1,\epsilon_2\} $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue0ORIGWIDTH110.8756PICTUREFILESIZE5282 /  vA/ ?txp_fig"6@ NNN?N` Qx SOURCE\\documentclass{slides}\pagestyle{empty} \begin{document} \begin{eqnarray*} \underline{\bf{T}}^{\delta_1,\delta_2}_{\chi}(X)&=&\{ w_i\in V_C|\underline{\tau}_{\chi} (w_i,X)\ge 1-\delta_1, \overline{\tau}_{\chi}(w_i,X)\ge 1-\delta_2\}\\ \overline{\bf{T}}^{\delta_1,\delta_2}_{\chi}(X)&=&\{ w_i\in V_C|\underline{\tau}_{\chi} (w_i,X)> \delta_1\ or\ \overline{\tau}_{\chi}(w_i,X)> \delta_2 \} \end{eqnarray*} \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATbmpmono.ORIGWIDTH 610.758PICTUREFILESIZE 83902H  0޽h ? 3f3f___PPT10i. !+D=' $= @B +  0 9r1rD q(    s *"` ) ,$D 0Q  <ݣ  q ,$ 0 Cex) when w1,w6 and w7 are mem -bers of lower approx. DDA4(r  S  wTN   f Z 0"` r_  [ <     4  Elements of lower approximation of a set of  yes when e1=1/7lW C=AC u,  A #"2&   > < ?XH, K1)=7, < <D  ?"`HX M3/4)=7, : < ?X, M3/4)=7, 8 <  ?"`X M1/4)=7, 6 <$ ?X, K0)=7, 4 <,$  ?"`X K0)=7, 2 <4- ?X, K1)=7, 0 <<6  ?"`X K0)=7, . <D? ?X,g M1/2)=7, , <LH  ?"`Xg M1/4)=7, * <TQ ?Xg,:  K1)=7, ( <\Z  ?"`gX:  K1)=7, m <dc ?X: ,  K1)=7, l <ll ?: X  K1)=7, k <tu ?Xu,H OUpper)=7, j <|~ ?uXH OLower)=7,`B z 0o ?u,uZB { s *1 ?H,H`B  0o ? , `B  0o ?u ZB  s *1 ?XuX `B  0o ?,u, ZB ) s *1 ?: ,: ZB - s *1 ?g,gZB 1 s *1 ?,ZB 5 s *1 ?,ZB 9 s *1 ?,ZB = s *1 ?,  <( <6# BAgreement ratiosAf  0"` r   <   _  F +  Elements of upper approx -imation of a set of  yes when e1=1/7@YC3A2 f  0"` ) *  dAtxp_fig  $@ 0b SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} $ (\delta_1,\delta_2)=(\frac{1}{4},0) $ \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300"TIMEOUT156BITMAPFORMATbmpmono8 DEBUGINTERACTIVETrue(ORIGWIDTH1506PICTUREFILESIZE90222 q s *"`,$D  02 r s *"`,$@  02 s s *"` ,$@  0"  < 3"`9 I ,A  B$    TRough Set under Multiple DTsE? V  |# #"2&q  } 6 ?Q   (3,0)H)=7, ~ 6< ?"` Q  (8,0)H)=7,  6¨ ?"`[  (6,0)H)=7,  6d ?"` [  (8,0)H)=7,  6ר ?"`   Kn)=7,  6 ?"`   Km)=7,  6 ?"`   Km)=7,  6 ?"`   Jw6)=7,  6 ?"` V  Jw7)=7,  6 ?"`   Jw5)=7,  6 ?"`   Jw4)=7,  60 ?"`7  Jw3)=7,  6! ?"`d7 Jw2)=7,  6* ?"`d Jw1)=7,  64 ?"` Opattern )=7,  6H% ?"` V  Kc)=7,  6E ?"`   Km)=7,  6N ?"`   Km)=7,  6W ?"`7  Km)=7,  6` ?"`d7 Kc)=7,  6i ?"`d Kc)=7,  6s ?"` LDe)=7,  6 | ?"` V  Ks)=7,  6p ?"`   Km)=7,  6쎩 ?"`   Ks)=7,  60 ?"`7  Ks)=7,  6 ?"`d7 Km)=7,  6 ?"`d Ks)=7,  6\ ?"` LFu)=7,  6 ?"` V  Kn)=7,  6Ʃ ?"`   Kc)=7,  6LЩ ?"`   Kn)=7,  6|٩ ?"`7  Kc)=7,  6 ?"`d7 Kc)=7,  6 ?"`d Kc)=7,  6 ?"` fSi)=7,  6 ?"` [V  Qno data)=7,  6 ?"` [  (0,1)H)=7,  6 ?"` [  (1,2)H)=7,  6" ?"`7[  (0,2)H)=7,  6/ ?"`d[7 (6,0)H)=7,  6: ?"`[d (6,1)H)=7,  65 ?"`[ MDT1)=7,  6O ?Q V  (6,0)H)=7,  6[ ?"` Q V  (2,0)H)=7,  6g ?"`[ V  (9,1)H)=7,  6s ?Q   (0,3)H)=7,  6( ?"` Q  (1,0)H)=7,  6 ?"`[  (1,4)H)=7,  6 ?Q   (1,5)H)=7,  6X ? Q  Qno data)=7,  6ԫ ?"`[  (1,3)H)=7,  6ĵ ?Q 7  Qno data)=7,  6 ?"` 7Q  (0,3)H)=7,  6ʪ ?[7  Qno data)=7,  6ժ ?Q d7 (1,3)H)=7,  6ܺ ?"` dQ 7 (1,3)H)=7,  6 ?"`[d 7 (0,1)H)=7,  6@ ?Q d (1,4)H)=7,  6 ?"` Q d (3,0)H)=7,  6x ?"`[ d (5,0)H)=7,  6$Ъ ?Q  MDT4)=7,  6$ ? Q  MDT3)=7,  6,/ ?[  MDT2)=7,`B  0o ?ZB  s *1 ?ZB  s *1 ?ddZB  s *1 ?77ZB  s *1 ?  ZB  s *1 ?  ZB  s *1 ?  `B  0o ?V V `B  0o ?V ZB  s *1 ?  V ZB  s *1 ?Q Q V `B  0o ?V ZB  s *1 ?[[V ZB  s *1 ?V ZB  s *1 ?V ZB  s *1 ?V ZB  s *1 ?V ZB  s *1 ?  f \ 0"`f ] 0"`f ^ 0"`f _ 0"`k f ` 0"`k f a 0"`k f b 0"`  f c 0"`[  f d 0"`  f e 0"`  f f 0"`b f g 0"`b  f  0"`b f  0"`}2f  0"`}k 2f  0"`}b 2f  0"`  lf  0"`b lf  0"`2k * C dAtxp_fig   SOURCE\documentclass{slides}\pagestyle{empty} \begin{document} \begin{eqnarray*} &\underline{\bf{T}}^{\delta_1,\delta_2}_{\varepsilon_1}(X)=\{ w_i\in V_C|\underline{\tau}_{\varepsilon_1} (w_i,X)\ge 1-\delta_1, %\\ \overline{\tau}_{\varepsilon_1}(w_i,X)\ge 1-\delta_2\}\\ &\overline{\bf{T}}^{\delta_1,\delta_2}_{\varepsilon_1}(X)=\{ w_i\in V_C|\underline{\tau}_{\varepsilon_1} (w_i,X)> \delta_1%\ \ \ \ \ \\ \ or\ \overline{\tau}_{\varepsilon_1}(w_i,X)> \delta_2 \} \end{eqnarray*} \end{document} 6EXTERNALNAMEtxp_fig$ BLEND False.TRANSPARENTTrue,KEEPFILES False.DEBUGPAUSE False*RESOLUTION300*TIMEOUT (none)&BOXWIDTH354(BOXHEIGHT370"BOXFONT10(BOXWRAP FalseL2WORKAROUNDTRANSPARENCYBUG FalseD*ALLOWFONTSUBSTITUTION False6BITMAPFORMATbmpmono0ORIGWIDTH602.8758PICTUREFILESIZE 82854H  0޽h ? 3f3f}0 TIMING|42.2|44.2=___PPT10.D+/ D' $= @B Dt' = @BA?%,( < +O%,( < +D' =%(D=' =%(DG' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*r%(D' =-6B'barn(inHorizontal)*<3<*rDG' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*s%(D' =-6B'barn(inHorizontal)*<3<*sDG' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*q%(D' =-6B'barn(inHorizontal)*<3<*qD' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+0 +  0  L(  x  c $\ 6̲ ?"` V  Kc)=7, ?\ 6ղ ?"`   Km)=7, @\ 6 ޲ ?"`   Km)=7, A\ 6 ?"`7  Km)=7, B\ 6 ?"`d7 Kc)=7, C\ 6 ?"`d Kc)=7, D\ 6 ?"` LDe)=7, E\ 6 ?"` V  Ks)=7, F\ 6 ?"`   Km)=7, G\ 6 ?"`   Ks)=7, H\ 6  ?"`7  Ks)=7, I\ 6$1 ?"`d7 Km)=7, J\ 6T: ?"`d Ks)=7, K\ 6\C ?"` LFu)=7, L\ 6dL ?"` V  Kn)=7, M\ 6lU ?"`   Kc)=7, N\ 6t^ ?"`   Kn)=7, O\ 6|g ?"`7  Kc)=7, P\ 6p ?"`d7 Kc)=7, Q\ 6y ?"`d Kc)=7, R\ 6 ?"` fSi)=7, S\ 6苳 ?"` [V  Qno data)=7, T\ 6 ?"` [  (0,1)H)=7, U\ 6$ ?"` [  (1,2)H)=7, V\ 6 ?"`7[  (0,2)H)=7, W\ 6 ?"`d[7 (6,0)H)=7, X\ 6dz ?"`[d (6,1)H)=7, Y\ 6ѳ ?"`[ MDT1)=7, Z\ 6ܳ ?Q V  (6,0)H)=7, [\ 6 ?"` Q V  (2,0)H)=7, \\ 6`ճ ?"`[ V  (9,1)H)=7, ]\ 6 ?Q   (0,3)H)=7, ^\ 6 ?"` Q  (1,0)H)=7, _\ 6 ?"`[  (1,4)H)=7, `\ 6& ?Q   (1,5)H)=7, a\ 60 ? Q  Qno data)=7, b\ 6; ?"`[  (1,3)H)=7, c\ 6E ?Q 7  Qno data)=7, d\ 6P ?"` 7Q  (0,3)H)=7, e\ 6PZ ?[7  Qno data)=7, f\ 6xe ?Q d7 (1,3)H)=7, g\ 6J ?"` dQ 7 (1,3)H)=7, h\ 6} ?"`[d 7 (0,1)H)=7, i\ 6 ?Q d (1,4)H)=7, j\ 6씴 ?"` Q d (3,0)H)=7, k\ 6\ ?"`[ d (5,0)H)=7, l\ 6ܩ ?Q  MDT4)=7, m\ 6IJ ? Q  MDT3)=7, n\ 6$ ?[  MDT2)=7,`B o\ 0o ?ZB p\ s *1 ?ZB q\ s *1 ?ddZB r\ s *1 ?77ZB s\ s *1 ?  ZB t\ s *1 ?  ZB u\ s *1 ?  `B v\ 0o ?V V `B w\ 0o ?V ZB x\ s *1 ?  V ZB y\ s *1 ?Q Q V `B z\ 0o ?V ZB {\ s *1 ?[[V ZB |\ s *1 ?V ZB }\ s *1 ?V ZB ~\ s *1 ?V ZB \ s *1 ?V ZB \ s *1 ?  f \ 0"`f \ 0"`f \ 0"`f \ 0"`k f \ 0"`k f \ 0"`k f \ 0"`  f \ 0"`[  f \ 0"`  f \ 0"`  f \ 0"`b f \ 0"`b  f \ 0"`b f \ 0"`}2f \ 0"`}k 2f \ 0"`}b 2f \ 0"`  lf \ 0"`b lf \ 0"`2k s$ q6 <w ] #""Hr6 Dw  * \ BӴ  ?"6@ NNN?N <w r(Si,n))=7,1 \ Bݴ  ?"6@ NNN?N w y (Fu,s),(Si,n) )=7,8 \ B\  ?"6@ NNN?N  w (De,c),(Fu,s),(Si,n))=7,* \ B$  ?"6@ NNN?N  w r(De,c))=7,1 \ B  ?"6@ NNN?N  w y (De,c),(Si,n) )=7, \ B  ?"6@ NNN?Nq  w Lw7)=7,8 \ B$  ?"6@ NNN?N <  (De,m),(Fu,m),(Si,n))=7,1 \ B  ?"6@ NNN?N   y (De,m),(Si,n) )=7,* \ B"  ?"6@ NNN?N  r(Si,n))=7,* \ B,  ?"6@ NNN?N  r(Fu,m))=7,1 \ B6  ?"6@ NNN?N    y (Fu,m),(Si,n) )=7, \ B`?  ?"6@ NNN?Nq   Lw6)=7, \ BH  ?"6@ NNN?NU <  O---(<)=7,* \ BR  ?"6@ NNN?N U   r(Fu,s))=7,1 \ B\  ?"6@ NNN?N U  y (De,c),(Fu,s) )=7,1 \ Bf  ?"6@ NNN?NU  y (De,c),(Si,c) )=7,* \ Bp  ?"6@ NNN?N U   r(De,c))=7, \ Bz  ?"6@ NNN?NqU   Lw1)=7, \ Bx  ?"6@ NNN?N6 <U  Lw1)=7, \ B  ?"6@ NNN?N 6 U  Lw2)=7, \ BT  ?"6@ NNN?N 6 U  Lw5)=7, \ B  ?"6@ NNN?N6 U  Lw4)=7, \ B  ?"6@ NNN?N 6 U  Lw3)=7, \ Bd  ?"6@ NNN?Nq6 U  B)=7,B \ Ho ?"0@NNN?Nq6 <6 B \ B1 ?"0@NNN?NqU <U B \ B1 ?"0@NNN?Nq < B \ B1 ?"0@NNN?Nq < B \ Ho ?"0@NNN?Nqw<wB \ Ho ?"0@NNN?Nq6 qwB \ B1 ?"0@NNN?N 6 wB \ B1 ?"0@NNN?N6 wB \ B1 ?"0@NNN?N 6 wB \ B1 ?"0@NNN?N 6 wB \ B1 ?"0@NNN?N6 wB \ Ho ?"0@NNN?N<6 <wH \ 0޽h ? 3f3f0 TIMING|42.2|44.2___PPT10i.D+D=' $= @B +  0 @/(  ~  s *| wTN    u,  # #"2&     <l ?XH, K1)=7,  <  ?"`HX M3/4)=7,  <P ?X, M3/4)=7,  <  ?"`X M1/4)=7,  < ?X, K0)=7,   <  ?"`X K0)=7,   < ?X, K1)=7,   <0  ?"`X K0)=7,   <! ?X,g M1/2)=7,   <*  ?"`Xg M1/4)=7,  <4 ?Xg,:  K1)=7,  <H%  ?"`gX:  K1)=7,  <E ?X: ,  K1)=7,  <N ?: X  K1)=7,  <W ?Xu,H OUpper)=7,  <` ?uXH OLower)=7,`B  0o ?u,uZB  s *1 ?H,H`B  0o ? , `B  0o ?u ZB  s *1 ?XuX `B  0o ?,u, ZB  s *1 ?: ,: ZB  s *1 ?g,gZB  s *1 ?,ZB  s *1 ?,ZB  s *1 ?,ZB  s *1 ?,   <e <6# BAgreement ratiosA`2 ! s *"``2 " s *"``2 # s *"` ? V  $# #"2& q  % 6v ?Q   (3,0)H)=7, & 6 ?"` Q  (8,0)H)=7, ' 6썶 ?"`[  (6,0)H)=7, ( 6 ?"` [  (8,0)H)=7, ) 6t ?"`   Kn)=7, * 6, ?"`   Km)=7, + 64 ?"`   Km)=7, , 6< ?"`   Jw6)=7, - 6DǶ ?"` V  Jw7)=7, . 6Lж ?"`   Jw5)=7, / 6Tٶ ?"`   Jw4)=7, 0 6\ ?"`7  Jw3)=7, 1 6d ?"`d7 Jw2)=7, 2 6l ?"`d Jw1)=7, 3 6t ?"` Opattern )=7, 4 68 ?"` V  Kc)=7, 5 6p ?"`   Km)=7, 6 6 ?"`   Km)=7, 7 6$" ?"`7  Km)=7, 8 6T+ ?"`d7 Kc)=7, 9 6\4 ?"`d Kc)=7, : 6d= ?"` LDe)=7, ; 6lF ?"` V  Ks)=7, < 6tO ?"`   Km)=7, = 6|X ?"`   Ks)=7, > 6a ?"`7  Ks)=7, ? 6j ?"`d7 Km)=7, @ 6s ?"`d Ks)=7, A 6| ?"` LFu)=7, B 6 ?"` V  Kn)=7, C 6 ?"`   Kc)=7, D 6 ?"`   Kn)=7, E 6 ?"`7  Kc)=7, F 6ĩ ?"`d7 Kc)=7, G 6̲ ?"`d Kc)=7, H 6H ?"` fSi)=7, I 6(Ÿ ?"` [V  Qno data)=7, J 6и ?"` [  (0,1)H)=7, K 6dݸ ?"` [  (1,2)H)=7, L 6\ ?"`7[  (0,2)H)=7, M 6 ?"`d[7 (6,0)H)=7, N 6 ?"`[d (6,1)H)=7, O 6| ?"`[ MDT1)=7, P 6 ?Q V  (6,0)H)=7, Q 6# ?"` Q V  (2,0)H)=7, R 6`0 ?"`[ V  (9,1)H)=7, S 60< ?Q   (0,3)H)=7, T 6lG ?"` Q  (1,0)H)=7, U 6T ?"`[  (1,4)H)=7, V 6 6 ?"`7  Ks)=7, ? 6 ?"`d7 Km)=7, @ 6 ?"`d Ks)=7, A 6( ?"` LFu)=7, B 60ȼ ?"` V  Kn)=7, C 68Ѽ ?"`   Kc)=7, D 6@ڼ ?"`   Kn)=7, E 6H ?"`7  Kc)=7, F 6P ?"`d7 Kc)=7, G 6X ?"`d Kc)=7, H 6D ?"` fSi)=7, I 6, ?"` [V  Qno data)=7, J 6T ?"` [  (0,1)H)=7, K 6(! ?"` [  (1,2)H)=7, L 6. ?"`7[  (0,2)H)=7, M 68 ?"`d[7 (6,0)H)=7, N 6|D ?"`[d (6,1)H)=7, O 6? ?"`[ MDT1)=7, P 6xY ?Q V  (6,0)H)=7, Q 6Te ?"` Q V  (2,0)H)=7, R 6q ?"`[ V  (9,1)H)=7, S 6} ?Q   (0,3)H)=7, T 6 ?"` Q  (1,0)H)=7, U 6h ?"`[  (1,4)H)=7, V 6 ?Q   (1,5)H)=7, W 6P ? Q  Qno data)=7, X 6̵ ?"`[  (1,3)H)=7, Y 6x ?Q 7  Qno data)=7, Z 6ʽ ?"` 7Q  (0,3)H)=7, [ 6\Խ ?[7  Qno data)=7, \ 6߽ ?Q d7 (1,3)H)=7, ] 6Ľ ?"` dQ 7 (1,3)H)=7, ^ 6 ?"`[d 7 (0,1)H)=7, _ 6 ?Q d (1,4)H)=7, ` 6 ?"` Q d (3,0)H)=7, a 6 ?"`[ d (5,0)H)=7, b 6& ?Q  MDT4)=7, c 6x/ ? Q  MDT3)=7, d 67 ?[  MDT2)=7,`B e 0o ?ZB f s *1 ?ZB g s *1 ?ddZB h s *1 ?77ZB i s *1 ?  ZB j s *1 ?  ZB k s *1 ?  `B l 0o ?V V `B m 0o ?V ZB n s *1 ?  V ZB o s *1 ?Q Q V `B p 0o ?V ZB q s *1 ?[[V ZB r s *1 ?V ZB s s *1 ?V ZB t s *1 ?V ZB u s *1 ?V ZB v s *1 ?  f w 0"`f x 0"`f y 0"` f z 0"`k f { 0"`k f | 0"`k f } 0"`  f ~ 0"`[  f  0"`  f  0"`  f  0"`b f  0"`b  f  0"`b f  0"`}2f  0"`}k 2f  0"`}b 2f  0"`  lf  0"`b lf  0"`2k y$ q6 <w # #""Hr6 Dw  *  BO  ?"6@ NNN?N <w r(Si,n))=7,1  BX  ?"6@ NNN?N w y (Fu,s),(Si,n) )=7,8  Bhb  ?"6@ NNN?N  w (De,c),(Fu,s),(Si,n))=7,*  B0l  ?"6@ NNN?N  w r(De,c))=7,1  Bu  ?"6@ NNN?N  w y (De,c),(Si,n) )=7,  B  ?"6@ NNN?Nq  w Lw7)=7,8  B  ?"6@ NNN?N <  (De,m),(Fu,m),(Si,n))=7,1  BH  ?"6@ NNN?N   y (De,m),(Si,n) )=7,*  B  ?"6@ NNN?N  r(Si,n))=7,*  B  ?"6@ NNN?N  r(Fu,m))=7,1  B  ?"6@ NNN?N    y (Fu,m),(Si,n) )=7,  BD  ?"6@ NNN?Nq   Lw6)=7,  BT¾  ?"6@ NNN?NU <  O---(<)=7,*  B̾  ?"6@ NNN?N U   r(Fu,s))=7,1  BP־  ?"6@ NNN?N U  y (De,c),(Fu,s) )=7,1  B`  ?"6@ NNN?NU  y (De,c),(Si,c) )=7,*  B$  ?"6@ NNN?N U   r(De,c))=7,  B  ?"6@ NNN?NqU   Lw1)=7,  B  ?"6@ NNN?N6 <U  Lw1)=7,  B  ?"6@ NNN?N 6 U  Lw2)=7,  B  ?"6@ NNN?N 6 U  Lw5)=7,  B  ?"6@ NNN?N6 U  Lw4)=7,  BD"  ?"6@ NNN?N 6 U  Lw3)=7,  B|+  ?"6@ NNN?Nq6 U  B)=7,B  Ho ?"0@NNN?Nq6 <6 B  B1 ?"0@NNN?NqU <U B  B1 ?"0@NNN?Nq < B  B1 ?"0@NNN?Nq < B  Ho ?"0@NNN?Nqw<wB  Ho ?"0@NNN?Nq6 qwB  B1 ?"0@NNN?N 6 wB  B1 ?"0@NNN?N6 wB  B1 ?"0@NNN?N 6 wB  B1 ?"0@NNN?N 6 wB  B1 ?"0@NNN?N6 wB  Ho ?"0@NNN?N<6 <wl  0L0  "`/J 6Decision rules inferring  yes : De= classic and Fu= simple Ac= yes , De= classic and Si= normal Ac= yes , Fu= multiple and Si= normal Ac= yes .x |    ,Z(H  0޽h ? 3f3f0 TIMING|42.2|44.2___PPT10i.D+D=' $= @B +}  0 @$(  r  S " wTN   r  S # T<   H  0޽h ? 3f3f___PPT10i.+D=' $= @B +} 0 `$(  r  S TSp S r  S Sp`  S H  0޽h ? 3f3f___PPT10i.l+D=' $= @B +< 0 L((  L^ L S D8\    L c $ D u    H L 0af ? 3380___PPT10.fs6xZklU>3nR7C-K *hKY?ZW(1ʏv[ئֵVcHJDCw1b$QLP̝NME=ޙs;wswp>u t029{*.V(PGMOf D@!C!LGAټ^[|Ysrdw0L=mO˧VlsWw_؏Кbx*ԀRp['L? =|Կ`dD;ɯN1*M,_SS/K⟛HY@XuӀ0( ԙidvC70ꕫWRJQ?&oaA.J{qCIe,z\$ٖg!,@^?q8Zi~ .Pl9sQRP.B}ՉZՅu)*d %_O> u53ϢVm֠֠Q]$!xå[K[Fp2VGWM|I4J~Y 6z@8uj++ݾ@CBjȌ5wW%*Ș!zV,? _i,[9jꋁw[Z_86vPdmb?"n:HӾ=؆`w(,u ծi$`xr3nunht{ϟinzeсXrR6V4nHwj0߷ u( 8bzekPU_:7V RE.J(V ~"߱^ʓů b,YieW&7_#p͏ދ\C?#>{S )U6d>NG<5d_F5hu( m8(6wއdO[|@if;SŏYu:kj;mT[PcUkFnMQ ,z\зzg.ZxTmV..`aQN!WߺSxYWdIUgUMQX bgyg*iA~wH waJuABoETTyVsjOU8Ga/X>Kj0@S{ʊ32+\Uqe<^=ދ˥|Ȉ}VG-w;{˝>WJ\>`eGi](KE] ˸B|"t[o[5"jOYO*\REaK#))8}>,ySĞ뛒lp<+pq|@Z"TZvFKR&bj1Cil풊U/"8KTM0US&_񿏳?1Mw,#GkX.3V'5G_nNFW2F#gl?L;3DoqF!m2:O}IvM|rhn~w0`0T%8۴&<׷=Qs՘aW"s\~*xZklU>sg-mW@ +Ŷ.!ݶ#uKLGYfXn]+40U I!@B?|& -2 1"C9e+Z3=w̝{{swg{\>~YahL8T_X{CtGɸ# "x!J4e XwNҧ4?{.Slʢ RFfIC@ǯ6&doG|өS*ky^]ߌ= > ~MnoH x?T+r景/c~Wz/[OtNN?nKRȪ+kp&f@|0lLDWm^c!sO<:/chЮ^N+Q?ɯ|O]FM:A\b8}@<|`7s2ds @+6q_7`a|Qnw;͵&"u@'IbPʯjlŢ`gHBTBOLizC\V{zђUn91? 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