1、 l : 2005- 12-29 “:SE1 S “( 60574011) #Te:f( 1966- ) , 3, a + ,v q,p V 3;f i 2( 1956- ) , 3, a g ,v q,p V3 =#第28卷第1期2007年 1月东 北 大 学 学 报 ( 自 然 科 学 版 )Journal of Northeastern University( Natural Science)Vol128, No. 1Jan. 2 00 7Y“ s“dMATLAB_ Q !9张雪峰, 张庆灵(v , a + 110004)K 1: V us1“M u Q,YV MWG ,4 Y“ s E
2、,YV1 e “,4K eT# MAT LAB) “f , p |Ma (/) aN1“aM1a MeaSMeaKl %?5 E LC# LC MATLAB_ Q !9# m (GUI)ZE, !9 z -“d #K L= 0T,wY“ 8 Ll #, L=il#1 o M:Y“; e; ;MATLAB;_; Qms |: TP 393.09 DS M : A cI|: 1005-3026( 2007) 01-0040-04Design of MATLAB Simulation Tool Box for Rough Set DataAnalysis SystemZHANG Xue-feng,
3、ZHANG Qing-ling(School of Sciences, Northeastern University, Shenyang 110004, China. Correspondent: ZHANG Qing-ling,professor, E-mail: qlzhang )Abstract: The two kernel concepts, indiscernibility relation and relative positive region, arefocused on. An algorithm is proposed to analyze the rough set
4、data analysis system, according tothe mutual dependency between different kinds of knowledge. The numbers of reduced attributesare compared to pick out a reduction result involving the minimum number of attributes. Takingthe advantage of MATLAB in dealing with set functions, the program realizations
5、 of manyalgorithms are given to solve relative core, upper approximation, lower approximation,equivalence relation, relative significance level, relative reduction of attributes, relative reductionof domain and minimal decision rules, thus designing the MATLAB simulation tool. By way ofgraphical use
6、r interface(GUI), the favorable main interface of man-machine interaction system isdesigned. An example resulting from running is given, which shows the practical significance tothe applications of rough set theory.Key words: rough set; attributes reduction; attribute core; MATLAB; simulation; tool
7、box“9,s 1p9 , 1V | .G # ?Vv Z4G E 4 N L= (B ,)“dA 1#Y“(Rough Set,eRS) o EZ. Pawlak1982 M4 1#1991 MPawlak , $ 2 #1997 MZ. Pawlak Y“ZE M % 3 # RS= E+ M?Z N, |T 7 “# B -o 9 ZE#Y“ZE MVr Mw 15 qsa f a Vs M1+ M4, VVC ? Mee,) a aca!aB M4 B ZE# !a M a9 aE e“d1 $#MATLAB -K a ? vrq 9 V j S/ qIB#5MATLAB 9 ?, M
8、ATLABKV710 Y“Z f Q# I nMATLAB C) “a # 1“f # d+, I nY“) “N1“+, MATLAB 7?Y“ s“d_ Q ?=1 , 1VC+ 9 YrT#Y“ s) qn,SROSETTA, ROSE,t qN, ?B,r q,S = # Y“ W 8 Ll, C E, 7?BY“ s“d v L=il 4#1 Y“eY“ M Tl, M) 4 B* s #Y“ VV ?C c M, U .? p# !X, YI U,R lU N1“,“X1R/ :R- (X)= G Y I U/ R: Y AX#R- (X) C M XFKv“, u,:POS(X)
9、# : R- (X)= G Y I U/ R: Y HX X #R- (X) “XMd bN i“, *t V ? XFKl“#“H ul:Bnd(X)= R- (X)- R- (X)#TBnd(X) b“,5X1R b ;Q,5X1RY“5#B“dS VV U: S = 3U, A,V,f4, , U “, ; A “; T “A VsHq “C % “D,CGD= A,CHD= ,5“d %“d %V# V1 U, U7 ,B Hq , % #V1 B“d L Table 1 An example of information systemU C1 C2 C3 C4 D1 1 0 0 1
10、12 1 0 0 0 13 0 0 0 0 04 1 1 0 1 05 1 1 0 2 26 2 1 0 2 27 2 2 2 2 2“d, 0“R AA,VsO1“IND(R):IND(R)= (x,y) I U U: r I R, r( x)=r(y),A IND(R) BN1“,x“R N xIND(R)lxIND( R) = y:y I U,yIND(R)x #eL n, 3j f /R9IND(R)#LRV UB1“,R Us ,UWN1“ H,U/ R= X1,X 2, , XnV U 1“R, U N B,1U M#e “ds %? MHq/, “ # TIND(R)= IND(
11、 R- r),rR V 8 # %Ve “ K HqOY B % ,| %Vc % Me#e %VHq e, T Hq %V x,5 , V #“dS, P,Q AA,5QPuPOSP(Q)lPOSP(Q) = G P- (X),X I U/Q #R V 1“, “R“,:CORE( R)6#2 RSDA“d LCY“ ZE“d4 s ? $, 1 X s ? M -4/,YV Me,w5 %s ?5#Y“ Q YVN1“ l,Y“ Q 4 , #yNY Y“w4, RS 8Armd #Y“ s( rough set dataanalysis, RSDA) Bs WM1GB|ZE# RSDA
12、VV 4 |?5as1o ,V7 %# 1S L !,?5 3 z#Y“ sZE L= %VeV,)V1f /#2.1 MATLAB“f MATLAB70 Q , sa ama )41第1期 张雪峰等: 粗糙集数据分析系统MATLAB仿真工具箱设计a|) am) alosa Z ea“dO MadL ea a * a ad9s# ? v O W,F 7? v S Q, PMATLAB s j,S= eW PB#MATLAB vf o,/ 7? P #1f 7cl #V2 MATLABs“f Table 2 Part of MATLAB set functionsf ? cat( d,A,B)
13、FAB d sort(A)| FA 6 intersect( a,b)Rab , _ 6 ismember(a,S)RB_ a“_, a “S setdiff( a,b)Rab ,_ 6 unique(a)R_ a ,Cstrvcat( t1,t2,t3, ,)31t1, t2, t3, ,_Funion( a,b)Rab, _ 6 setxor( a,b)“s 2.2 1MATLABRough“ Q9 VsO1“$,YV “/ “,“ l#YRough“ 4#Y“t Qa 4 ,E #?Z,+Y 5L= “#_/ TB V4 7?“dr q, MATLAB v s) V j q P S 7?
14、 n ,Y“ QZE MATLABf LC ?_,/ 1MATLAB#(1)f w= Rsupper(y, a, x) p | %Vxy“,1a VsO1“ “#/xM V1 , /:function w= Rsupper(y,a,x)z= ind( a,x); w = ; p,q = size(z);for u= 1:pzz= setdiff( z(u,:),0);zzz= intersect(zz,y);zp, zq= size(zzz);if zq = 0, w = cat(2, w,zz);endend w = sort( w,2) ; , |a= 4,y= 1 2 4 5#Tm y
15、= Rsupper(y,a,x) = 1 2 3 4 5 6 7 #(2)f w = Rslower(y, a, x) p | %Vx“y,1a VsO1“/ “#(1)/L3/ B9MRslower(y, a,x)#if ismember( zz,y), w= cat(2, w, zz); end, , a,y , 74 U/,my= Rlower(y,a,x)= 1 4#(3)f y= ind(a,x) p | %Vx a VsO1“# p VsO1“KO(| A | | U| 2),yK f /1 “ Q, BQ, N BQ# E: n5 “I ,I , BR V,O(| A | | U
16、| lg| U| )#1 :function y= ind( a,x)p, q = size(x); ap,aq = size( a);y= x;for i= 1:p, v(i)= code( aq,y(i,:),10); endy= v. ; yy,I = sort(y); y= yy I;b,k,l = unique(yy); y= lI; m= max(l);aa= zeros( m,p);for ii= 1: m for j= 1:pif l(j)= = ii, aa(ii,j)= I(j); endend end y= aa;function yy= code(a,x,b)yy= 0
17、; for i= 1:a, yy= yy+ x(i)* b(a- i); |a= 5,m y= ind(a, x)= 3,4,1,2,5, 6,7#(4)f y,b= pos(p,q) p | %VxH,QP,y | POSP(Q)| /| U|, bQP“# , |a= 1:4,b= 5,my, b= pos(ind( a,x), ind(b,x),y= 1,b= 1 2 3 4 5 6 7#(5)f y= redu( c, d,x) p | %VxHq c % d e# ,V1 U“d, |c= 1: 4,d= 5,my= redu( c,d,x)= 1 2 4#(6)f y= core(
18、 c,d, x) p | %VxHq c % d # c,d,x ,Tm y= core( c, d, x)= 1 24#f pos(p, q),redu(c,d, x)core(c, d,x) 8 EnD7#6,9BtV 4Rough“ ,$4 42 东北大学学报(自然科学版) 第28卷MRough“ 4#4M ZY“ ,1 EFM VZL LCMZ E 8- 9#3 m MATLAB+Y“_vvh IT ,B q , = ?% B,“N,m 9 %“ qQ#MATLABm P“d Q4, a Ma 1f Y?5#9 VYViworkspaceq s) # !9 MATLABGUIDE ?#
19、RSDA“d 1 = eqf , f ,I ?s Y“f m1 ,/ eqBrowse ,f Callback #Function browse- Callback ( hObject, eventdata,handles)filename, pathname, filterindex = uigetfile (c * .txtc,cu 7c,cD: MATLAB6p5 WORK A. TXTc) ;set( handles. readx,cstringc,pathname, filename )MATLAB4 U/o rsdav3 75 m1 U_ Q , V Browse f V,M Hq
20、 C % D |,#) A,R, Y“ = ,5 VBs# , redu5 Ve,T|results output A U #m1 Y“_ Q Fig.1 Main interface of rough set simulation tool box4 MATLAB“f #m 7? !9Y“_ QZE#|MATLABY“ , LC Y“5“d !9r_# e, #Y“ ,wY“ L=B4rT AT#ZE 8 L VnD10#qI KKl) , Q !9 ? ,“d ?B4, v “d1#BT 9F Q ?, E,9FMY“ va va ea qZE “ZE Y“) ZE Q v,MATLAB
21、d+,t5 VZL) Z# ID: 1 Pawlak Z. Rough sets J . International Journal ofComputer and Information Science, 1982, 11( 5) : 341-356. 2 Pawlak Z. Rough sets ) theoretical aspects of reasoning aboutdata M . Norwell: Kluwer Academic Publisher, 1991: 1-5. 3 Pawlak Z. Rough set approach to knowledge-based deci
22、sionsupport J . European Journal of Operational Research,1997, 99( 1) : 48- 57. 4 f#Y“ s“d 7? D# +:v, 2004#( Zhang Xue-feng. Thelaunch and research for rough set dataanalysis system D . Shenyang: Northeastern University,2004. ) 5 Pawlak Z, Busse J G, Slowinski R, et al. Rough sets J .Communicationof
23、 the ACM, 1995, 38( 11) : 89- 95. 6 y +,;,#Y“- * #pZE J#v:1 S, 2003, 24( 3): 252- 255#( Hao L-i na, Wang Wei, Wu Guang-yu, et al. Research onrough set- neural network fault diagnosis method J. Journalof Northeastern University: NaturalScience, 2003, 24( 3) :252- 255. ) 7 Zhang X F, Zhang Q L. Progra
24、m realization of rough setattributes reduction C MProceedings of 6th World Congresson Control and Automation ( WCICA2006) . Piscataway:IEEE, 2006: 5995- 5999. 8 Wong S K M, Ziarko W. On optimal decision tables indecision tables J . Bulletin of the Polish Academy ofSciences, 1985, 33: 694- 696. 9 Now
25、icki R, Slowinski R, Stefanowski J. Evaluation ofvibroacoustic diagnosticsymptoms by means of therough setstheory J . Computers in Industry, 1992, 20( 2) : 141-152. 10, # 5MATLAB p M #: bv, 2004: 377- 382#( XueDing-yu, Chen Yang-quan. T hesolution on MAT LABof advanced application mathematics M . Beijing: T singhuaUniversity Press, 2004: 377- 382. )43第1期 张雪峰等: 粗糙集数据分析系统MATLAB仿真工具箱设计
