漳州师范学院硕士学位论文不完备决策信息系统下的集对粗糙集拓展模型及其约简姓名：李长清申请学位级别：硕士专业：基础数学指导教师：李克典200905012? ?:?3AbstractThe classical rough set theory based on complete decision information systemsis greatly restricted under incomplete decision information systems.Now there areseveral extensions. Unfortunately,these extensions have their own limitations.Thispaper further extend under determinism of incomplete decision information systemsand set-pair analysis,which is rough set extension based on set-pair connectivity sim-ilarity relation.attribution reduction under incomplete decision information systemsis proposed,which is more extensive than extensive decision reduction.Variable preci-sion rough set model is proposed, which can processes data from many levels.Becauseof neglect of attribution difference under incomplete decision information systemsformerly,weignt valued is defined,and a heuristic algorithm is proposed.When weigntvalued is ignored,discernibility degree is gived,then another heuristic algorithm is re-searched.Finally,containing set is defined,and a new approach of ruler extracting isreachered under incomplete decision information systems.Key Words: incomplete decision information systems;connectivity similarity rela-tion; attribution recuction;ruler extracting? ? ? ? ? ? ? ? ?!“#$%?ABC?DEFGHIJDKL?*+MN,O?VG?/3?WXY4?,?Z?_a+b?cd,Mefg?hi?jkh?l?MeZ.m?nopqrs7?l?tu;v?pqwxyzno|D?U?;?U?,?3?l?D?89?no?$%?; ?3?7?r?D?pU?l?,?l?1rp?;?_jm?a7?“,2r S2 I,?I = (x,x)|x U. SP(,)? ?SPB(,)(x) = y U|(x,y) SPB(,).?X U,X?SPB(X)?SPB(X)?SPB(X) = x U|SPB(,)(x) X,SPB(X) = x U|SPB(,)(x) X 6= .?(,)?x =(1,2,),y = (,),z = (,),?x,y,z?x?y?y?z?x,y,z?5? 3.2?3.2.110?hU,Adi?B A,?x,y U,?x,y?F(x,y)?F(x,y) =( 1,x = y|PB(x)|+|PB(y)| 2|B|, x 6= y?PB(x) = b B|b(x) 6= ,?0 F(x,y) 1.?3.2.2?hU,A di?B A, 0 , 1,?J(,)?JB(,) = (x,y) U U|B(x,y) = S1+ S2i + S3j (S1 S2) (S3= 1 F(x,y) ) I,?I = (x,x)|x U.?J(,)? ?x?JB(,)(x) = y U|(x,y) JB(,).?U/JB(,) = JB(,)(x)|x UU?X U,X?JB(X)?JB(X)?JB(X) = x U|JB(,)(x) X,JB(X) = x U|JB(,)(x) X 6= .?3.2.1?hU,Adi?TA?JA(,)? = = = 0?JA(,) = TA.?JA(,) TA.?(x,y) JA(,),?(x,y) I,?UA(x,y) = S1+ S2i + S3jS1 ,S2 ,?UA(x,y) = S1+ S2i + S3jS3= 1,F(x,y) .?(x,y) I,?a A,?a(x) = a(y),?(x,y) TA.?UA(x,y) = S1+S2i+S3jS1 ,S2 .? = 0,?N(x,y) = ,?a A?a(x) = a(y) = a(x) = a(y),?(x,y) TA.?UA(x,y) = S1+ S2i + S3jS3= 1,F(x,y) ,? = 0,?0 F(x,y) 1,?F(x,y) ?S3= 1,?K(x,y) = A,?a A?a(x) = a(y) = ,?(x,y) TA.?TA JA(,).6?(x,y) TA,? = 0,?S2= 0?N(x,y) = ,?M(x,y) K(x,y) = A.?M(x,y) 6= ,?S1 0,? = 0,?S1 ,?(x,y) JA(,).?K(x,y) = A,?S3= 1.?0 F(x,y) 1, = 0,?F(x,y) ?(x,y) JA(,). 2?3.2.2?hU,Adi?SPA(,)?(,)?JA(,)?0.5 0.5?JA(,) =SPA(,). 2?3.2.3?hU,A di?LA?JA(,)?x U,P(x) 6= ,? = = 0,0.5 1 .? = 1?JB(x) = JB(x),J B(x) = JB(x),?4.2.1?hU,A di?B A,X U,U/d =D1,D2,Dn?U?d?(1) JB(X Di) = X J B(Di)(i n);(2) JB(Di) J B(Dj) = (i,j ni 6= j);(3) JB(Di) J B(Di)(i n);(4) J B(Di) J B(Dj) = (i,j ni 6= j)?4.2.2?hU,A di?B A,?JB= (JB(D1),J B(D2),J B(Dn),J B= (J B(D1),J B(D2),J B(Dn).(1)?JB= JA,?B?B? 6= C B,C?B?(2)?J B= J A,?B?B? 6= C B,C?B?4.2.2?hU,A di?B A,?x U,?EB(x) = Di U/d|x JB(Di),F B(x) = Di U/d|x J B(Di),?(1) B?x U,EB(x) = E A(x);(2) B?x U,FB(x) = F A(x).?(1)JB(Di) = J A(Di)(i n)?x JB(Di) x J A(Di)(i n),?x U,EB(x) = E A(x).(2)?2?4.2.3?hU,A di?B A,?(1) B? B?14?(2) B? B?(1)?B?x U,Di U/d,?D(Di/JB(,)(x) = D