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1、Chapter9Uncertainty-BasedInformation9.1InformationandUncertainty•Uncertainty:何謂uncertainty?所謂的uncertainty即是意指資訊量的不足.suchas,incomplete,imprecise,fragmentary,vague,contradictory,unreliable•一般而言,資訊量增加相當於不確定性(uncertainty)的減少(Uncertainty-BasedInformation)suchas,newfact,measureme
2、nt,experience,knowledge•接著我們嘗試利用數學理論去建造一個數學model來判斷一個系統的不確定性(uncertainty)程度如何,其流程如下面此範例e.q.settheoryprobabilistictheoryinformationtheorymeasureifprobabilisticuncertainty(ClaudeShannon)generalizedinformationtheorye.q.FuzzysettheoryFuzzymeasuretheoryPossibilitytheoryEvidencet
3、heoryUncertainty-Basedinformation•不確定性(uncertainty)通常有三種種類,分別如下:1.nonspecificity(orimprecision)-cardinalities2.fuzziness(vagueness)-imprecisionboundaries3.strife(discord)-conflictions9.2NonspecificityofCrispSets•首先我們要量測一個系統的uncertainty,必須先著重在settheory,定義如下式其中:cardinalityofs
4、etAb>1,c>0:determinetheunitofuncertaintye.q.b=2,c=1:Hortlyfunctionuncertaintyismeasureinbitsonebitofuncertainty=thetotaluncertaintyregardingthetruthonfalsityofoneproposition.•Formally,U:-•然而所謂的不確定性(uncertainty)完全是根據不同的setA而有不同的解釋e.q.predicativeuncertainty:Aisasetofpredicted
5、statesofavariablediagnosticuncertainty:Aisasetofpossiblediseasesofapatientretrodictiveuncertainty:Aisasetofpossibleanswertoaquestionprescriptiveuncertainty:Aisasetofpossiblepolicies•任何一個集合都存在著潛在的nonspecificity如這兩種情形:Largesetslessspecific,Singletonsfullspecificity•若把集合A縮減成集合
6、B則theamountofuncertainty-basedinformationI(A,B)=theamountofreduceduncertaintyU(A)-U(B)i.e.,I(A,B)=U(A)-U(B)==where
7、B
8、=1I(A,1)==U(A)U(A)mustalsobeconceivedastheamountofinformationcharacterizeoneelementofsetA•Let,:universalsets:arelation:domainofR:rangeofRLet,,U()=,U()=simple
9、uncertainty:單純的兩個集合,其各自的uncertainty.U(,)=Jointuncertainty:而其中uncertainty是具有結合性質,可將兩集合合併,依舊可以得知此新的集合其uncertainty的程度.•ConditionaluncertaintydefinedbyU(
10、)=:theaveragenumberifelementsofgivenanelementofU(
11、):theaveragenonspecificityofgiven(p.s此定義可以配合Example9.1就可以清楚了解)U(
12、)=•U(
13、)==
14、-=U(
15、)-U()---(9.8)U(
16、)=U(
17、)-U()---(9.9)(9.8)-(9.9)U()-U()=U(
18、)-U(
19、)(而其中可分為Noninter
