模糊信息處理 北京大學(xué) 譚營 智能信息處理知識講解

1、1,智能信息處理課程,第二講,模糊信息處理技術(shù),主講,譚,營,教授,北京大學(xué)信息科學(xué)技術(shù)學(xué)院智能科學(xué)系,2007,年,9,月,14,日,星期五,3,4,節(jié),二教,421,2,普通集合,集合的概念,3,普通集合,集合的表示方法,4,普通集合,集合的并、交、差、補(bǔ),5,集合運(yùn)算規(guī)則,6,對應(yīng)關(guān)系,7,特征函數(shù),8,特征函數(shù)的運(yùn)算,集合的特征函數(shù)表示,9,集合的直積,10,關(guān)系矩陣,11,12,Let A be a set,Define a function, called characteristic function,A,X,0, 1,A,x,if,A,x,if,x,A,1,0,Example,

2、A = set of all even number,A,2) = 1,A,3) = 0,Crisp sets,13,Fuzzy sets,A,X,0, 1,The tree height is 22 m,24,0,24,22,900,45,sin,22,1,22,20,10,5,0,20,0,x,if,t,if,x,t,if,t,if,x,x,if,x,A,14,模糊集,15,16,模糊集例子,17,模糊集合,18,模糊性與隨機(jī)性,模糊性總是伴隨著復(fù)雜性而出現(xiàn),復(fù)雜性意味著因素的多樣性、關(guān)聯(lián)的多樣性,隨機(jī)性：事件是否發(fā)生的因果律被破壞而造,成的一種不確定性,模糊性：事物本身性態(tài)和屬性的不確定

3、性,從信息觀點(diǎn)看：隨機(jī)性只涉及信息的量，模糊,性關(guān)系到信息的意義、信息的定性問題,模糊性是一種比隨機(jī)性更深刻的不確定性,19,模糊集合的表示,Zadeh,表示法,20,模糊集合的表示,向量表示法,21,模糊集合的表示,隸屬函數(shù)表示法,22,隸屬函數(shù)的確定,1,Fuzzy,統(tǒng)計法,23,怎樣確定隸屬函數(shù),1,Subjective,evaluation,and,elicitation,As,fuzzy,sets,are,usually,intended,to,model,peoples,cognitive,states,they,can,be,determined,from,either,simp

4、le,or,sophisticated,elicitation,procedures,At,they,very,least,subjects,simply,draw,or,otherwise,specify,different,membership,curves,appropriate,to,a,given,problem,These,subjects,are,typically,experts,in,the,problem,area,Or,they,are,given,a,more,constrained,set,of,possible,curves,from,which,they,choo

5、se,Under,more,complex,methods,users,can,be,tested,using,psychological,methods,2,Ad-hoc,forms,While,there,is,a,vast,hugely,infinite,array,of,possible,membership,function,forms,most,actual,fuzzy,control,operations,draw,from,a,very,small,set,of,different,curves,for,example,simple,forms,of,fuzzy,numbers

6、,This,simplifies,the,problem,for,example,to,choosing,just,the,central,value,and,the,slope,on,either,side,24,3,Converted,frequencies,or,probabilities,Sometimes,information,taken,in,the,form,of,frequency,histograms,or,other,probability,curves,are,used,as,the,basis,to,construct,a,membership,function,Th

7、ere,are,a,variety,of,possible,conversion,methods,each,with,its,own,mathematical,and,methodological,strengths,and,weaknesses,However,it,should,always,be,remembered,that,membership,functions,are,NOT,necessarily,probabilities,4,Physical,measurement,Many,applications,of,fuzzy,logic,use,physical,measurem

8、ent,but,almost,none,measure,the,membership,grade,directly,Instead,a,membership,function,is,provided,by,another,method,and,then,the,individual,membership,grades,of,data,are,calculated,from,it,5,Learning,and,adaptation,25,隸屬函數(shù)的確定,2,幾種常見的隸屬函數(shù)形式,26,常見的隸屬函數(shù)形式,27,28,模糊集合的基本運(yùn)算,29,30,例子,31,模糊集合運(yùn)算的基本規(guī)則,32,33,34,模糊關(guān)系,定義,35,36,模糊關(guān)系矩陣和關(guān)系圖,37,38,截矩陣,39,截矩陣的性質(zhì),40,模糊關(guān)系的運(yùn)算,41,例子,42,43,模糊關(guān)系的性質(zhì),44,模糊邏輯,模