西安电子科技大学：《神经网络与模糊系统 Neural Networks and Fuzzy Systems》课程PPT课件讲稿（2004）Chapter 08-2 Fuzzy Associative Memories 模糊联想记忆 FUZZY ASSOCIATIVE MEMMORIESⅡ

模糊联想记忆 FUZZY ASSOCIATIVE Presented by Yang Baisheng E.E.Dept. Xidian University

模糊联想记忆 FUZZY ASSOCIATIVE MEMMORIESⅡ Presented by Yang Baisheng E.E. Dept. Xidian University

OUTLINE Fuzzy Hebb FAMs(续) 6.Binary Input-Output FAMs 7.Multiantecedent FAM Rules 8.Adaptive Decompositional Inference Adaptive FAMs (Product-Space Clustering in FAM Cells) 1.Adaptive FAM-Rule Generation 2.Adaptive BIOFAM Clustering 3.Adaptive BIOFAM Example: Inverted Pendulum

OUTLINE  Fuzzy Hebb FAMs（续） 6.Binary Input-Output FAMs 7. Multiantecedent FAM Rules 8. Adaptive Decompositional Inference  Adaptive FAMs (Product-Space Clustering in FAM Cells) 1.Adaptive FAM-Rule Generation 2.Adaptive BIOFAM Clustering 3.Adaptive BIOFAM Example: Inverted Pendulum

Binary Input-Output FAMs BIOFAMs map system-variable to control, classification,or other output data. For example: A BIOFAM maps traffic densities to screen (and red)light durations. In inverted-pendulum example,the system maps the system-variable (d,v,d)to control data(并

Binary Input-Output FAMs BIOFAMs map system-variable to control, classification, or other output data. For example: A BIOFAM maps traffic densities to screen (and red) light durations. In inverted-pendulum example, the system maps the system-variable ( ) to control data ( ). ,d,v,dv f

Multiantecedent FAM Rules (多前提FAM规则) 1.Consider the FAM rule:"IF X is A,THEN C isZ,”or(A,C)for short M4c=47.C 2.The rule is "IF X is AAND Y is B,THEN C is Z,”or(A,B,C)for short. What to do?

Multiantecedent FAM Rules (多前提FAM规则) 1.Consider the FAM rule: “IF X is A, THEN C is Z,” or for short. 2.The rule is “IF X is A AND Y is B, THEN C is Z,” or for short. C T A AC M =  (A,B;C) (A,C) What to do?

Multiantecedent FAM Rules （多条件FAM规则) 2 Single-antecedent FAMs: (A,C) MAC=A.C (B,C) MBC=BT.C Defuzzify it to yield the exact output. Multiantecedent FAM Rules:(4,B;C) F(A,B)=[AMACIO[BMBC] =C,∩C,=C B

Multiantecedent FAM Rules (多条件FAM规则) 2 Single-antecedent FAMs: Multiantecedent FAM Rules: ( , ) [ ] [ ] ' ' ' ' F A B = A  M AC  B  MBC M AC A A C  ' ' = ' ' ' C B C A = C  = C ' = BC B M B C  ' ' = C T B BC M =  (B,C) (A,C) C T A AC M =  (A,B;C) Defuzzify it to yield the exact output

Multiantecedent FAM Rules Suppose we present the exact inputs x,,y,to the single-FAM-rule system F that stores(A,B;C). We present the unit bit vectors and I to F as nonfuzzy set inputs.Then F(xy )=F(Ix,I) Property of =[I%MAc]O[Iy MEC] Hebb Matrix =a,∧C∩b,AC =mm(a,b,)ΛC

Multiantecedent FAM Rules Suppose we present the exact inputs , to the single-FAM-rule system that stores(A,B;C). We present the unit bit vectors and to as nonfuzzy set inputs.Then i x ( , ) ( , ) j Y i i j X F x y = F I I [ ] [ ] BC j AC Y i = I X  M  I  M = ai C bj C = min( ai ,bj ) C j y F i X I j Y I F Property of Hebb Matrix

Multiantecedent FAM Rules Representing Cwith its membership function mc ◆For all z in Z min(a,b,)Λmc(2） BIOFAM prescription

Multiantecedent FAM Rules  Representing with its membership function  For all in : z min( a ,b ) m (z) i j  C Z C mC BIOFAM prescription

Multiantecedent FAM Rules IF we encode (4,C)and (B,C)with correlation- product encoding,decompositional inference gives the BIOFAM version of correlation-product inference: F(xy )=[IA'C]O[IB"C] a,C⌒b.C Correlation- min(a,,b,)C Product Encoding min(a;,b;)mc(z) Also,We can get the FAM rules:(4,B;C.D)

Multiantecedent FAM Rules Also, We can get the FAM rules: (A,B;C, D) F(x ,y ) [I A C] [I B C] j T Y i T i j X =    = ai C bj C = min( ai ,bj )C min( a ,b )m (z) = i j C IF we encode : and with correlation￾product encoding, decompositional inference gives the BIOFAM version of correlation-product inference: (A,C) (B,C) Correlation￾Product Encoding

Adaptive Decompositional Inference Let Nx:I”→I'define an arbitrary neural. network system that maps fuzzy subset 4 of to fuzzy subsets C of Z.Ny:I can define a different neural-network. F(A,B)=Nx(A)∩N(B) =C∩Cg The neural- network change with C time

Adaptive Decompositional Inference  Let define an arbitrary neural￾network system that maps fuzzy subset of to fuzzy subsets of . can define a different neural-network. n q X N : I → I ( , ) ( ) ( ) ' ' ' ' F A B = NX A  NY B ' ' A B = C C ' = C p q Y N : I → I ' A X ' C Z The neural￾network change with time

Adaptive FAMs(Product-Space Clustering in FAM Cells) Adaptive FAM-Rule Generation Adaptive BIOFAM Clustering Adaptive BIOFAM Example: Inverted Pendulum

Adaptive FAMs(Product-Space Clustering in FAM Cells)  Adaptive FAM-Rule Generation  Adaptive BIOFAM Clustering  Adaptive BIOFAM Example: Inverted Pendulum