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 correlationproduct encoding, decompositional inference gives the BIOFAM version of correlation-product inference: (A,C) (B,C) CorrelationProduct 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 neuralnetwork 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 neuralnetwork 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