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