**6.5 Simplified fuzzy ARTMAP module**

In context of the circuit partitining in VLSI design to recognize the subcircuit with minimum interconnection between them, the size of input layer is 4 and output layer is 10. Hence it outcomes in 2-10 layered Fuzzy ARTMAP model.

Match and choice function for fuzzy ARTMAP in context to circuit partitioning is defined by,

For input vector I and cluster j from DBSCAN algorithm, Choice function given by

$$\text{CFj(I)} = \frac{|\text{I}^\text{\textdegree} \text{Wj}|}{\alpha + |\text{ Wj}|} \tag{14}$$

Where is small constant about 0.0000001,Wj is top-down weight

Winner node is one with highest activation /choice function, that is,

$$\text{Wimner} \equiv \max(\text{CFj}) \tag{15}$$

Match function which is very much used to find out whether the network must adjust its learning parameters is given by,

$$\text{IFj}(\text{I}) = \frac{|\text{I} \cap \text{Wj}|}{|\text{I}|} \tag{16}$$

If MF j (I) vigilance parameter () then Network is in state of resonance, where is in range 0 1.

If MF j (I) vigilance parameter () then Network is in state of mismatch reset.
