Fuzzy Graph Pattern Recognition for ISNet

To map experimental ISNets onto their ISNet cluster centers, the ISNets have to be subjected to two screening procedures, namely  

When an ISNet is matched to its cluster center, it may output a number of topological mappings as illustrated in Fig. 7. The best mapping will be used for the fuzzy graph similarity calculation. 

If each observed chemical shift obeys a Gaussian distribution, the membership function of each mapping pair ju.(c5, - csjj may be ealcu-lated as 

It is interesting to analyze (22)-(24) individually. Equation (22) indicates that can be zero if the value of one of the member functions is zero. 

Equation (23) indicates that 5ms( .) is a generalized Euclidean distance that will not be zero unless every p, value is zero. Equation (24) is a fuzzy similarity relationship that always takes the minimum value as the similarity, no matter what other /a values are. 

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