Fuzzy Inference System Details

Adaptive generation of rule base and input variable membership functions

A quantization of the input and output space is based on years of age for the sake of simple natural linguistic interpretation. Since the discrimination power of a feature may differ in various age groups, the domains of input variables are divided into a fuzzy set describing feature values corresponding to one or several consecutive age groups by an adaptive algoritm. Fuzzy sets of the output variable (refer to as the bone age) represent classes corresponding to the years of age.

Interpretation of operators

A Mamdani fuzzy reasoning system is used as a classifier. The knowledge is represented as a set of if-then rules linking the features and the skeletal age. A connection of input variables and an implication are interpreted by a minimum operator. An aggregation of rules is performed by a maximum operator.

Evaluation example

Evaluation of input membership values for given features

Evaluation of outputs: on left several rules for one ROI, on right all ROIs and aggregated final bone age