Design and Implementation - Segmentation of Hand Bone for Bone Age Assessment - page 84

Dark Moderate Bright

1

0.8

0.6

0.4

0.2

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

NCL

Fig. 3.14 Membership function of NCL

reside in the X universe. The fuzzy relations of intersection and union in
Mandani implication rules are represented as follow:

µ A ∪ B ( x ) = max [µ A ( x ) , µ B ( x )]

(3.59)

µ A ∩ B ( x ) = min [µ A ( x ) , µ B ( x )]

(3.60)

2. In antecedent part of fuzzy linguistic rules, evaluate the minimum or product of
all membership functions as the resultant antecedent membership function.
3. Evaluate the consequent membership function and the resultant antecedent
membership function from 2) using the either Mamdani max-min inference
method (clipped method) or max-product inference method (scaled method).

The overview of the fuzzy system framework can be illustrated using Fig. 3.18 .
The seven linguistic inference rules presented in Fig. 3.12 are restated in lin-
guistic semantic rules as follows:

1) Rule 1

Rule antecedent If NDE is close

and NCL is dark

Rule Consequent then Quadruple division is least likely