Image Processing Reference
In-Depth Information
Examples of t-conorms are shown in Figure 8.4.
Figure 8.4. Four examples of t-conorms. First line:
T 0 (highest t-conorm)
and Lukasiewicz t-conorm. Second line: algebraic sum and maximum
(smallest t-conorm)
Here are a few other useful properties of these operators:
- any t-norm or t-conorm is distributive over the “min” and the “max”, and there-
fore we have equalities of the type:
[0 , 1] 3 ,t x, min( y, z ) =min t ( x, y ) ,t ( x, z ) ;
( x, y, z )
- the only mutually distributive t-norms and t-conorms are the “min” and the
- the only idempotent t-norm is the “min”, and the only idempotent t-conorm is
the “max”;
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