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
)

∈

[8.51]

- the only mutually distributive t-norms and t-conorms are the “min” and the

“max”;

- the only idempotent t-norm is the “min”, and the only idempotent t-conorm is

the “max”;

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