Fuzzy Sets and Possibility Theory - Information Fusion in Signal and Image Processing - page 145

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”;