Fuzzy Sets and Possibility Theory - Information Fusion in Signal and Image Processing - page 155

These operations can be arranged in two different orders depending on the values
to combine:
x + y ≤ 1= ⇒ σ 0 ( x, y ) ≤ σ min ( x, y ) ≤ σ max ( x, y ) ≤ σ + ( x, y ) , [8.75]

x + y ≥ 1= ⇒ σ 0 ( x, y ) ≥ σ min ( x, y ) ≥ σ max ( x, y ) ≥ σ + ( x, y ) . [8.76]

The four examples in Table 8.2 are illustrated in Figure 8.9.

Figure 8.9. Four examples of symmetric sums. First line: σ 0 and σ + .

Second line: σ min and σ max

8.5.5. Adaptive operators

There are many operators found in other works that we will not discuss here. We
will simply mention adaptive operators according to conflict between possibility dis-
tributions [DUB 92a], which behave like a min when the distributions are consonant
and like a max when they produce a strong conflict. Let π 1 and π 2 be two possibility