Fuzzy Sets and Possibility Theory - Information Fusion in Signal and Image Processing - page 157

when the conflict is equal to 1 (see the example in Figure 8.10). However, this operator
is not associative. Let us note that the min could be replaced with another t-norm.

The last formula (equation [8.81]) is illustrated in Figure 8.10 for two possibility
distributions with an increasing conflict.

π

π 1 π 2

π

'

h=1

s

π

'

π

π 1

π 2

h=0.5

s

π

π 1

π 2

π

'

h=0

s

Figure 8.10. Example of adaptive operators varying from the min
to the max when the conflict between two distributions increases

When the sources are unequally reliable and information is available regarding
this reliability, the level of conflict between two sources indicates to what extent the
information provided by the less reliable source can be taken into account. If, for
example, π 1 is more reliable than π 2 , we can consider that if they are in agreement
with each other, π 2 can provide information and make the fusion more accurate by
conjunction. If, on the other hand, the two sources are in conflict, it is preferable not
to take into account π 2 . The following operator models this behavior:
min π 1 , max π 2 ,h π 1 ,π 2 . [8.82]