Image Processing Reference

In-Depth Information

Fuzzy fusion operators fall into three categories. T-norms, which generalize set

intersection to fuzzy sets, are conjunctive CICB operators, since for any t-norm
t
,we

have:

[0
,
1]
2
,t
(
x, y
)

∀

(
x, y
)

∈

≤

min(
x, y
)
.

On the other hand, t-conorms which generalize union are disjunctive CICB opera-

tors, since for any t-conorms
T
,wehave:

[0
,
1]
2
,T
(
x, y
)

∀

(
x, y
)

∈

≥

max(
x, y
)
.

Mean operators are also CICBs and have a compromise behavior, since they verify:

[0
,
1]
2
,
min(
x, y
)

∀

(
x, y
)

∈

≤

m
(
x, y
)

≤

max(
x, y
)
.

Let us note that Bayesian fusion, in which the operator involved is a product, and

fusion of belief functions using Dempster's orthogonal sum are also conjunctive.

In the CIVB operator class we have, for example, certain symmetric sums. Gener-

ally speaking, any associative symmetric sum
σ
(except for medians) has the following

behavior [DUB 88]:

- conjunctive if max(
x, y
)
<
1
/
2:
σ
(
x, y
)

≤

min(
x, y
);

- disjunctive if min(
x, y
)
>
1
/
2:
σ
(
x, y
)

≥

max(
x, y
);

- compromise if
x

≤

1
/
2

≤

y
:
x

≤

σ
(
x, y
)

≤

y
(and the opposite inequality if

y

≤

1
/
2

≤

x
).

Non-associative symmetric sums also have a variable behavior, but according to

less simple rules [BLO 96b].

In the CIVB operator class, we also have the operators suggested in the MYCIN

system for combining certainty factors [SHO 75].

Examples of CD operators are found in possibility theory. Earlier, we presented

operators that depended on an overall measure of the conflict between two sources of

information [DUB 92a], which are applicable to cases where one of the two elements

of information is reliable, but where we do not know which one, so that:

- they are conjunctive if the sources are consonant (low conflict): in this case, the

two sources are necessarily reliable and therefore the operator can be strict;

- they are disjunctive if the sources are dissonant (high conflict): a disjunction then

favors all of the possibilities provided by both sources;

Search WWH ::

Custom Search