IEEE Systems, Man and Cybernetics Magazine - April 2021 - 5

their applications are investigated
Data Fusion
have been published. Since then,
The problem of data fusion, a synThe OWA operator
the family of these functions has
thesis of information or aggregating
is different from the
been axiomatized and developed in
criteria used to form overall decivarious ways [10], [11], [27].
sions, is of considerable importance
classical weighted
The goal of this article is to proin many fields of human knowledge.
average because
vide a short review of OWA operaBecause data are obtained more
its weights are not
tors, to identify trends in the
easily, this field is of increasing
literature, and to synthesize some
interest. Some of the fields that use
directly associated
of the most significant results.
aggregation functions are mathewith a particular
matics, economics, biology, educaOWA
tion, artificial intelligence, robotics,
attribute but rather
Both the weighted mean and the
vision, fuzzy logic controllers, and
with an ordered
OWA operator are used to combine
knowledge acquisition.
position.
values with respect to a set of
One of the most prominent
weights. The main difference is
groups of applications of aggregathat the weights have different
tion functions comes from decision
meanings in each function. On one
theory. Making decisions often
hand, the weighted mean allows the system to compute an
leads to aggregating preferences or scores on a given set of
aggregate value from the ones corresponding to several
alternatives, the preferences being obtained from several
sources, taking into account the reliability of each infordecision makers, experts, voters, or representing different
mation source. Each source has an attached weight that
points of view, criteria, or objectives. This concerns decimeasures its reliability. On the other hand, the OWA operasions under multiple criteria or multiple attributes, multitor permits weighting the values in relation to their orderperson decision making, and multi-objective optimization.
ing. In this way, a system can give more importance to a
Another group comes from artificial intelligence: fuzzy
subset of the input values than to another subset. For
logic. Pattern recognition and classification as well as
instance, the influence of extreme values to the result can
image analysis are typical examples. Aggregation funcbe diminished, increasing the influence of central values.
tions are inevitably used as a generalization of logical conThe function, however, is symmetric, i.e., any permutation
nectives in rule-based systems. In artificial intelligence,
of the arguments gives the same result. Therefore, while in
these techniques are used mainly when a system has to
the weighted mean the weights measure the importance of
make a decision. The system can have one single criterion
an information source with the independence of the value
for each alternative, or several ones. This case correthat the source has captured, in the OWA, the weights measponds to a multicriteria decision-making problem. Fursure the importance of a value (in relation to other values)
thermore, if a system needs a good representation of an
independently from the information source where it origienvironment, it needs the knowledge supplied by informanated. The need for symmetry is rather frequent in practition sources to be reliable. However, the information supcal applications, which gives preference to OWA operators
plied by a single information source (by a single expert or
against weighted arithmetic means.
sensor) is often not reliable enough. That is why the inforIn other words, the OWA operator is different from the
mation provided from several sensors (or experts) should
classical weighted average because its weights are not
be combined to improve data reliability and accuracy and
directly associated with a particular attribute but rather
also to include some features that are impossible to perwith an ordered position. The structure of these operators
ceive with individual sensors.
is in the spirit of combining the criteria under the guidance
The main factor in determining the structure of the
needed aggregation function is the relationship among the
of a quantifier. This means that the requirement described
criteria. At one extreme is the case in which we desire all
by a linguistic variable as, for instance, " most " of the critethe criteria to be satisfied. At the other extreme is the situria is to be satisfied, corresponds to one of these OWA operation in which we want the satisfaction of any of the criteators [30]. Fodor et. al. showed that it is also possible to
ria. These two extreme cases lead to the use of " and " and
describe the class of OWA operators axiomatically; i.e., by
" or " operators to combine the criteria functions.
means of their properties [11]. It was proved that the class
In 1988, Yager [26] defined an alternative aggregation
of the OWA aggregators is the operators that satisfy the
function, the so-called OWA operator, to provide the means
properties of neutrality, monotonicity, and stability for the
for aggregating the scores associated with the satisfaction
same positive linear transformations and ordered linkage.
of multiple criteria, which unifies in one operator the conjunctive and disjunctive behavior. This function has attractDefinition 1
ed the interest of several researchers. A considerable
An OWA operator of dimension n is the mapping F : I n " I if
number of articles in which their properties are studied and
it has an associated weighting vector w = (w 1, w 2, ..., w n),

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