The Importance of Aggregation Operator Characteristics in Marketing Research.

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THE IMPORTANCE OF AGGREGATION OPERATOR
CHARACTERISTICS IN MARKETING RESEARCH
Kris Brijs, Benoˆ ıt Depaire, Koen Vanhoof, Tom Brijs, Geert Wets
Faculty of Applied Economics, Hasselt University, Campus Diepenbeek, 3590 Diepenbeek, Belgium
kris.brijs@uhasselt.be, benoit.depaire@uhasselt.be, koen.vanhoof@uhasselt.be, tom.brijs@uhasselt.be, geert.wets@uhasselt.be
Keywords:
Uninorm’s neutral value, OWA’s orness, customer satisfaction, country-of-origin.
Abstract:
Our paper demonstrates that aggregation operator characteristics count as a promising avenue for applied
fuzzy set research. It is shown by means of two cases that these characteristics are particularly valuable
as proxies for hard to measure domain knowledge within the fields of customer satisfaction and country-of-
origin. More in detail, the uninorm’s neutral element could be identified as a useful asset for representing
customers’ expectations while the OWA operator’s orness contributes to the quantification of consumers’
degreeofoptimismwhenevaluatingproductscomingfromabroad. Boththeoreticalandempiricalvalidationis
provided to support the basic assumption that aggregation operator characteristics enable us to obtain superior
consumer information with substantial managerial relevance.
1INTRODUCTION
Over the last ten years, a whole range of aggregation
operators (AGOPs) have been developed and exten-
sively studied in the lap of fuzzy set and non-classical
decision theory [Dubois and Prade, 2004].
mathematically well-founded constructs have found
their way into several application domains, such as
economics, biology, education, knowledge-based sys-
tems and robotics [Torra, 2002].
To which extent an AGOP is useful within a cer-
tain domain depends, among others, on how well the
AGOP’s mathematical properties match the underly-
ing information fusion process. Certain AGOPs pos-
sess mathematical characteristics which can be inter-
preted as behavioral parameters, i.e., their values have
an influence on the behavior of the operator (e.g., the
orness or maxness determines how strongly the or-
dered weighted averaging (OWA) operator behaves
like the maximum operator).
Past research on AGOP applications has mainly
focused on the AGOP’s domain representation power
or decision-making strength [Torra, 2002]. However,
as this study shows, certain AGOP’s characteristics
which play a role in the AGOP’s behavior (i.e. behav-
ioral parameters) can be of great importance to practi-
These
tioners, especially when these behavioral parameters
are proxies for domain-specific information which is
difficult to measure directly or to derive statistically.
In such cases, these AGOP’s behavioral parameters
become much more than just another mathematical
characteristic.
The main objective of this paper is to illustrate
that two different AGOPs, i.e., the uninorm and OWA
operator, can both be successfully applied within the
field of marketing research. More in detail, we will
argue that each operator contains a behavioral param-
eter which can be used as a proxy for marketing-
specific knowledge that cannot always be obtained by
means of statistical techniques traditionally used by
marketing scholars.
As for the outline of this paper, the next two sec-
tions present two case studies, one for each AGOP.
Section two will discuss the use of uninorms in cus-
tomer (dis)satisfaction theory. It will be shown that
the uninorm’s neutral element is a good proxy for cus-
tomer’s expectations. The third section will comment
on the estimation of country-of-origin (coo) effects.
Here, it will be shown that the use of the OWA opera-
tor’s orness can be a valuable approach for determin-
ing how country-related feelings impact on the for-
mation of consumers’ attitude toward foreign sourced

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products. Finally, once the case-study analyses have
been completed, a fourth section will be reserved for
an overall conclusion.
2THE UNINORM AGGREGATOR
IN CUSTOMER SATISFACTION
THEORY
2.1 Marketing Context
Over the last four decades, customer (dis)satisfaction
has taken an important role in marketing research,
both from an academic as from a managerial point
of view. Although this hasn’t always been the case,
customer (dis)satisfaction is now widely recognized
as an important cornerstone for customer-orientated
companies, irrespective of the industry they operate in
[Vanhoof et al., 2003,Szymanski and Henard, 2001]
and has an influence on several important aspects
of a competitive business [Szymanski and Henard,
2001,Anderson et al., 1994,Anderson et al., 2004].
The last three decades, the focus of customer sat-
isfaction research has shifted from what it was about
the product or service that customers found satisfying
to how and why customers became satisfied. Several
theoretical models have tried to explain the human
behavior in a customer satisfaction context. In this
article, we will focus on the expectancy disconfirma-
tion model [Oliver, 1996], which is one of the more
dominant models in customer satisfaction research.
On the one hand, this model focuses on the discrep-
ancy between perceived performance and customer’s
expectation and on the other hand on the customer’s
expectation itself. According to this paradigm, every
customer holds pre-purchase product/service expecta-
tions, which have a direct influence on the customer’s
satisfaction. Furthermore, these expectations act as a
reference, used by the customer to compare the per-
ceived performance against, which leads to positive
or negative disconfirmation. Both expectation and
disconfirmation seem to be positively correlated with
customersatisfaction[Oliver, 1996], butinmostcases
one of the two factors will dominate the other.
Expectation plays an important role in Oliver’s
expectation disconfirmation paradigm, both directly
and indirectly by acting as a reference point. How-
ever, measuring unbiased pre-purchase expectations
directly is very difficult. Firstly, post-purchase ques-
tionnaires measure post-purchase expectations, which
can differ from pre-purchase levels of expectation
because expectations and performance are inevitably
confounded once performance observations have be-
gun [Oliver, 1996]. Second, several levels of expec-
tations exists and it is not always clear which level
is used as reference. Oliver summarizes no less than
eight types of expectations, ranging from intolerable
expectations over needed and deserved expectations
to ideal expectations. Also, Cadotte et al. showed that
the reference norm does not necessarily have to be
the product’s or brand’s expectation. Other standards,
based on experience, are also possible, although ex-
pectations cannot be ruled out [Cadotte et al., 1987].
Furthermore, Oliver mentions in a 1980 paper that
“disconfirmationtakesplaceattheindividualattribute
level” [Oliver, 1996].This implies that the con-
sumer has a certain expectation and perceives a spe-
cific performance and disconfirmation for each prod-
uct/service attribute or attribute dimension. There-
fore, the consumer must aggregate all these expec-
tations and disconfirmations into an overall satisfac-
tion response. This aggregation is a heuristic based
decision-making process. Vanhoof et al. [Vanhoof
et al., 2005] identify two main heuristics in the cus-
tomer’s (dis)satisfaction process, i.e., ‘anchoring and
adjustment’ and ‘reinforcement’.
The first heuristic, ‘anchoring and adjustment’ is
closely related to the assimilation effect of the ex-
pectancy disconfirmation paradigm. If the perceived
attributes’ performances lie close to the expected per-
formance level, compensation behavior between the
perceived disconfirmations will occur, assimilating
theoverallsatisfactionlevelintothe expectationlevel.
The second heuristic, ‘reinforcement’, is closely
related to the contrast effects in the expectancy dis-
confirmation paradigm. If attribute performances sig-
nificantly fall short of or exceed expectations, peo-
ple tend to increasingly exaggerate evaluations and
final (dis)satisfaction. “As a consequence, average
attribute-level satisfaction scores that all fall below
(exceed) the product-level norm are expected to ag-
gregate to an overall product-level satisfaction score
that is lower (higher) than the weighted average of the
attribute-level scores” [Vanhoof et al., 2005].
Finally, Oliver also mentions it is unlikely that all
customers show the same relationships among per-
formance, expectation, disconfirmation and satisfac-
tion [Oliver, 1996]. Therefore, most customers will
have a unique expectation level and aggregation pro-
cess.
2.2Behavioral Parameter: The
Uninorm’s Neutral Element
The uninorm aggregation operator is the result of the
unification of the t-norm and the t-conorm operator,
studied and presented by Yager et al. [Yager and

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Rybalov, 1996].
Definition 1 [Yager and Rybalov, 1996] A uni-norm
U is a mapping U : [0,1]×[0,1] → [0,1] having the
following properties:
i) U(a,b) =U(b,a) (Commutativity)
ii) U(a,b) ≥U(c,d) if a ≥ c and b ≥ d (Monotonic-
ity)
iii) U(a,U(b,c)) =U(U(a,b),c) (Associativity)
iv) There exists some element e ∈ [0,1] called the
identity element such that for all a ∈ [0,1],
U(a,e) = a
According to definition 1, a uninorm can be regarded
as a function that takes two values (attribute perfor-
mances) and maps it to the ‘aggregated’ value (over-
all satisfaction). The commutativity property implies
that the ‘aggregated’ value is independent of the or-
der of the arguments of the uninorm. The mono-
tonicity is a mathematical property that ensures that
the aggregated value cannot decrease as one of the
uninorm arguments increases. The associativity al-
lows the extension of the standard uninorm to an n-
argument function. These first three properties are
also common to the t-norm and the t-conorm opera-
tor, but the fourth property is more general in the case
of uninorms in that it allows any value for the identity
element e. This element acts as the neutral element or
null vote, i.e. the argument’s impact on the aggrega-
tion will be null if its value equals the neutral element.
Furthermore, the neutral element determines
whether the aggregation contains reinforcement
or compensation behavior.
downward [upward] reinforcement behavior, i.e.
U(a,b) ≤ min(a,b) [U(a,b) ≥ max(a,b)], if both the
aggregator’s arguments belong to the interval [0,e]
([e,1])(cfTable1customers1and3). Ifoneargument
belongs to the interval [0,e] and the other argument
belongs to the interval ]e,1], the uninorm shows com-
pensationbehavior(min(a,b) ≤U(a,b) ≤ max(a,b))
(cf Table 1 customer 2).
Therefore, if the neutral element is different from
zero or one, the same uninorm can both model full
reinforcement and compensation behavior [Yager and
Rybalov, 1998]. Because the neutral element plays
such a crucial role in the final modeling behavior, we
refer to it as a behavioral parameter.
The uninorm shows
Table 1: Illustration Uninorm and Neutral Element
abU(a,b)
Satisfaction
e
Customere.g. Pricee.g. TasteExpectation
1
2
3
3
3
3
6
6
6
7
4
1
2
5
8
Previous research showed that the neutral element
is a proxy for the expectation or reference standard in
the customer (dis)satisfaction process [Vanhoof et al.,
2003]. The expectation or reference standard plays
an important role in the customer’s (dis)satisfaction
response, but is difficult to measure directly. There-
fore, this uninorm’s behavioral parameter can be of
great interest to marketeers.
Of all candidate uninorms, we chose Dombi’s ag-
gregation operator [Dombi, 1982], which belongs to
the set of generated uninorms. This type of uninorm
can be constructed with the help of a generator func-
tion g(x) [Fodor et al., 1997], which must be a con-
tinuous and strictly increasing generator function, by
means of equation 1.
U(x1,x2) = g?g−1(x1)+g−1(x2)?
Based on the associativity property, this can be
generalized into
(1)
U(X) = g
?
X
∑g−1(x)
?
(2)
Furthermore, Dombi showed that the generator
function g(x) displaced by d, g(x+d) = gd(x), also
possesses the properties of a uninorm generator func-
tion. The displaced generator function gd(x) gener-
ates a new uninorm with a different neutral element.
This implies that several uninorms, each with differ-
ent neutral elements e, can be generated from one sin-
gle generator function.
To derive the neutral element, we can use the
following property which holds for Dombi’s uni-
norm [Dombi, 1982].
U(x,n(x)) = e
(3)
The negation function n(x) can be derived math-
ematically from the generator function by means of
equation 4
n : [0,1] → [0,1] : n(x) = g−1(1−g(x))
In sum, first the generator must be learned for
each respondent, based on his attribute performance
scores, his overall satisfaction score and an ‘a priori’
specified functional form for the generator. This al-
lows us to construct the corresponding uninorm and
the corresponding negation function. By means of the
negation function it is possible to calculate the neu-
tral value, which can be interpreted as proxy for the
hard-to-measure expectation level in the customer’s
(dis)satisfaction process.
(4)

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2.3 Data
This research includes data from a customer satisfac-
tion survey within the financial sector. The survey
measures performance on 70 attributes, which can be
classified into 8 domains (cf, Table 2). Furthermore,
the survey includes an overall satisfaction score and
a performance score for all eight plus two additional
domains, which are ‘Value for money’ and ‘Qual-
ity’. Allperformancescoresweremeasuredonascale
from 1 [extremely low] to 5 [extremely high]. The
overall satisfaction score was obtained by means of a
scale going from 0 [extremely low] to 10 [extremely
high]. The final data set contains 1201 cases.
Table 2: Attribute Dimensions.
Attribute dimension Number of attributes
Value for money
Image
Price
Quality
Products
Sales service
Maintenance
Invoices
Administration
Communication
/
10
6
/
9
10
15
6
6
8
2.4 Validation
2.4.1Theoretical Validation
Theoretical validation is provided when the AGOP’s
modeling capacities fit the domain’s theoretical
framework well. For the domain of customer
(dis)satisfaction, an AGOP is needed which is able
to model the heuristics present in the (dis)satisfaction
formation process. After the previous discussion on
the customer (dis)satisfaction process and the uni-
norm’s properties, it is clear that the uninorm suc-
ceeds well in this task.
Firstly, the uninorm’s compensation behavior is
capable of modeling the (dis)satisfaction process’ as-
similation effect and the ‘anchoring and adjustment’
heuristic.Secondly, the contrast effects and ‘re-
inforcement’ heuristic can be modeled by the uni-
norm through its reinforcement behavior. In addi-
tion, the uninorm calculates the (dis)satisfaction score
based on the attribute’s performance or disconfirma-
tion scores. This reflects the idea that (dis)satisfaction
is ultimately formed at the attribute level. Finally, a
uninorm can be constructed for each correspondent.
This further strengthens the match between the uni-
norm and the (dis)satisfaction process because it al-
lows us to perform customer (dis)satisfaction analysis
at a single-customer level. All these aspects provide
substantialtheoreticalvalidation, makingtheuninorm
a good candidate to model customer (dis)satisfaction.
2.4.2Empirical Validation
Theoretical validation is a good foundation, but is
clearly not enough to prove the useability of a behav-
ioral parameter as proxy for domain-specific knowl-
edge. In addition to the theoretical validation, further
empirical validation is required. The latter implies
that the results ‘make sense’ in the applied domain.
Previous research has already validated the use of
the uninorm’s neutral element as a proxy for the cus-
tomer’s expected value [Vanhoof et al., 2003,Vanhoof
et al., 2005]. We will further strengthen this valida-
tion by comparing our results with conclusions from
Szymanski and Henard’s meta-analysis of 85 existing
research studies on customer satisfaction [Szymanski
and Henard, 2001]. A substantial part of their paper
focuses on the relationships between customer satis-
faction and several of its antecedents. Table 3 shows
the results of Szymanski and Henard, compared with
our results.
We limited our study to the correlations between
directly measured elements (performance and sat-
isfaction) and uninorm-derived elements (expecta-
tions and disconfirmation), with the exception of the
‘performance-satisfaction’ correlate.
According to Szymanski and Henard’s study, per-
formance is predominantly positively correlated with
overall satisfaction. In line with these findings, our
study establishes that all 10 domain’s performance
scores are positively correlated with the overall sat-
isfaction. This indicates a certain level of trustworthi-
ness in the survey’s results.
Table 3 also shows that the uninorm-derived mea-
sures, which are expectation and disconfirmation,
closely follow the empirically expected patterns. The
correlates ‘expectation-satisfaction’ and ‘expectation-
performance’ are 100% significantly positively corre-
lated, which is the predominant pattern in other stud-
ies. The relation ‘disconfirmation-satisfaction’ shows
the weakest similarity with empirical evidence. How-
ever, it should be kept in mind that our disconfirma-
tion score represents the objectively calculated dis-
confirmation, which is not necessarily the same as the
subjective disconfirmation. Overall, together with re-
sultsobtainedbyVanhoofetal.[Vanhoofetal., 2003],
we can conclude that the uninorm’s neutral element is
a valid proxy for customer’s expectation.

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Table 3: Validation of the Satisfaction-Related Correlations
Szymanski and HenardOur results
Positive Correlations
13
121
136
22
Negative Correlations
1
1
17
1
Positive Correlations
1
4
10
10
Negative Correlations
0
1
0
0
Expectation†- satisfaction
Disconfirmation‡- satisfaction
Performance - satisfaction
Expectation†- performance
NOTE IOnly statistically significant correlations at alpha ≤ .05 were considered.
NOTE IIExpectation, disconfirmation and performance is measured or derived for the attribute domain level.
†expectation = uninorm’s neutral element.
‡disconfirmation = performance - expectation.
2.5Implications
Figure 1 illustrates the implications of the availabil-
ity of expectation measures. This figure shows the
average performance scores and average expectation
measures for each attribute domain. The performance
scores for each domain are measured directly by the
survey.The expectation measures are derived by
use of the uninorm approach, with the attribute per-
formances as the uninorm’s arguments and the at-
tribute domain performance as the uninorm’s aggre-
gated value.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Image
Price
Products
Sales service
Maintenance
Invoices
Administration
Communication
Performance
Expectation
Figure 1: Average domain performance and expectation.
Based solely on the performance scores, a mar-
keteer or manager would conclude that the firm was
performing well on all its attribute domains, except
‘price’. Furthermore, ‘products’, ‘sales service’ and
‘maintenance’ would be identified as the top three
performing domains.
However, the expectation scores create a rather
different picture of the company. First of all, it seems
that all domain performances lie in the neighborhood
of the expected performance, except for ‘adminis-
tration’. Even ‘price’, the least performing domain,
seems to be doing rather well compared to its ex-
pected performance. Figure 1 shows that the ‘price’
domain is not more problematic than the ‘sales ser-
vice’ or ‘maintenance’ domains which are two of the
top three domains. On the other hand, it seems that
‘administration’, which did not belong to the top three
domains, is by far the most successful attribute do-
main.
It is clear that the possibility to derive proxies for
expectation scores offers new insights into the com-
pany’s performance. Also, these expectation scores
can offer new possibilities in other contexts. Vanhoof
et al. [Vanhoof et al., 2005] for instance use expecta-
tion scores to identify an attribute domain as a ‘basic’,
‘performance’ or ‘excitement’.
In sum, it seems justified to conclude that our
AGOP’s behavioral parameter approach is valuable in
the customer (dis)satisfaction research. Next, we will
study a comparable approach in a different marketing
domain.
3 THE OWA OPERATOR IN
COUNTRY-OF-ORIGIN
THEORY
3.1 Marketing Context
Research on country-of-origin (coo) effects is con-
cerned with the influence this marketing stimulus ex-
erts on the formation of consumers’ attitude toward
foreign sourced products [Bilkey and Nes, 1982]. The
basic premise is that coo can be a valuable asset for
the positioning of products on the international mar-
ket.
Most studies approach the coo-phenomenon from
an information theoretic perspective. It is assumed
that the processing of coo-cues is mainly cognitively
driven. In other words, people’s attitudinal disposi-
tion toward a product is believed to be the outcome
of logical reasoning with rational use being made
of country-related information offered. For instance,
German made cars are positively evaluated based on
the idea that Germany is a well known car producing
country.
Recently however, several scholars have ques-
tioned the overwhelming predominance of this cog-
nitively oriented stream [Verlegh and Steenkamp,
1999].As they argue, classic studies neglect the
coo-cue’s capacity to arouse all kinds of symbolic
and emotional connotations that might interfere in the
process of forming an attitude toward internationally
marketed products. The boycott of Danish products

Page 6

in the Middle East, due to the publication of a series
of controversial Muslim cartoons, indeed supports the
idea that country-specific feelings can be of capital
importance for the positioning of products in other
countries.
The lack of knowledge on how these country-
related feelings precisely operate, explains the urgent
need for more insight into this particular topic.
The concept of ‘attitude’ can be defined as an
overall evaluative judgement toward a person, object
or event [Eagly and Chaiken, 1993]. One of the most
popular models on product attitude formation is the
Expectancy Value Model [Fishbein and Ajzen, 1975].
It is based on the key proposition that overall prod-
uct evaluation is mediated by the evaluation of salient
attribute beliefs. Thus, people integrate knowledge
about the product’s attributes in order to arrive at a
final evaluation.
Interestingly, the literature on advertising and
emotions has put some of the basic principles behind
this theory into a broader perspective. More specifi-
cally, it was posited by Peterson et al. [Peterson et al.,
1986] that advertising cues (like coo) elicit various af-
fective reactions which can influence product attitude
formation.
According to the Encoding Specificity Theory
developed by Tulving and Thomson [Tulving and
Thomson, 1973], such ad-related affects experienced
by the individual can activate internally stored
thoughts that are relevant and related to those affects.
Or, as put by Cacioppo and Petty [Cacioppo and
Petty, 1989], such affects can “bias issue-relevant
thinking by making affectively consonant thoughts
and ideas more accessible in memory.”
for instance, happy people have been found to
show better recall of positive material offered to
them [Isen, 1989]. Thus apparently, ad-affects
regulate an individual’s processing of information
about a product’s attributes in such a manner that
greater (lesser) receptiveness goes out toward the
attribute-related information which corresponds most
(least) intimately to the individual’s actual emotional
state. This brings us to the following hypothesis:
This way
“Consumers expressing more positive feelings to-
ward the product’s coo will process the favorable
(i.e., the stronger valued) attribute beliefs while
consumers expressing less positive feelings toward
the product’s coo will process the unfavorable (i.e.,
the weaker valued) attribute beliefs.”
Paraphrased somewhat differently, we might say that
the emotional state into which consumers have been
brought by advertisement stimuli will determine con-
sumers’ degree of optimism (or pessimism) during
their evaluation of the product being confronted with.
Unfortunately, the marketing literature has no
scales at its disposition that might help us in assessing
theevaluator’slevelofoptimism. Inaddition, conven-
tional statistical techniques used to study coo-effects
are not capable of distracting this kind of information
from the data. As will become clear throughout the
following sections, it is here more precisely that the
application of aggregation operators can become par-
ticularly useful. More in detail, we will demonstrate
that the orness can provide us with the desired quan-
tification of the evaluator’s degree of optimism. Also,
the interpretation of the orness is much more straight-
forward than the rather complex LISREL-models as
they have been traditionally used within the literature.
3.2Behavioral Parameter: The OWA
Operator’s Orness
The ordered averaging operator (OWA) was selected
as evaluation function, which allows for aggregation
of product attribute satisfaction scores, unifying con-
junctive and disjunctive behavior [Yager and Rybalov,
1998].
Definition 2 [Yager and Kacprzyck, 1997]
AnOWAoperator
having an associated
W = [W1
W2
...
Wi∈ [0,1]
(bk1,...,bkn) being the value-ordered (in decreasing
order) set of attributes (a1,...,an) of a specific
instance k.
isa mapping
weighting
such
f : Rn→ R
vector
∑iWi= 1,
i=1Wibi,
Wn]T
that
andf(a1,...,an) =∑n
with
A fundamental aspect of the OWA operator is the
re-ordering step. This way, a weight Wiis associated
with a particular ordered position i of the arguments,
instead of a specific argument ai. The ‘orness’ quanti-
fies the structure of the weight vector and can be used
to express the nature of the behavior of the evaluator
like pessimistic or optimistic. This characteristic is
defined as:
orness(W) =
1
n−1
n
∑
i=1
(n−i)Wi
(5)
If the orness of a weight factor equals 1, the OWA
operatordegeneratestothemaximumoperator, aggre-
gating the set of attributes into the value of the largest
attribute. In contrast, an orness value of zero indicates
that the OWA operator behaves as the minimum op-
erator, aggregating the set of attributes into the value
of the smallest attribute. Consequently, a large or-
ness value indicates more emphasis on the highly val-

Page 7

ued attributes during the aggregation process, thereby
modeling optimistic behavior. A small orness value
implies low-valued attributes dominate the aggrega-
tion process, thereby modeling pessimistic behavior
[Salido and Murakami, 2003] (cf Table 4).
Table 4: Illustration OWA and Orness
a1
a2
a3
W1
W2
W3
f(a1,a2,a3)
Orness
4731007
6
1.00
0.80
0.15
0.00
(= b2)(= b1)(= b3)
0.7
0.1
0
0.2
0.1
0
0.1
0.8
1
3.5
3
As will be indicated next under the data sec-
tion, our specific case-study corresponds to a situation
where a collection of k respondents (observations) are
given, each comprised of an n-tuple of product belief
values (ak1,ak2,...,akn) called the arguments and an
associated single value dk, referred to as the aggre-
gated value (i.e., the quality of the product).
Our goal will be to obtain a single OWA operator
for a given group of respondents K = 1,...,k, hereby
learning the weighting vector W and its associated or-
ness. This results in the following constrained mini-
mization problem, with ekbeing the error made for
each customer k:
Min.
ek=1
2(bk1W1+bk2W2+...+bknWn−dk)2
s.t.



∑n
i=1Wi= 1
Wi∈ [0,1],
i = (1,...,n)
(6)
Introducing the following transformation
Wi=
eλi
j=1eλj
∑n
(7)
the weights Wiwill be positive and will sum to 1
for any value of the parameters λi, resulting in the fol-
lowing unconstrained nonlinear programming prob-
lem:
Minimize
the instantaneous errors ek
?
bk2
∑n
with respect to the parameters λj
whereek
=
1
2
bk1
eλ1
j=1eλj+
∑n
eλ2
j=1eλj+...+bkn
eλn
j=1eλj
∑n
?2
(8)
The gradient descent method was used to learn the
weights [Filev and Yager, 1998].
It should be noticed that the methodology de-
scribed above measures the orness from a sample
rather than a population, making it susceptible to ran-
dom error. Yet, it would be interesting to infer sta-
tistically about the results based on a sample. Such
inference could answer questions whether the orness
(or any other similar characteristic) differs between
different groups, to construct confidence intervals for
the quantities under investigation and to test hypothe-
ses for the population values.
however, there is no such technique for statistical in-
ference available. We base our statistical inference
on resampling methods, namely non-parametric boot-
strap [Efron and Tibshirani, 1993]. For details about
implementation of this technique, we refer to [Brijs
et al., 1998].
To our knowledge,
3.3 Data
In order to test our basic theoretical assumption, a
large-scale field survey was designed. Two products
and two countries-of-origin were chosen in order to
determine how coo-related feelings affect consumers’
cognitive processing of attribute beliefs. Products se-
lected were beer and DVD-players. The decision to
work with two different product categories (the for-
mer being utilitarian in nature while the latter is rather
hedonic-oriented) was taken so that the external va-
lidity of our study could be incremented. Spain and
Denmark were selected as countries-of-origin for two
particular reasons. First of all, respondents were suf-
ficiently familiar with both countries. Secondly, two
samples could be obtained of which the overall level
of intensity of country-specific feelings aroused sub-
stantially varied.
Data collection was done by means of two sur-
veys (one for Spain/Spanish products and one for
Denmark/Danish products). The sample consisted of
respectively 616 and 609 Belgian graduate students.
More details about the data collection procedure can
be found in [Brijs et al., 1998].
3.4Validation
3.4.1Theoretical Validation
Marketing theory expects certain attributes to be more
influential than others during the evaluation process
in function of coo-related feelings. The basic princi-
ple is that optimistic (pessimistic) customers will as-
sign higher (lower) weights to the better (worse) per-
forming attributes. Of particular interest for theoreti-
cal validation is that the attributes’ weights depend on
their relative performance and that the OWA operator
is able to model this heuristic.

Page 8

Firstly, the OWA operator uses weights to aggre-
gate the arguments (attribute scores) which allows
certain attributes to be more influential in the aggre-
gation process. Secondly, OWA’s re-ordering step al-
lows us to give the better performing attributes higher
or lower weights, rather than assigning weights to
specific attributes.
3.4.2Empirical Validation
Tables 5(a), 5(b), 5(c) and 5(d) present the results of
the orness and the OWA weights (with standard errors
between brackets) for Spanish/Danish DVD players
and beer based on the outcome of the questionnaire.
Standard errors are based on B=1000 bootstrap repli-
cations using the procedure described above.
Table 5: OWA and Country-Of-Origin Effects
(a) Results for Spanish DVD players.
Data set
OrnessW1
W2
W3
W4
All cases (616) 0.4742
(0.0259)
0.5499
(0.0619)
0.4061
(0.0556)
0.1338
(0.0326)
0.1931
(0.0682)
0.1495
(0.0560)
0.2758
(0.0858)
0.3866
(0.2188)
0.2065
(0.1350)
0.4695
(0.0870)
0.2971
(0.2191)
0.3567
(0.1734)
0.1207
(0.0382)
0.1230
(0.0734)
0.2871
(0.1124)
Group A: (137)
Group B: (134)
SignificanceS NSNSNSNS
(b) Results for Spanish beer
Data set
OrnessW1
W2
W3
W4
All cases (616) 0.4290
(0.0220)
0.4489
(0.0521)
0.3438
(0.0443)
0.1554
(0.0299)
0.2015
(0.0620)
0.1824
(0.0666)
0.3171
(0.0706)
0.1483
(0.1568)
0.1907
(0.1070)
0.1866
(0.0798)
0.4452
(0.1983)
0.1023
(0.1217)
0.3407
(0.0471)
0.2047
(0.1038)
0.5243
(0.0938)
Group A: (137)
Group B: (134)
Significance NS NSNSSS
(c) Results for Danish DVD players
Data set
OrnessW1
W2
W3
W4
All cases (609)0.5265
(0.0215)
0.5336
(0.0504)
0.5133
(0.0582)
0.1901
(0.0473)
0.2491
(0.0919)
0.1727
(0.1030)
0.3774
(0.07370)
0.2712
(0.1652)
0.3005
(0.1934)
0.2544
(0.0651)
0.3107
(0.1670)
0.4207
(0.1867)
0.1780
(0.0310)
0.1688
(0.0595)
0.1060
(0.0902)
Group A: (194)
Group B: (74)
SignificanceNSNS NSNSNS
(d) Results for Danish beer
Data set
OrnessW1
W2
W3
W4
All cases (609)0.4216
(0.0204)
0.4166
(0.0357)
0.3733
(0.0548)
0.2099
(0.0372)
0.2399
(0.0699)
0.2266
(0.07800)
0.1683
(0.0732)
0.1223
(0.1116)
0.0775
(0.1238)
0.2983
(0.0759)
0.2855
(0.1205)
0.2849
(0.1406)
0.3233
(0.0399)
0.3522
(0.0780)
0.4109
(0.0867)
Group A: (194)
Group B: (74)
SignificanceNSNSNS NS NS
If we compare the group of respondents with high
positive feelings toward coo (group A) versus those
expressing less positive feelings toward coo (group
B), Table 5(a) shows that the orness for group A is
higher than for group B. When constructing 95% con-
fidence intervals we found that for group A the inter-
valis[0.439, 0.672], whileforgroupB[0.347, 0.521],
which implies a certain overlap. Statistically speak-
ing, the differences between group A and B are not
significant on a 5% level. According to our bootstrap
results, it is however significant on the 10% level al-
though this decision depends on the bootstrap exper-
iment used. Qualitatively also, it is clear that group
A has a larger orness, which somehow confirms our
hypothesis that people expressing high positive feel-
ings toward coo tend to use a more optimistic evalua-
tion function toward evaluating the quality of Spanish
DVD-players. They tend to base their quality evalua-
tion more on the more positively evaluated attributes.
Confirmation of the encoding-specificity principle
should, however, also be reflected by the individual
OWA weights (W1to W4) such that for group A ver-
sus group B, the ordered weights W1and W2should
show higher values and the ordered weights W3and
W4should show lower values. Based on results de-
picted in Table 5(a) we can conclude that indeed W1
and W2are higher in group A compared to group B.
However, their individual differences are not statisti-
cally significant. Similarly, it can be seen from the
values for W3and W4that they are higher in group B
compared to group A, although their individual dif-
ferences are again not statistically significant.
Table 5(b) presents the results obtained for Span-
ish beer. Here also, the orness for group A is sur-
passing that for group B, although in this case the dif-
ference is not statistically significant. The 95% con-
fidence interval for group A is [0.351, 0.555] while
for group B [0.262, 0.435]. Yet, there is a clear in-
dication that group A has a larger orness. This can
again be seen as supportive evidence for our hypothe-
sis. However, in this case the results for the weight
values are less convincing since the value of W2is
larger in group B than in group A, and the value of
W3is larger in group A than in group B.
Table 5(c) and 5(d) show the results for Danish
DVD-players and beer. Even though there is a ten-
dency that the orness is again slightly higher for group
A than for group B, the differences are much smaller
compared to the results for Spain and not statistically
significant. For example, for Danish DVD-players,
the 95% confidence interval for group A is [0.435,
0.626] and for group B [0.402, 0.641], showing a
large overlap. With respect to the values of W1to W4
the results are not consistent.

Page 9

3.5Implications
From a practical point of view, our second case-study
showshowmildercoo-specificfeelingsserveasause-
ful device for advertisers to direct consumers’ pro-
cessing of attribute beliefs. More in detail, their func-
tioning can be understood as some kind of encoding-
specificity mechanism.That is, consumers during
their product evaluation ascribe most importance to
those attribute beliefs which are closer in line with
their internal affective state.
From a technical point of view, we opted for an
alternative methodology in using the OWA-operator.
In our opinion, this is a useful approach while the in-
terpretation of the OWA-weights is more straightfor-
ward compared to the more complex LISREL-models
as they have been traditionally used for instance by
Han (1988). An additional advantage lies in the fact
that the ‘orness’ gives us the needed quantification of
the optimistic degree of an evaluation. This aspect is
already a huge advantage of the fuzzy set approach
compared to the more traditional LISREL approaches
where this degree of optimism cannot be extracted
from the data. Finally, we introduced a bootstrap pro-
cedure to estimate the orness and the level of uncer-
tainty around it. This enables us to construct confi-
dence intervals and conduct hypothesis tests. As far
as we know, estimating this degree of uncertainty of
the orness has never been introduced in the literature
before.
4CONCLUSION
Within the fuzzy set field, past application-oriented
research has mainly been focused on AGOP’s domain
representation power or decision-making strength. As
far as we know, the AGOP’s characteristics them-
selves have not been of any significant importance in
this particular type of research.
However, this paper has demonstrated that the
value of certain characteristics for applied research
should not be disregarded. It is illustrated that ag-
gregation operator characteristics carry the potential
of functioning as valid proxies for domain specific
knowledge, which is hard to measure directly or to
derive statistically from the data.
The presence of such potential has been proven to
exist by means of two marketing case-studies. The
first case-study examined the use of the uninorm in
customer satisfaction theory. It could be established
that the uninorm’s neutral value is a proxy for cus-
tomers’ expectations.This approach in turn pro-
vides the manager with new and important informa-
tion about the company’s performance. The second
case-study has explored the value of the OWA oper-
ator for country-of-origin research. The orness was
found to be suitable for the quantification of the cus-
tomers’ degree of optimism (pessimism) during the
process of product evaluation. Such method for quan-
tification in itself already counts as a technical con-
tribution toward the coo-field. In addition, managers
have gained more insight into the precise role of coo-
related feelings. As such, they are capable now of
dealing more effectively with this particular market-
ing phenomenon.
The validity of both operator characteristics as do-
main specific proxies has been verified theoretically
as well as empirically, which adds indirectly to the
value of our findings.
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