THE IMPORTANCE OF AGGREGATION OPERATOR

CHARACTERISTICS IN MARKETING RESEARCH

Kris Brijs, Beno

ıt Depaire, Koen Vanhoof, Tom Brijs and Geert Wets

Faculty of Applied Economics, Hasselt University, Campus Diepenbeek, 3590 Diepenbeek, Belgium

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’

degree of optimism when evaluating products coming from abroad. Both theoretical and empirical validation is

provided to support the basic assumption that aggregation operator characteristics enable us to obtain superior

consumer information with substantial managerial relevance.

1 INTRODUCTION

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). These

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-

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

237

Brijs K., Depaire B., Vanhoof K., Brijs T. and Wets G. (2007).

THE IMPORTANCE OF AGGREGATION OPERATOR CHARACTERISTICS IN MARKETING RESEARCH.

In Proceedings of the Ninth International Conference on Enterprise Information Systems - AIDSS, pages 237-246

DOI: 10.5220/0002353702370246

 SciTePress

products. Finally, once the case-study analyses have

been completed, a fourth section will be reserved for

an overall conclusion.

2 THE 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

customer satisfaction (Oliver, 1996), but in most cases

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

“disconﬁrmation takes place at the individual attribute

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

the overall satisfaction level into the expectation level.

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 perfor-

mance, expectation, disconﬁrmation and satisfaction

(Oliver, 1996). Therefore, most customers will have

a unique expectation level and aggregation process.

2.2 Behavioral 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 Ry-

balov, 1996).

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238

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. The uninorm shows

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]) (cf Table 1 customers 1 and 3). If one argument

belongs to the interval [0, e] and the other argument

belongs to the interval ]e, 1], the uninorm shows com-

pensation behavior (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.

Table 1: Illustration Uninorm and Neutral Element.

a b U(a, b) e

Customer

e.g. Price e.g. Taste Satisfaction Expectation

1 3 6 7 2

3 6 4 5

3 6 1 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(x

, x

) = g



−1

) + g

−1

)



(1)

Based on the associativity property, this can be

generalized into

U(X) = g

∑

−1

(x)

(2)

Furthermore, Dombi showed that the generator

function g(x) displaced by d, g(x + d) = g

(x), also

possesses the properties of a uninorm generator func-

tion. The displaced generator function g

(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)) (4)

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.

2.3 Data

This research includes data from a customer satisfac-

tion survey within the ﬁnancial sector. The survey

THE IMPORTANCE OF AGGREGATION OPERATOR CHARACTERISTICS IN MARKETING RESEARCH

239

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’. All performance scores were measured on a scale

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 10

Price 6

Quality /

Products 9

Sales service 10

Maintenance 15

Invoices 6

Administration 6

Communication 8

2.4 Validation

2.4.1 Theoretical 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

substantial theoretical validation, making the uninorm

a good candidate to model customer (dis)satisfaction.

2.4.2 Empirical 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

customer’s expected value (Vanhoof et al., 2003; ?).

We will further strengthen this validation by compar-

ing our results with conclusions from Szymanski and

Henard’s meta-analysis of 85 existing research stud-

ies on customer satisfaction (Szymanski and Henard,

2001). A substantial part of their paper focuses on the

relationships between customer satisfaction and sev-

eral 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

results obtained by Vanhoof et al. (Vanhoof et al.,

2003), we can conclude that the uninorm’s neutral el-

ement is a valid proxy for customer’s expectation.

2.5 Implications

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

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240

Table 3: Validation of the Satisfaction-Related Correlations.

Szymanski and Henard Our results

Positive Correlations Negative Correlations Positive Correlations Negative Correlations

Expectation

†

- satisfaction 13 1 1 0

Disconﬁrmation

‡

- satisfaction

121 1 4 1

Performance - satisfaction

136 17 10 0

Expectation

†

- performance

22 1 10 0

NOTE I

Only statistically signiﬁcant correlations at alpha ≤ .05 were considered.

NOTE II

Expectation, disconﬁrmation and performance is measured or derived for the attribute domain level.

†

expectation = uninorm’s neutral element.

‡

disconﬁrmation = performance - expectation.

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.

0.5

1.5

2.5

3.5

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

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 IMPORTANCE OF AGGREGATION OPERATOR CHARACTERISTICS IN MARKETING RESEARCH

241

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.” This way

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:

“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

the evaluator’s level of optimism. In addition, 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.

3.2 Behavioral 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)

An OWA operator is a mapping f : R

→ R

having an associated weighting vector

W = [W

. . . W

]

such that

∑

= 1,

∈ [0, 1] and f(a

, . . . , a

) =

∑

i=1

, with

, . . . , b

) being the value-ordered (in decreasing

order) set of attributes (a

, . . . , a

) of a speciﬁc

instance k.

A fundamental aspect of the OWA operator is the

re-ordering step. This way, a weight W

is associated

with a particular ordered position i of the arguments,

instead of a speciﬁc argument a

. 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) =

n− 1

∑

i=1

(n− i)W

(5)

If the orness of a weight factor equals 1, the OWA

operator degenerates to the maximum operator, 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-

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).

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242

Table 4: Illustration OWA and Orness.

f(a

, a

) Orness

4 7 3 1 0 0 7 1.00

(= b

) (= b

)

0.7 0.2 0.1 6 0.80

0.1 0.1 0.8 3.5 0.15

0 0 1 3 0.00

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 (a

, a

, . . . , a

) called the arguments and an

associated single value d

, 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 e

being the error made for

each customer k:

Min. e

+ b

+ . . . + b

− d

)

s.t.







∑

i=1

= 1

∈ [0, 1], i = (1, . . . , n)

(6)

Introducing the following transformation

∑

j=1

(7)

the weights W

will be positive and will sum to 1

for any value of the parameters λ

, resulting in the fol-

lowing unconstrained nonlinear programming prob-

lem:

Minimize the instantaneous errors e

where e



∑

j=1

∑

j=1

+ . . . + b

∑

j=1



with respect to the parameters λ

(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. To our knowledge, how-

ever, there is no such technique for statistical infer-

ence available. We base our statistical inference on re-

sampling methods, namely non-parametric bootstrap

(Efron and Tibshirani, 1993). For details about imple-

mentation of this technique, we refer to (Brijs et al.,

2006).

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., 2006).

3.4 Validation

3.4.1 Theoretical 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.

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.

THE IMPORTANCE OF AGGREGATION OPERATOR CHARACTERISTICS IN MARKETING RESEARCH

243

3.4.2 Empirical 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 Orness W

All cases (616) 0.4742 0.1338 0.2758 0.4695 0.1207

(0.0259) (0.0326) (0.0858) (0.0870) (0.0382)

Group A: (137) 0.5499 0.1931 0.3866 0.2971 0.1230

(0.0619) (0.0682) (0.2188) (0.2191) (0.0734)

Group B: (134) 0.4061 0.1495 0.2065 0.3567 0.2871

(0.0556) (0.0560) (0.1350) (0.1734) (0.1124)

Signiﬁcance S NS NS NS NS

(b) Results for Spanish beer

Data set Orness W

All cases (616) 0.4290 0.1554 0.3171 0.1866 0.3407

(0.0220) (0.0299) (0.0706) (0.0798) (0.0471)

Group A: (137) 0.4489 0.2015 0.1483 0.4452 0.2047

(0.0521) (0.0620) (0.1568) (0.1983) (0.1038)

Group B: (134) 0.3438 0.1824 0.1907 0.1023 0.5243

(0.0443) (0.0666) (0.1070) (0.1217) (0.0938)

Signiﬁcance NS NS NS S S

Data set Orness W

All cases (609) 0.5265 0.1901 0.3774 0.2544 0.1780

(0.0215) (0.0473) (0.07370) (0.0651) (0.0310)

Group A: (194) 0.5336 0.2491 0.2712 0.3107 0.1688

(0.0504) (0.0919) (0.1652) (0.1670) (0.0595)

Group B: (74) 0.5133 0.1727 0.3005 0.4207 0.1060

(0.0582) (0.1030) (0.1934) (0.1867) (0.0902)

Signiﬁcance NS NS NS NS NS

(d) Results for Danish beer

Data set Orness W

All cases (609) 0.4216 0.2099 0.1683 0.2983 0.3233

(0.0204) (0.0372) (0.0732) (0.0759) (0.0399)

Group A: (194) 0.4166 0.2399 0.1223 0.2855 0.3522

(0.0357) (0.0699) (0.1116) (0.1205) (0.0780)

Group B: (74) 0.3733 0.2266 0.0775 0.2849 0.4109

(0.0548) (0.07800) (0.1238) (0.1406) (0.0867)

Signiﬁcance NS NS NS 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-

val is [0.439, 0.672], while for group B [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 (W

to W

) such that for group A ver-

sus group B, the ordered weights W

and W

should

show higher values and the ordered weights W

and

should show lower values. Based on results de-

picted in Table 5(a) we can conclude that indeed W

and W

are 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 W

and W

that 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 W

larger in group B than in group A, and the value of

is 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 W

to W

the results are not consistent.

3.5 Implications

From a practical point of view, our second case-study

shows howmilder coo-speciﬁc feelings serve as a use-

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

ICEIS 2007 - International Conference on Enterprise Information Systems

244

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.

4 CONCLUSION

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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