Quantitative methods in marketing 227
proposal for generalizing classical set theory.
The Pawlak rough set model is based on the
concept of an equivalence relation. Research
has shown that a generalized rough set model
need not be based on equivalence relations
axions. Lingras and Yao (1998) demonstrated
that a generalized rough set model could be
used for generating rules from incomplete
databases. These rules are based on plausibility
functions. These authors also emphasized the
importance of rule extraction from incomplete
databases in data mining.
An RST approach was used by Dimitras et
al. (1999) to provide a set of rules able to
discriminate between healthy and failing firms
in order to predict business failure. The evalu-
ation of its predictive ability was the main
objective of the study. The results were very
encouraging, compared with those from dis-
criminate and logit analyses, and proved the
usefulness of the method. The rough set
approach discovers relevant subsets of charac-
teristics and represents in these terms all
important relationships between the key con-
structs. The method analyses only facts hidden
in the input data and communicates with the
decision maker in the material language of
rules derived from his or her experience.
A recent development in RST is the variable
precision rough set (VPRS) model, by Ziarko
(1993a, b). Unlike RST, which constructs deter-
ministic rules (i.e. 100 per cent in correct
classification by a rule), the VPRS model enables
a level of confidence in correct classification by a
rule. That is, they are probabilistic rules.
Dissatisfied customers pose numerous
potential problems for any organization – for
example, negative word of mouth, reduced
change of repeat lower brand loyalty. All of these
problems will negatively affect the measure-
ments of any business, e.g. profits and market
shares. Therefore, assessing customer satisfac-
tion level and more importantly why they are
dissatisfied has great benefits to any company.
This is particularly true in high competitive
globalized markets, where search costs are low
and the cost of switching supplier negligible.
Variable precision rough sets (VPRS)
A further RST innovation has been the devel-
opment by Ziarko (1993a, b) of a variable
precision rough sets (VPRS) model, which
incorporates probabilistic decision rules. This is
an important extension since, as noted by
Kattan and Cooper (1998), when discussing
computer-based decision techniques in a corpo-
rate failure setting, ‘In real world decision
making, the patterns of classes often overlap,
suggesting that predictor information may be
incomplete... This lack of information results
in probabilistic decision making, where perfect
prediction accuracy is not expected.’
Anet al. (1996) applied VPRS (which they
termed ‘enhanced RST’) to generating probabi-
listic rules to predict the demand for water.
Relative to the traditional rough set approach,
VPRS has the additional desirable property of
allowing for partial classification compared to
the complete classification required by RST.
More specifically, when an object is classified
using RST it is assumed that there is complete
certainty that it is a correct classification. In
contrast, VPRS facilitates a degree of confidence
in classification, invoking a more informed
analysis of the data, which is achieved through
the use of a majority inclusionrelation.
This paper extends previous work by
providing an empirical exposition of VPRS,
where we present the results of an experiment
which applies VPRS rules to the corporate
failure decision. In addition, we mitigate the
impact of using the subjective views of an
expert (as employed in previous studies) to
discretize the data, by utilizing the sophisti-
cated FUSINTER discretization technique,
which is applied to a selection of attributes
(variables) relating to companies’ financial and
non-financial characteristics. The discretized
data, in conjunction with other nominal attri-
butes, are then used in this new VPRS frame-
work to identify rules to classify companies in a
failure setting.
To facilitate a comparison of our experi-
mental VPRS results with those of existing