This is not the document you are looking for? Use the search form below to find more!

Report home > World & Business

Marketing Intelligent Systems for consumer behaviour modelling by ...

0.00 (0 votes)
Document Description
n its introduction this paper discusses why marketing professionals do not make satisfactory use of the marketing models posed by academics in their studies. The main body of this research is characterized by the proposal of a brand new and complete methodology for knowledge discovery in databases (KDD), to be applied in marketing causal modelling and with utilities to be used as a marketing management decision support tool. Such methodology is based on Genetic Fuzzy Systems, a specific hybridization of artificial intelligence methods, highly suited to the research problem we face. The use of KDD methodologies based on intelligent systems like this can be considered as an avant-garde evolution, exponent nowadays of the so- called knowledge-based Marketing Management Support Systems; we name them as Marketing Intelligent Systems.
File Details
  • Added: April, 05th 2011
  • Reads: 339
  • Downloads: 1
  • File size: 1.56mb
  • Pages: 18
  • Tags: marketing modelling, management support, analytical method, knowledge discovery, genetic fuzzy systems, methodology
  • content preview
Submitter
  • Name: amadej
Embed Code:

Add New Comment




Related Documents

Challenges in Case-Based Reasoning for Context Awareness in Ambient Intelligent Systems

by: nayu, 13 pages

One of the most important issues in an ambient intelligent environment, indeed in any problem-solving situation, is the ability of a system to appreciate its environment and assess the situation in ...

ANALYSIS OF CONSUMER BEHAVIOUR IN REGARD TO DAIRY PRODUCTS IN KOSOVO

by: shinta, 10 pages

Consumer behaviour in Kosovo in respect of dairy products (white cheese, yoghurt, fruit yoghurt, Sharri cheese, curd and caciocavalo) was studied during 2007 using different ...

Complete Testbank for Essentials of Accounting for Governmental and Not-for-Profit Organizations, 10ed, by Copley 9780073527055 TB DOWNLOAD NOW

by: dishdash2010, 67 pages

Complete Testbank for Essentials of Accounting for Governmental and Not-for-Profit Organizations, 10ed, by Copley 9780073527055 TB DOWNLOAD NOW Make Payment and Receive Testbank for Essentials of ...

Most Complete Testbank for Consumer Behavior - Michael Solomon (9th ed) DOWNLOAD NOW

by: dishdash2010, 173 pages

Most Complete Testbank for Consumer Behavior - Michael Solomon (9th ed) DOWNLOAD NOW

Course on Artificial Intelligence and Intelligent Systems

by: arto, 10 pages

The language of Constraint Handling Rules, CHR, is an extension to Prolog intended as a declarative language for writing constraint solvers for CLP systems; here we give a very compact introduction ...

Understanding Consumer Behaviour

by: niklas, 18 pages

By Ghaayathri P GAPR09Rm082 Consumer Behavior Study of People How and why they buy what they Buy? How to identify needs and satisfy ...

Marketing Aptitude books for Bank Clerk Exam

by: exam_eduriteteam, 3 pages

Banks organize exams for its various posts like Clerk, PO and RRB. Candidates, who want to enter in the bank as Clerk, can give Bank Clerk Exam. The first and foremost eligibility criteria to give ...

RELATIONSHIP BETWEEN MARKETING MIX STRATEGY AND CONSUMER MOTIVE: AN EMPIRICAL STUDY IN MAJOR TESCO STORES

by: samanta, 16 pages

This paper investigates the relationship between Marketing Mix Strategy and Consumer Motives at major TESCO stores in Malaysia. A quantitative approach was used and the survey was conducted at TESCO ...

An Intelligent Agent for a Vacuum Cleaner

by: mersada, 4 pages

This paper introduces an Intelligent agent for the vacuum cleaner named as VROBO. Objectives of this work are to prepare a pedagogical device for Artificial Intelligence students and to practically ...

Hybrid Intelligent Systems

by: leona, 50 pages

Hybrid Intelligent Systems

Content Preview
Industrial Marketing Management 38 (2009) 714–731
Contents lists available at ScienceDirect
Industrial Marketing Management
Marketing Intelligent Systems for consumer behaviour modelling by a descriptive
induction approach based on Genetic Fuzzy Systems
Francisco J. Martínez-López a , ⁎, Jorge Casillas b ,1
a Department of Marketing, Business Faculty, University of Granada, Granada, E-18071, Spain
b Department of Computer Science and Artificial Intelligence, Computer and Telecommunication Engineering School, University of Granada, Granada, E-18071, Spain
a r t i c l e i n f o
a b s t r a c t
Article history:
In its introduction this paper discusses why marketing professionals do not make satisfactory use of the
Received 2 March 2007
marketing models posed by academics in their studies. The main body of this research is characterised by the
Received in revised form 26 December 2007
proposal of a brand new and complete methodology for knowledge discovery in databases (KDD), to be
Accepted 12 February 2008
applied in marketing causal modelling and with utilities to be used as a marketing management decision
Available online 14 April 2008
support tool. Such methodology is based on Genetic Fuzzy Systems, a specific hybridization of artificial
intelligence methods, highly suited to the research problem we face. The use of KDD methodologies based on
Keywords:
intelligent systems like this can be considered as an avant-garde evolution, exponent nowadays of the so-
Marketing modelling
called knowledge-based Marketing Management Support Systems; we name them as Marketing Intelligent
Management support
Systems. The most important questions to the KDD process–i.e. pre-processing; machine learning and post-
Analytical method
processing
Knowledge discovery
–are discussed in depth and solved. After its theoretical presentation, we empirically experiment
Genetic Fuzzy Systems
with it, using a consumer behaviour model of reference. In this part of the paper, we try to offer an overall
Methodology
perspective of how it works. The valuation of its performance and utility is very positive.
© 2008 Elsevier Inc. All rights reserved.
1. Introduction
ever to provide this support to marketing managers' decision making, in
order to give useful and valuable information about market behaviour.
Firms operate in markets that are increasingly “turbulent” and
Specifically, we highlight the following: models and methods of analysis.
“volatile.” How to deal with this turbulence and survive in these
It is expected that MkMSS will improve their performance in the
hypercompetitive conditions has become a strategic question (Agarwal,
near future, taking advantage of the synergies caused by the
Shankar, & Tiwari, 2007; Christopher, 2000). Consequently, the idea of
integration of modelling estimation techniques based on classic
the achievement and support of a sustainable competitive advantage
econometrics with new methods and systems based on artificial
gave rise, in the nineties, to another focused on its continuous
intelligence (Gatignon, 2000; Van Bruggen & Wierenga, 2000). The
development (D'Aveni, 1994), which is more realistic these days. One
adoption of these new methods represents a worthwhile opportunity
of the main implications of this reformed strategic approach is a search
to improve the efficiency of the marketing managers' decision making
for new suitable market opportunities. Of course, such opportunities
and consequently, if well applied, the accuracy of marketing strategies
need to be correctly identified and addressed by firms. This premise
(Li, Kinman, Duan, & Edwards, 2000).
justifies the transcendental relevance recently given to the creation and
The paper we present here focuses on the exploration and analysis
management of knowledge about markets (Drejer, 2004). In this vein,
of the suitability of certain brand new methods based on knowledge
the marketing function of companies and, most especially, their
discovery in databases (KDD) to be applied in marketing modelling.
Marketing Management Support Systems (MkMSS) plays a notable
Specifically, our main aim is twofold: first, we aim to make a modest
role in this task, as they must contribute to the reduction of the
contribution to the methods used in consumer behaviour modelling.
uncertainty related to the firms' markets of reference. As we know, this
In any case, this is the marketing field we have focused on to develop
question does not only imply having access to good marketing
and experiment our methodology, though it also applies to marketing
databases. On the contrary, the key question is having the necessary
causal modelling, in general, as well as to other Science and Social
level of knowledge to take the right decisions (Campbell, 2003; Lin, Su, &
Sciences fields that work with similar causal models.
Chien, 2006). The analytical capabilities of MkMSS are more critical than
We propose a complete knowledge discovery methodology, whose
main questions are shown in this paper, to extract useful patterns of
information with a descriptive rule induction approach based on
⁎ Corresponding author. Tel.: +34 958 242350.
Genetic Fuzzy Systems; this is a novel hybridization of methods
E-mail addresses: fjmlopez@ugr.es (F.J. Martínez-López), casillas@decsai.ugr.es
(J. Casillas).
belonging to the field of artificial intelligence, highly appropriate for
1 Tel.: +34 958 240804.
the marketing problem we face. With this purpose, we have had to
0019-8501/$ – see front matter © 2008 Elsevier Inc. All rights reserved.
doi:10.1016/j.indmarman.2008.02.003

F.J. Martínez-López, J. Casillas / Industrial Marketing Management 38 (2009) 714–731
715
give solutions, adapted from our academic field, to the diverse
he can for making the model conform to reality in structure,
questions related to the main stages of the KDD process; i.e. data
parameterization, and behaviour.
preparation, data mining, and knowledge interpretation. Moreover,
an important characteristic of our methodology is that it has been
Consequently, it seems clear that modellers should be driven by the
designed under the base there is a causal model of reference; a
requirements of models users (i.e. demand-side), instead of by a supply-
consumer behaviour model in our case. In other words, the knowledge
side orientation (Gatignon, 2000). This practice is expected to improve
discovery process is guided by a prior theoretic structure that defines
the use of the academic models among the practitioners (Roberts, 2000).
the elements (variables) of the model. Hence, this machine learning
In this sense, a firm focused on consumption markets with access not
approach is not only interesting for practitioners, but also for
only to more representative models of real systems being modelled but
academic researchers' purposes.
also to more powerful methods of analysis to extract knowledge from
To address these questions, the paper is structured as follows.
huge databases and able to simulate with models ought to improve its
Section 2 reflects on the suitability of evolving our marketing
competitiveness and competitive advantage (Van Bruggen & Wierenga,
modelling methods towards a growing importation and use of
2000). This is a premise that has significantly conditioned the evolution
artificial intelligence methods to support professional and academic
of MkMSS from the early 80s, specifically with the appearance of the
marketing problems. Section 3 presents an overview and justification
Marketing Decision Support Systems, until now (Li et al., 2000; Talvinen,
of the artificial intelligence tools employed (fuzzy rules, genetic
1995; Wierenga & Van Bruggen, 1997, 2000).
algorithms, etc.). Section 4 illustrates with some examples the
The late 80s saw the increasing use of diverse methods from
behaviour of the proposed KDD tools. Section 5 shows the methodo-
Computer Science and Artificial Intelligence to the detriment of those
logical proposal in detail. Next, in Section 6 we experiment with the
from the Operational Research and, especially, the econometrics and
methodology, show some significant results and dedicate a brief
statistics fields. This tendency has increasingly intensified in the last
closing part to illustrate both the intrinsic and complementary
two decades (Bucklin, Lehmann, & Little, 1998; Eliashberg & Lilien,
advantages of our fuzzy modelling-based method. Section 7 discusses
1993; Leeflang & Wittink, 2000; Leeflang, Wittink, Wedel, & Naert,
the main contributions of our research, reflecting on the academic and
2000; Li, Davies, Edwards, Kinman, & Duan, 2002).
managerial implications. Finally, in Section 8 we comment on some
This evolution in the methods used in marketing modelling has not
research limitations and opportunities (our future research agenda).
been accidental. In this sense, Lilien, Kotler, and Moorthy (1992) noted
that this tendency was to be expected as modellers and users needed
2. Background and starting reflections
techniques that were more flexible, powerful and robust, capable of
providing greater and improved information with respect to the real
Is there a gap between what marketing modellers offer and what
systems being modelled. Of course, this implies a greater adaptation to
marketing managers demand? If marketing modelling had got to a
both the characteristics of current databases–i.e. huge, imprecise, with
stage of maturity, as Leeflang and Wittink (2000) argue, one would
data gathered in formats of a different nature (numerical, categorical,
expect to find a significant use of academic models among marketing
linguistic, etc.)–and the type of decision problems to be supported by
practitioners. Notwithstanding, it seems that marketing managers
such models. Under these circumstances, it seems an evolution of the
rarely apply them (Roberts, 2000; Wind and Lilien, 1993; Winer,
marketing modelling methods towards systems based on artificial
2000). It is essential that we academics meditate on this. Maybe, the
intelligence is only logical (Shim et al., 2002; Wedel, Kamakura, &
answer is much less complex than we would primarily expect.
Böckenholt, 2000), which justifies the growing predominance of the
We think that the efforts of marketing academics are not
knowledge-based MkMSS in the last two decades (Wierenga & Van
productive in terms of the managerial applications of their models.
Bruggen, 2000).
This is not due to deficiencies in the theoretic aspects that support the
In sum, MkMSS clearly tend to be based on knowledge discovery
models' structure, but due to a lack of involvement by not offering
methods that make use of diverse artificial intelligence methods to be
useful methods of analysis that allow the models' users (marketing
applied during the machine learning process; e.g.: evolutionary
managers) to “play” with these models to support their decisions. This
algorithms, fuzzy logic, artificial neural networks, rules induction,
is what has guided our research, hence the gist of this paper.
decision trees, etc. Specifically, it is expected that the use of artificial
The academics may be too focused on testing hypotheses and
intelligent methods in the MkMSS framework will evolve towards the
validating models and theories without paying enough attention to
use of intelligent systems based on the hybridization of these
what our “customers”–the marketing managers, users of our scientific
techniques (Carlsson & Turban, 2002; Shim et al., 2002). We like to
production–need. Indeed, marketing modellers cannot afford to fall
call them as Marketing Intelligent Systems. It might be the inexorable
into marketing myopia! In this regard, we should not forget that the
fate of marketing modelling methods. This fact, which is more evident
main purpose of our research efforts ought to be the contribution to
from a professional perspective–i.e. under the framework of applica-
the development of our field, and this necessarily implies looking after
tion of the MkMSS–, has still to take hold in academic studies.
the practical applicability of our models, too.
Therefore, how can we strengthen the utility of our models to
3. Knowledge extraction based on fuzzy rules and genetic
achieve a better explanation of markets, thus better matching them to
algorithms
marketing managers' needs? Research efforts can be addressed to the
improvement of three main areas of interest in marketing modelling
3.1. The KDD process
(Roberts, 2000): theoretic aspects defining the models; understanding
of managers' (users) needs, hence the framework of application of
In general terms, KDD is a recent research field belonging to artificial
models; and refinement of the statistical tools (i.e. techniques and
intelligence whose main aim is the identification of new, potentially
methods in general) applied to estimate the models. The pursuit of
useful, and understandable patterns in data (Fayyad, Piatesky-Shapiro,
these improvement guidelines is not too distant from what Little
Smyth, & Uthurusamy, 1996). Furthermore, KDD implies the develop-
(1970, p. B-483) asked of researchers a few decades ago when building
ment of a process compounded by several stages that allow the
models to support marketing managers' decision making:
conversion of low-level data into high-level knowledge (Mitra, 2002).
Though KDD is synthetically viewed as a three-stage process–i.e. pre-
Although the results of using a model may sometimes be personal
processing, data mining and post-processing–(Freitas, 2002), we believe
to the manager […] the researcher still has the responsibilities of a
that, for our academic field, it is more interesting to present it within a
scientist in that he should offer the manager the best information
wider structure. Specifically, we prefer the following five-stage process

716
F.J. Martínez-López, J. Casillas / Industrial Marketing Management 38 (2009) 714–731
(Cabena, Hadjinian, Stadler, Verhees, & Zanasi, 1998; Han & Kamber,
21 years of age belongs to the fuzzy set labelled young to a degree of 0.55
2001): (1) identification and problem delimitation; (2) data preparation
(colloquially speaking, 55%), while a 27 year-old belongs entirely to the
(pre-processing); (3) data mining (machine learning); (4) analysis,
fuzzy set young, or a 37-year-old belongs to young people to a 0.3 degree
evaluation and interpretation of results; and (5) presentation, assimila-
and also to adult people to a degree of 0.7. If we used classical (crisp) sets
tion and use of knowledge. It is important to highlight that the success of
and fixed the boundary between young and adult at 35 years of age, a
such process, applied to solve or support the resolution of a particular
person aged 34.9 years would be considered 100% young while another
problem of information in marketing, depends on the suitable
aged 35.1 years would not be young to any degree.
development of every stage. The reader will be more conscious of this
Fuzzy rules can be considered a useful representation of knowledge
question when observing the lengths we go in order to explain how to
to discover intrinsic relationships contained in a database (Freitas,
prepare marketing data (pre-processing) or how to analyse the output
2002). Thus, by means of fuzzy rules we can represent the relationship
(knowledge) of the data mining stage (post-processing).
existing among different variables, thus deducing the patterns
contained in the data examined. Useful patterns allow us to do non-
3.2. Knowledge representation by fuzzy rules
trivial predictions about new data. There are two extremes to express a
pattern: black boxes, whose internal behaviour is incomprehensible;
Nowadays, one of the most successful tools for the development of
and white boxes, whose construction reveals the pattern structure. The
descriptive models is fuzzy modelling (Lindskog, 1997). This is an
difference lies in whether the patterns generated are represented by a
approach used to model a system making use of a descriptive language
structure that is easy to examine and which can be used to reason and
based on fuzzy logic with fuzzy predicates. The way to express fuzzy
to inform further decisions. In other words, when the patterns are
predicates is by means of IF–THEN rules, as in the following example:
structured in a comprehensible way, they will be able to help explain
something about the data. The trouble with KDD, the interpretability-
IF Age_of_Consumer is Young and Purchasing_Power is Very_High
accuracy trade-off, is also being tackled in current fuzzy modelling
THEN Trend_To_Buy_Sports_Cars is High
(Casillas et al., 2003a,b) and will be considered by our proposal.
The use of fuzzy rules when developing the knowledge discovery
These rules set logical relationships among variables of a system by
process has some advantages, which are (Freitas, 2002; Dubois, Prade, &
using qualitative values. Such a representation mode easily matches the
Sudkamp, 2005): they allow us to deal with uncertain data; they ade-
humans' way of reasoning. Hence, the performance of both the analysis
quately consider multi-variable relationships; results are easily under-
and interpretation steps of the modelling process improves thanks to
standable by humans; additional information is easily added by an expert;
the true behaviour of a system that is more effectively revealed.
the accuracy degrees can be easily adapted to the needs of the problem,
Notwithstanding, it should be noted that though human reasoning may
and the process can be highly automatic with low human intervention.
deal without difficulty with terms like high or young, when this issue is
Therefore, we will use fuzzy logic as a tool to structure the
tackled by means of an automatic process its treatment is more complex.
information of a consumer behaviour model in a clear and intelligible
To work properly with these kinds of qualitative valuations,
way that is close to that of the human being. Fuzzy logic methods are
linguistic variables (Zadeh, 1975a,b, 1976) based on both Fuzzy Sets
expected to offer benefits to marketing decision makers when
Theory and Fuzzy Logic (Zadeh, 1965) are used, so the previously
integrated with current MkMSS (Metaxiotis, Psarras, & Samouilidis,
exemplified rule is known as a fuzzy rule. The use of fuzzy logic
2004). The fuzzy system will allow us to represent adequately the
provides several benefits, such as a higher generality, expressive
interdependence of variables and the non-linear relationships that
power, ability to model real problems and, last but not least, a
could exist between them.
methodology to exploit tolerance in the face of imprecision.
For example, we can consider the linguistic variable Age_of_Consu-
3.3. Multiobjective genetic algorithms
mer, which could take in the linguistic terms (values) teenager, young,
adult, and old. These linguistic terms (also know as labels) are
In the previous section, we introduced the proposed representation
mathematically expressed by simple functions that return the member-
of knowledge based on fuzzy rules. However, we also need an algorithm
ship degree (with a real value between 0 and 1) to each fuzzy set.
to automatically extract a set of fuzzy rules with good properties. In this
Therefore, instead of considering that a consumer could be 100% young
paper, we propose the use of a genetic algorithm. The main reasons for
or 100% adult, with fuzzy sets we can say that the consumer belongs to
using it instead of other well-known machine learning techniques are
the set of young people with one degree and also to the set of adults with
the following. Firstly, since there are usually contradictory objectives to
another degree. So, the boundaries between sets are fuzzy instead of
be optimised in KDD (such as accuracy and interpretability, or support
crisp, thus providing a powerful linguistic expression and a gradual
and confidence), we perform multiobjective optimisation. It is one of the
transition of the membership to the different fuzzy sets.
most promising issues and one of the main distinguishing features of
Fig. 1 represents an example of how the age of a person can be
genetic algorithms compared to other techniques. Furthermore, we
expressed by fuzzy sets. In this figure, we could say that a person of
consider a flexible representation of fuzzy rules that can be developed
Fig. 1. Illustrative example of the linguistic variable age, composed of the linguistic terms teenager, young, adult and old, and their corresponding fuzzy sets. A 37-year-old has a
membership degree 0.3 to young and 0.7 to adult.

F.J. Martínez-López, J. Casillas / Industrial Marketing Management 38 (2009) 714–731
717
Fig. 2 shows the structure of a simple GA.
A fitness function must be devised for each problem to be solved.
Given a particular chromosome (i.e. a solution), the fitness function
returns a numerical value that is supposed to be proportional to the
utility or adaptation of the solution represented by this chromosome.
In our case, we will consider two different measures to assess the
quality of a solution (fuzzy rule): support and confidence.
There are a number of ways to do selection. We might view the
population as a mapping on a roulette wheel, where each individual is
represented by a space that proportionally corresponds to its fitness.
By repeatedly spinning the roulette wheel, individuals are chosen
using stochastic sampling with replacement to fill the intermediate
population. Another possibility, called binary tournament, consists in
doing a number of tournaments equal to the size of the population. In
each tournament, two chromosomes of the old population are chosen
Fig. 2. Structure of a genetic algorithm.
at random, and the best one according to fitness is included in the new
population. We will employ this second approach in our proposal.
properly by genetic algorithms. This flexible representation improves the
After selection has been carried out, the construction of the
description capability of the fuzzy rule, an important issue in KDD.
intermediate population is completed and crossover and mutation can
Genetic algorithms demonstrated good results for management
occur. The crossover operator combines the features of two parent
and marketing applications, thus arousing the interest of researchers
structures to form two similar offspring. Classically, it is applied at a
and practitioners in the nineties (Hurley, Moutinho, & Stephens, 1995;
random position with a probability of performance, the crossover
Nissen, 1995). However, one of the novelties of this paper for market-
probability. The mutation operator arbitrarily alters one or more
ing is that, in this instance, fuzzy logic and genetic algorithms will not
components of a selected structure so as to increase the structural
be applied separately to tackle a particular marketing problem, but in
variability of the population. Each position of each solution vector in
cooperation. In the following, genetic algorithms and multiobjective
the population undergoes a random change according to a probability
optimisation are briefly introduced.
defined by a mutation rate, the mutation probability.
Fig. 6 in Section 4 illustrates graphically the use of a genetic
3.3.1. Genetic algorithms
algorithm to extract fuzzy rules from available data in the marketing
Genetic algorithms are general-purpose search algorithms that use
problem we are dealing with in this paper.
principles inspired by natural population genetics to evolve solutions
to problems. The basic principles of genetic algorithms were first laid
3.3.2. Multiobjective optimisation
down rigorously by Holland (1975) and are well described in many
Many real-world problems involve simultaneous optimisation of
texts (e.g.: Goldberg, 1989; Michalewicz, 1996).
multiple objectives. In principle, multiobjective optimisation is very
The basic idea is to maintain a population (i.e., a set) of knowledge
different from single-objective optimisation. The second case
structures that evolves over time through a process of competition and
attempts to obtain the best solution; i.e. the global minimum or the
controlled variation. Each structure in the population represents a
global maximum depending on the problem. However, in the case of
candidate solution to the specific problem and has an associated fitness
multiple objectives, there may not be a single solution that is better
to determine which structures are used to form new ones in the process of
than the rest with respect to all objectives.
competition. The new individuals are created using genetic operators such
In a typical multiobjective optimisation problem, there is a set of
as crossover and mutation. Genetic algorithms have had a great measure
solutions that are superior to the rest of the solutions in the search
of success in search and optimisation problems. The main reason for this
space when all the objectives are considered, but which are inferior to
success is their ability to exploit accumulative information about an
other solutions in the space occupied only by some of them. These
initially unknown search space in order to bias subsequent search into
solutions are known as non-dominated solutions (Chankong & Haimes,
useful subspaces, i.e., their robustness. This is their key feature, especially in
1983), while the rest of the solutions are known as dominated
large, complex and poorly understood search spaces, where the classical
solutions. Since none of the solutions in the non-dominated set is
search tools (enumerative, heuristic, etc.) are inappropriate, offering a
worse in all the objectives than the other ones, all of them are
valid approach to problems requiring efficient and effective search.
acceptable solutions.
A genetic algorithm starts with a population of randomly generated
Mathematically, the concept of Pareto-optimality2 or non-dominance
solutions, chromosomes, and advances towards better solutions by
is defined as follows. Let us consider, without loss of generality, a mul-
applying genetic operators, modelled on the genetic processes occurring
tiobjective maximization problem with m parameters (decision vari-
in nature. As previously mentioned, in these algorithms we maintain a
ables) and n objectives:
population of solutions (in our case, fuzzy rules) for a given problem; this
population undergoes evolution in a form of natural selection. In each
Maximise
f ðxÞ ¼ f
ð 1ðxÞ; f2ðxÞ; N ; fnðxÞÞ
generation, relatively good solutions reproduce to give offspring that
replace the relatively bad solutions, which die. An evaluation or fitness
with x = (x1,x2,…,xm)∈X. A decision vector a∈X dominates b∈X (noted
function plays the role of the environment to distinguish between good
as a ⪯b) if, and only if:
and bad solutions. The process of evolving from the current population to
8ia 1
f ; N ; ngj f
f
gj f
the next one constitutes one generation in the execution of a genetic
i a
ð Þ z fi b
ð Þ and aja 1; N ; n j a
ð Þ N fj b
ð Þ:
algorithm.
Any vector that is not dominated by any other is said to be Pareto-
Although there are many possible variants of the basic genetic
optimal or non-dominated. These concepts are depicted graphically in
algorithm, the fundamental underlying mechanism involves three
Fig. 3.
operations (Goldberg, 1989):
(1) evaluation of individual fitness,
2 The concept Pareto optimality is an important notion in neoclassical economics. It
(2) formation of a gene pool (intermediate population), and
is named after the French–Italian economist Vilfredo Pareto (1848, Paris–1923,
(3) crossover and mutation.
Geneva).

718
F.J. Martínez-López, J. Casillas / Industrial Marketing Management 38 (2009) 714–731
Fig. 3. Example of multiobjective optimisation.
Thanks to the use of a solution population, genetic algorithms can
features such as discontinuities, multimodality, disjoint feasible spaces,
simultaneously search for many Pareto-optimum solutions. For this
and noisy function evaluations, reinforces the potential effectiveness of
reason, genetic algorithms have been recognised as possibly being well
genetic algorithms in multiobjective search and optimisation. Generally,
suited to multiobjective optimisation (Coello, Van Veldhuizen, & Lamont,
the multiobjective approaches only differ from the rest of the genetic
2002). Furthermore, the ability to handle complex problems, involving
algorithms in the fitness function and/or in the selection operator.
4. An illustrative example on how to extract knowledge from data to analyse consumer behaviour
This section serves as a bridge between the technical concepts included in the previous section and the modelling methodology proposed in
the next one. Therefore, to introduce the reader to the methodology, we propose extracting useful knowledge from data that can aid better
understanding the existing relationships between variables by presenting in this section a toy problem (with a few variables and a small data set
size) to illustrate the basic behaviour and powerful nature of the proposed KDD process. Some parts of the process have been intentionally
simplified with the aim of focusing on the most relevant aspects. The rigorous description of the proposal can be found in Section 5, while Section
6 amply describes the experimental results in a real-world problem.
To illustrate the proposed use of KDD, we will consider a simple measurement (causal) model depicted in Fig. 4(a), compounded by three
construct or latent variables (depicted by circles), two exogenous and one endogenous: (1) fashion consciousness, (2) conservatism, and
(3) hedonism; extracted from MacLean and Gray (1998). Likewise, imagine that the three constructs have been measured by means of several
seven-point interval scales (e.g. Likert-type and differential semantic scales). Finally, Fig. 4(b) shows an example of a data set available for this
problem, which consists of three variables, each made up of a set of values. There are just four cases (e.g., questionnaires), which are not realistic at
Fig. 4. Example of a simple measurement (causal) model–extracted from (MacLean & Gray, 1998)–and a data set from four hypothetical consumers' responses.

F.J. Martínez-López, J. Casillas / Industrial Marketing Management 38 (2009) 714–731
719
Fig. 5. Example of transformation of a seven-point Likert-type scale into a fuzzy semantic. According to that, the membership degree of 5 to the fuzzy set associated to the linguistic
term Medium is 0.67, while the membership degree of 6 is 0.33.
all–i.e. think that a consumer database usually has hundreds or even thousands of collected individuals' responses–, though it is useful for our
illustrative purpose.
The first step we perform is to transform the interval scale into fuzzy semantics. This allows us to use linguistic terms to describe the different
items by means of linguistic variables. We can consider the following three membership functions to describe the terms Low, Medium, and High:
8
8 x À 1
>
>
>
>
(
>
< 4 À x
>
if 1 V x V 4
< 3
7 À x
A
ð Þ ¼
if 2 V x V 4
ð Þ ¼
ð Þ ¼
if 5 V x V 8
Low x
3
; AMedium x
7 À x
; AHigh x
3
:
>
>
> 0
otherwise
>
if 4 b x V 7
>
> 3
0
otherwise
:
: 0
otherwise
A graphical representation of these membership functions is depicted in Fig. 5.
Once we have defined the variables in terms of fuzzy sets, we can use fuzzy rules to express relationships (i.e., patterns) among the variables
(refer to Section 3.2. for a description of these kinds of rules). To do that, we will consider the two exogenous variables and the endogenous one,
antecedents and consequent respectively in this example.
These fuzzy rules can represent many different relationships among the variables; however, not all of them will match the existing data
exactly. Therefore, we need some measures to assess the quality of each rule with respect to the data. These measures can be considered a kind
of statistical computation. In this paper, we will consider two important values: support and confidence. On the one hand, support (whose real
value is in [0,1]) will give us an idea about in which degree the rule represents the cases of the data set. For example, a support of 0.25 could be
understood as the rule that covers 25% of the available cases. We are interested in obtaining fuzzy rules with a support as high as possible since
the rule will be more general and will represent a higher portion of the sample. On the other hand, confidence (whose real value is also in [0,1]),
indicates how accurate the fuzzy rule is. Since the fuzzy rule predicts a relationship between the antecedent and the consequent, we need
to know in which degree such a prediction appears in the available data set. For example, if a fuzzy rule has a confidence of 0.9, we can say
that, according to the available data, the fuzzy rule is 90% true. Of course, we are interested in obtaining fuzzy rules with a high degree of
confidence.
As one can imagine, support and confidence are two contradictory features. Inasmuch as the degree of representation is higher, it is more
difficult to accurately express the relationships among variables. One fuzzy rule will be clearly preferable to another if the former has higher
values of both support and confidence.
In the following, we will show some examples of fuzzy rules and the computation of the corresponding support and confidence values from
the data set of Fig. 4(b).
R1: If Fashion_Consciousness is LOW and Conservatism is MEDIUM then Hedonism is MEDIUM


A
Yð1Þ Þ ¼
f
g ¼
f
g ¼
Low
x
max A
max 1; 0:67; 1
1
1
Low 1
ð Þ; ALow 2
ð Þ; ALow 1
ð Þ


A
Yð1Þ Þ ¼
f
g ¼
f
g ¼
Medium
x
max A
max 0:67; 0:33
0:67
2
Medium 5
ð Þ; AMedium 6
ð Þ
À
Á
n



o
A
ð Þ ¼
Yð1Þ
Yð1Þ
¼
f
g ¼
A 1
ð Þ x 1
min ALow x
; A
x
min 1; 0:67
0:67
1
Medium
2


A
Yð1Þ Þ ¼
f
g ¼
f
g ¼
Medium
y
max AMedium 1
ð Þ; AMedium 2
ð Þ
max 0; 0:33
0:33




À
Á


A
Yð2ÞÞ ¼
Yð2Þ Þ ¼
ð Þ ¼
Yð2Þ Þ ¼
Low
x
0; A
x
0:33; A
0; A
y
0:33
1
Medium
2
A 1
ð Þ x 2
Medium




À
Á


A
Yð3Þ Þ ¼
Yð3Þ Þ ¼
ð Þ ¼
Yð3Þ Þ ¼
Low
x
0; A
x
0:33; A
0; A
y
0
1
Medium
2
A 1
ð Þ x 3
Medium




À
Á


A
Yð4Þ Þ ¼
Yð4Þ Þ ¼
ð Þ ¼
Yð4Þ Þ ¼
Low
x
0; A
x
0:67; A
0; A
y
0:67
1
Medium
2
A 1
ð Þ x 4
Medium
1 X
4 




YðeÞ
0:67 Á 0:33 þ 0 þ 0 þ 0
Support R
ð 1Þ ¼
A
Á A
y
¼
¼ 0:05556
4
A 1
ð Þ
x e
ð Þ
B 1
ð Þ
4
e¼1
P

À
Á
n
À
Á

o
4
A
ð Þ Á
ðeÞ
max 1 À A
; A
Y
y


e¼1
A 1
ð Þ x e
A 1
ð Þ x e
ð Þ
B 1
ð Þ
0:67 Á max 1
f À 0:67; 0:33g þ 0 þ 0 þ 0
Conf idence R
ð 1Þ ¼
P
¼
¼ 0:33333
4
A
ð Þ
ð
Þ
0:67 þ 0 þ 0 þ 0
e¼1
Að1Þ x e

720
F.J. Martínez-López, J. Casillas / Industrial Marketing Management 38 (2009) 714–731
R2: If Fashion_Consciousness is MEDIUM and Conservatism is MEDIUM then Hedonism is MEDIUM


À
Á


À
Á
A
Yð1Þ Þ ¼
ð Þ ¼
Yð2Þ Þ ¼
¼
Medium
x
0:33; A
0:33
A
x
0; A
0
1
A 2
ð Þ x 1
Medium
1
A 2
ð Þ x 2
ð Þ


À
Á


À
Á
A
Yð3Þ Þ ¼
ð Þ ¼
Yð4Þ Þ ¼
ð Þ ¼
Medium
x
0; A
0
A
x
1; A
0:67
1
A 2
ð Þ x 3
Medium
1
A 2
ð Þ x 4
0:33 Á 0:33 þ 0 þ 0 þ 0:67 Á 0:67
Support R
ð 2Þ ¼
¼ 0:13889
4
0:33 Á max 1
f À 0:33; 0:33g þ 0 þ 0 þ 0:67 Á max 1
f À 0:67; 0:67g
Conf idence R
ð 2Þ ¼
¼ 0:44445:
0:33 þ 0 þ 0 þ 0:67
As we can observe, the fact of using the linguistic term “medium” for the fashion consciousness variable instead of “low” (as in rule R1) allows
us to cover better the data set and, at the same time, to improve the accuracy of the rule.
R3: If Fashion_Consciousness is MEDIUM and Conservatism is {LOW or MEDIUM} then Hedonism is MEDIUM


n



o
À
Á
A
Yð1Þ ¼
Y 1
ð Þ
þ
Yð1Þ
¼
¼
Low or Medium
x
min
1; A
x
A
x
0:67; A
0:33
2
Low
2
Medium
2
A 3
ð Þ x 1
ð Þ


À
Á
A
Yð2Þ ¼
ð Þ ¼
Low or Medium
x
1; A
0:33
2
A 3
ð Þ x 2


À
Á
A
Yð3Þ ¼
ð Þ ¼
Low or Medium
x
1; A
0:33
2
A 3
ð Þ x 3


À
Á
A
Yð4Þ ¼
ð Þ ¼
Low or Medium
x
1; A
0:67
2
A 3
ð Þ x 4
Support R
ð 3Þ ¼ 0:16667
Conf idence R
ð 3Þ ¼ 0:66667:
This third rule includes two linguistic terms in the variable conservatism. Doing that, the support is higher since we can cover the data set to a
higher degree compared to rule R2 (it is obvious since R3 is more general than R2). Moreover, the confidence is also improved, so this third rule is
clearly better than the previous ones.
Once we have shown some examples of fuzzy rules and how to compute their associated support and confidence values from a data set, we will
illustrate a simplification of how the data mining process works. Fig. 6 depicts a scheme of the behaviour of a genetic algorithm to reveal fuzzy rules
from data. The genetic algorithm, as explained in Section 3.3.1, optimises generation by generation the population, in our case a set of different
fuzzy rules, i.e., patterns. To analyse alternative fuzzy rules, new ones are generated from the existing one by applying the crossover and mutation
operators. The genetic algorithm encodes the rules in a format that is easily tractable in a computer, in this case by using a binary representation.
In the example of Fig. 6, the mutation takes a solution from the current population and applies a slight alteration; in this case, it changes the
linguistic term used in the first variable from “low” to “medium.” The new generated rule is included in the next population since its corresponding
values of support and confidence are better. In other example, the crossover takes two solutions and combines them by generating a new rule that
contains the linguistic terms considered in each parent rule. This new rule, better than its parents, is included in the new population.
5. A marketing intelligent system for consumer behaviour analysis
theoretical constructs (i.e. unobserved variables), should be made.
Consequently, we think that time should be spent analysing the
This section introduces the process in which we propose perform-
adaptation of the fuzzy rule-based KDD to the latter case, inasmuch as
ing knowledge discovery related to consumers by fuzzy rules.
its treatment seems to be the more controversial.
Basically, it consists of preparing the data and of fixing the scheme
Previously, it could be said that measuring streams for these latent
we follow to represent the knowledge existing in the data. Once these
variables in consumer modelling was classified into two groups
aspects are defined, a machine learning method is used to auto-
depending on if they declared that these constructs could or could not
matically extract interesting fuzzy rules. Finally, a post-processing
be perfectly measured by means of observed variables (indicators):
stage is carried out. All these questions are now presented in detail.
the operational definition philosophy and the partial interpretation
philosophy respectively. This latter approach of measurement, cur-
5.1. Data gathering
rently predominant in the marketing modelling discipline, recognises
the impossibility of doing perfect measurements of theoretical
First step is to collect the data related to the variables defining the
constructs by means of indicators, so it poses joint consideration of
theoretical model of the consumer behaviour proposed. In this sense,
multiple indicators–imperfect when considered individually, though
as has been done traditionally in Marketing Science in particular,
reliable when considered together–of the subjacent construct to
and in Social Sciences in general, data is obtained by means of a
obtain valid measures (Steenkamp & Baumgartner, 2000).
questionnaire. This questionnaire gathers the measures for the set of
Therefore, our methodological approach should be aware of this
constituent elements of the model.
question when adapting the data (observed variables) to a fuzzy rule
learning method. Notwithstanding, we would like to highlight that
5.2. Data processing
our method does not have any problem with processing elements of a
model for which we have just a single variable or indicator associated
Next, it is necessary to adapt the collected data to a scheme easily
to each of them, even when they have been measured by varied
tractable by fuzzy rule learning methods. Thus, at first, attention
measurement scales. The problem comes, hence the challenge to face,
should be paid to how modellers face and develop the measurement
when there are multiple variables related to the measurement of a
process of the elements/variables contained in the complex beha-
particular element of the model. Some intuitive solutions and aprioristic
vioural models. In this respect, reflections about the measurement of
analyses of the internal consistency of the multi-item scales associated
such variables, with a special focus on those usually known as
to such elements have been proposed, with the aim of keeping just

F.J. Martínez-López, J. Casillas / Industrial Marketing Management 38 (2009) 714–731
721
Fig. 6. A simplified example of the behaviour of a genetic algorithm when extracting knowledge in form of fuzzy rules from the data set available in Fig. 4(b).
one indicator (the best) per construct (see: Casillas, Martínez-López, &
5.3.1. Fuzzy semantics from expert knowledge
Martínez, 2004). The weakness of these approaches is that the data must
Once the marketing modeller has finally determined both the
be transformed, so relevant information may be lost.
elements of the model and the observed variables associated to each
We propose a solution based on a more sophisticated process
one (i.e. the measurement model), a transformation into linguistic
that allows working with the original format without any pre-
terms (fuzzy semantic) of the original marketing scales used for
processing stage (Martínez-López & Casillas, 2007): the multi-item
measuring those observed variables should be done. This is necessary
fuzzification. Thus, a T-conorm operator (e.g., maximum), tradition-
for the derivation of fuzzy rules later. This question implies treating
ally used in fuzzy logic to develop the union of fuzzy sets, can be
the application of the fuzzy set theory to the measurement in
applied to aggregate the partial information given by each item.
marketing. In this regard, as far as we know, Viswanathan, Bergen,
Since it is not pre-processing data but a component of the machine
Dutta, and Childers (1996) were the ones who first researched this
learning design, the details of that treatment of the items is des-
question by proposing a methodology for the scale development in
cribed in Section 5.4.2.
marketing. In any case, as this is not the central theme of this paper,
we are not going to treat this issue in depth, though it is thoroughly
5.3. Representation and inclusion of the marketing expert's knowledge
analysed in the research that supports this study.
Several marketing scale types can be used to measure the variables
Several issues should be tackled at this step of our methodological
associated to the constituent elements of a consumer behaviour model.
proposal: the set of variables/constructs to be processed, the
With the aim of focusing the problem, we take Stevens (1946, 1959) as
transformation of the marketing scales used for measuring such
a base to summarize them in four categories with regard to their level of
variables into fuzzy semantic, the relations among constructs (i.e. the
measurement, i.e. nominal, ordinal, interval and ratio. Considering
causal model), and the fuzzy rules' sets to be generated. All of them are
those types, a transformation into fuzzy semantic is meaningful for
based on the expert's capability to express his knowledge in a hu-
the majority with the exception of variables measured by means of
manly understandable format by fuzzy logic.
a nominal scale, where the nature of categories defining the scale

722
F.J. Martínez-López, J. Casillas / Industrial Marketing Management 38 (2009) 714–731
are purely deterministic. In general terms, this transformation should
This structure uses a more compact description that improves
be practiced taking into account two main questions:
interpretability. Moreover, the structure is a natural support to allow
for the absence of some input variables in each rule (simply making Ãi
a) The number of linguistic terms to be used, which determines the
to be the whole set of linguistic terms available).
granularity (the scale sensitivity) of certain fuzzy variable, must be
defined. Thus, although more terms are used, the analysis of
5.4.2. Multi-item fuzzification
relations among variables is more accurate, but more complex too.
In order to properly consider the set of items available for each
Consequently, the marketing modeller should take time to think
input/output variable (as discussed in Section 5.2), we propose an
about what the most convenient degree of sensitivity is in the
extension of the membership degree computation, the so-called multi-
fuzzy scales used in his/her study. Three or five linguistic terms
item fuzzification. The process is based on a union of the partial
(fuzzy sets) seem good options.
information provided by each item. Given Xi and Yj measured by the
b) The membership function type and shapes defining the behaviour of a

(i)
(i)
(i)

( j)
vectors of items x
( j)
( j)
i = (x1 ,…, xh ,…, xp ) and yj = (y1 ,…,yt ,…,yq ), res-
certain fuzzy variable should be also defined. Such behaviour can be
i
i
j
j
pectively, the fuzzy propositions “Xi is Ãi” and “Yj is Bj” are respectively
broadly treated considering the use of linear vs. non-linear member-
interpreted as follows:
ship functions to characterise the fuzzy sets. Thus, trapezoidal and
triangular functions can be used to obtain a linear behaviour, while
 
 
 


p
q
A
Y
i
j
x
¼ max A xi
and A
Y
y
¼ max A yðjÞ :
Gaussian functions can be used for a non-linear one.
˜A
i
˜
B
j
B
i
h
t
h
Ai
i
j
j
j
i ¼1
tj¼1
We are now going to focus on those marketing scales mainly used for
measuring the observed variables related to the elements (theore-
Therefore, the T-conorm of maximum is considered to interpret the
tical constructs) of a particular marketing model; i.e.: Likert-type and
disjunction of items.
differential semantic. Firstly, we have considered that it is more
appropriate to use linear functions, inasmuch as it facilitates the
5.4.3. Discovery process
interpretation of relations later. Second, we believe that a trans-
In order to perform descriptive induction we will apply a method
formation into a triangular function is more convenient if special
with some similarities to subgroup discovery, widely used in learning
characteristics of these marketing scales are considered; scales
classification rules (Lavrac, Cestnik, Gamberger, & Flach, 2004) where
valuations are punctual. Then, when the membership degree of
the interest property is the class associated to the consequent variable.
certain linguistic terms is equal to one, such a term should be
Therefore, this technique seeks to group the set of data into different
associated to a point of the scale. In this regard, this choice has also
subgroups, including in each of them the example set by the corres-
been justified in the marketing context, with the argument that
ponding consequent, and to discover a set of rules representing this
trapezoidal functions facilitate the later process of fuzzy inference
subgroup. In that case, the most usual approach involves running the
(Li et al., 2002).
algorithm once for each subset of examples holding the property fixed
for the consequent.
To sum up, Fig. 5 shows an example based on the transformation of
Instead of that, our algorithm considers the subgroup division
a seven-point rating scale into a three-triangular fuzzy semantic, with
according to the used fuzzy set in the consequent; therefore, the
the three linguistic terms (Low, Medium, and High) represented by the
subsets of examples can be overlapped. Moreover, we propose per-
corresponding fuzzy sets characterised by the three membership
forming a simultaneous subgroup discovery where niches of fuzzy
functions shown in Section 4.
rules, in accordance with the consequent, are formed and optimised in
parallel to generate a final set of suboptimal solutions in each sub-
5.3.2. Input/output linguistic variables from expert knowledge
group. To perform this process, as explained in the following sections,
Once the causal model has been fixed by the marketing expert, fuzzy
we vary the concept of multiobjective dominance and we design the
rules are used to relate input (antecedents) with output (consequents)
genetic operators for acting only on the antecedent part.
variables. Obviously, the theoretic relations defining the model can be
directly used to define the IF–THEN structures by considering the
5.4.4. Coding scheme
dependences shown among the variables. Thus, we obtain a set of fuzzy
Each individual of the population represents a fuzzy rule. The rule
rules for each considered consequent (i.e. endogenous element of the
is encoded by a binary string for the antecedent part and an integer
model) and its respective set of antecedents. Several examples of fuzzy
coding scheme for the consequent part. The antecedent part has a size
rules from the model included in Fig. 4(a) can be found in Section 4.
equal to the sum of the number of linguistic terms used in each input
variable. The allele ‘1’ means that the corresponding linguistic term is
5.4. Machine learning (data mining process)
used in the corresponding variable. The consequent part has a size
equal to the number of output variables. In that part, each gene
5.4.1. Fuzzy rule structure
contains the index of the linguistic term used for the corresponding
In data mining, it is crucial to use a learning process with a high
output variable.
degree of interpretability preservation. To do that, we can opt for
For example, assuming we have three linguistic terms (S [small],
using a compact description as the disjunctive normal form. This kind
M [medium], and L [large]) for each input/output variable, the fuzzy
of fuzzy rule structure has the following form (González & Pérez,
rule [IF X1 is S and X2 is {M or L} THEN Y is M] is encoded as [100|
1998):
011||2].
R: IF X1 is Ã1 and … and Xn is Ãn THEN Y1 is B1 and … Ym is Bm
5.4.5. Objective functions
with each input variable Xi, i∈{1,…, n}, taking as a value a set of linguistic
We consider the two criteria most often used to assess the quality
terms Ãi ={Ai1 or … or Ain}, whose members are joined by a disjunc-
of association rules (Dubois et al., 2005): support and confidence. In
i
tive (T-conorm) operator, while the output variables Yj, j∈{1,…, m},
Section 4, the reader can see some examples of how these measures
remain a usual linguistic variable with single labels associated. We use
are computed.
the bounded sum as T-conorm in this paper:
(1) Support: This objective function measures the representation
(
)
degree of the corresponding fuzzy rule among the available
X
ni
A ˜A
data. It is computed as the mean covering degree of the rule for
iðxÞ ¼ min
1;
A ð Þ
A
x
:
ik
k¼1
each data. As covering, we consider the conjunction of the

F.J. Martínez-López, J. Casillas / Industrial Marketing Management 38 (2009) 714–731
723
membership degrees of both antecedent and consequent
To perform simultaneous subgroup discovery properly, we need to
variables. Therefore, the support measure (for maximization)
redefine the dominance concept. Thus, one solution (fuzzy rule) do-
of the fuzzy rule R: A ⇒ B is defined as follows:
minates another when, besides being better or equal in all the ob-
jectives and better in at least one of them, it has the same consequent
1 X
N




as the other rule. In that way, those rules with different consequents
YðeÞ
Sup R
ð Þ ¼
A
ð Þ
Á A
y
are not dominated between them, thus inducing the algorithm to form
N
A x e
B
e¼1
a search niche (Pareto set) for each considered consequent (subgroup).
→(e)
→(e)

with N being the data set size, x(e) =(x 1 ,…, x n ) and ye the
À
Á
5.4.7. Genetic operators
eth input/output multi-item data instance, and
A
ð Þ ¼
A x e


The initial population is built by defining the same amount of
ðeÞ
min
A
Y
˜
x
the covering degree of the antecedent of the
i
groups (with the same size) as the consequents considered. In each of
ia 1
f ; N ;ng Ai
rule R for each example (i.e., the T-norm minimum is considered to
them, the chromosomes are generated by fixing the consequent and
interpret the connective ‘and’ of the fuzzy rule). As shown, the T-
by randomly defining a simple antecedent to which each variable is
norm of the product is considered as joint antecedent and con-
assigned only one linguistic term. The two genetic operators (cross-
sequent. Note that we use the multi-item fuzzi


fication described
over and mutation) act only on the antecedent part. This allows the
ðeÞ

in Section 5.4.2 to compute A
Y
(e)
algorithm to keep a constant size for each subgroup.
˜
x
and μ
).
A
i
B( y
i
The crossover operator randomly chooses two cross points (in the
(2) Confidence: This second objective measures the reliability of the
antecedent) and exchanges the central string of the two selected
relation between antecedent and consequent described by the
parents. If all the linguistic terms of a variable are set off after cross-
analysed fuzzy rule. We have used a confidence measure that
over, a linguistic term used in the parents is randomly chosen and set
avoids the accumulation of low cardinalities (Dubois et al.,
to ‘1’. It is interesting to note that no constraints are imposed on
2005). It is computed (for maximization) as following:
selecting the parents, so the crossover can be applied to parents with
different consequents (i.e., belonging to different subgroups). It allows
P
 À Á
n
À
Á

o
N
A
ð Þ Á
ðeÞ
max 1 À A
ð Þ ; A Y
y
migrations between niches, thus improving the search process.
e¼1
A x e
A x e
B
Conf R
ð Þ ¼
P
:
The mutation operator randomly selects an input variable of the
N
A
ð Þ
ð
Þ
e¼1
A x e
fuzzy rule encoded in the chromosome and one of the three following
possibilities is applied: expansion, which flips to ‘1’ a gene of the selected
Therefore, the Dienes' S-implication, I(a,b)=max{1 −a,b}, is used.
variable; contraction, which flips to ‘0’ a gene of the selected variable; or
Note that this implication operator is a fuzzy interpretation of the
shift, which flips to ‘0’ a gene of the variable and flips to ‘1’ the gene
classical interpretation p ⇒q≡¬p∨q used in Boolean logic where
immediately before or after it. The selection of one of these mechanisms
the negation is interpreted as 1 −a and the disjunction as max{a,b}.
is made randomly among the available choices (e.g., contraction cannot
Multi-item fuzzification is again considered.
be applied if only one gene of the selected variable has the allele ‘1’). Note
that it is always possible to perform at least one of these options.
5.4.6. Evolutionary scheme
We consider a generational approach with the multiobjective elitist
6. Experimentation and knowledge interpretation
replacement strategy of NSGA-II (Deb, Pratap, Agarwal, & Meyarevian,
2002). Crowding distance in the objective function space is used.
6.1. Marketing model and data source used for the experimentation
Binary tournament selection based on the non-domination rank (or
the crowding distance when both solutions belong to the same front)
Regarding other published marketing-related studies that have
is

Download
Marketing Intelligent Systems for consumer behaviour modelling by ...

 

 

Your download will begin in a moment.
If it doesn't, click here to try again.

Share Marketing Intelligent Systems for consumer behaviour modelling by ... to:

Insert your wordpress URL:

example:

http://myblog.wordpress.com/
or
http://myblog.com/

Share Marketing Intelligent Systems for consumer behaviour modelling by ... as:

From:

To:

Share Marketing Intelligent Systems for consumer behaviour modelling by ....

Enter two words as shown below. If you cannot read the words, click the refresh icon.

loading

Share Marketing Intelligent Systems for consumer behaviour modelling by ... as:

Copy html code above and paste to your web page.

loading