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Studies in Fuzziness and Soft Computing

Rafael Bello
Rafael Falcon
José Luis Verdegay Editors

Uncertainty
Management
with Fuzzy and
Rough Sets
Recent Advances and Applications
Studies in Fuzziness and Soft Computing

Volume 377

Series editor
Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland
e-mail: kacprzyk@ibspan.waw.pl
The series “Studies in Fuzziness and Soft Computing” contains publications on
various topics in the area of soft computing, which include fuzzy sets, rough sets,
neural networks, evolutionary computation, probabilistic and evidential reasoning,
multi-valued logic, and related fields. The publications within “Studies in Fuzziness
and Soft Computing” are primarily monographs and edited volumes. They cover
significant recent developments in the field, both of a foundational and applicable
character. An important feature of the series is its short publication time and
world-wide distribution. This permits a rapid and broad dissemination of research
results.

More information about this series at http://www.springer.com/series/2941

Rafael Bello Rafael Falcon
• •

José Luis Verdegay

Editors

Uncertainty Management
with Fuzzy and Rough Sets
Recent Advances and Applications

123
Editors
Rafael Bello Rafael Falcon
Department of Computer Science School of Electrical Engineering
Universidad Central “Marta Abreu” and Computer Science
de Las Villas University of Ottawa
Santa Clara, Villa Clara, Cuba Ottawa, ON, Canada

José Luis Verdegay and

Department of Computer Science
and Artificial Intelligence, Technical Research & Engineering Division
School of Informatics and Larus Technologies Corporation
Telecommunications Engineering Ottawa, ON, Canada
University of Granada
Granada, Spain

ISSN 1434-9922 ISSN 1860-0808 (electronic)

Studies in Fuzziness and Soft Computing
ISBN 978-3-030-10462-7 ISBN 978-3-030-10463-4 (eBook)
https://doi.org/10.1007/978-3-030-10463-4

Library of Congress Control Number: 2018964931

© Springer Nature Switzerland AG 2019

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar
methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a specific statement, that such names are exempt from
the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this
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jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To our families

To our friends and colleagues at ISFUROS

2017
Preface

Granular computing (GrC) has been gaining momentum as a suitable computa-

tional paradigm to solve different kinds of problems. GrC allows analyzing infor-
mation from different perspectives by generating different granulations of the
universe of discourse. The information granules in each granulation of the universe
bring together objects that are related according to an underlying property, such as
inseparability, similarity, or functionality. Then, we operate at the level of infor-
mation granules instead of at the level of the original objects. Different separability
relationships give rise to different granulations, with a varying number of infor-
mation granules, hence yielding different levels of data abstraction. Fuzzy set
theory (FST) and rough set theory (RST) are two landmark methodologies under
the GrC umbrella.
These two theories can also be employed in the context of handling uncertainty
in a wide variety of computational models. Uncertainty can manifest itself both in
the data used to solve a problem, and in the knowledge of the application domain
fed to the problem-solving method. There are several types of uncertainty, such as
inaccuracy, vagueness, inconsistency, and missing data. The term soft computing is
utilized to bring together different computational techniques to actively consider the
uncertainty as an essential part of problem-solving. FST and RST are two
remarkable members of the soft computing family, which allow modeling vague-
ness and inconsistency, respectively. Given the increasing complexity of the
problems to be tractably solved, it is often necessary to combine two or more
techniques to generate new problem-solving approaches. These are the so-called
hybrid systems.
In FST, a universe of (possibly continuous) values for a system variable is
reduced to a discrete set of values, i.e., the set of linguistic terms. These terms are
defined as fuzzy sets via a membership function. Linguistic terms represent
information granules. Hence, the set of linguistic terms constitutes a granulation
of the universe for the linguistic variable under consideration. Linguistic variables
constructed in this way are used to represent knowledge of the application domain
in a more human-centric manner.

vii
viii Preface

In RST, the objects in the universe are brought together in an information

granule by using a separability (indiscernibility) relation. This leads to a granulation
of the universe according to that relation. In the classical RST formulation, the
underlying relation is an equivalence relation, which induces a partition of the
universe into a set of equivalence classes. In many cases, however, it is necessary to
replace the equivalence relation with a more flexible one (e.g., a tolerance relation).
In this case, the set of obtained information granules indicates a covering of the
universe of discourse.
A case that illustrates the need to combine both theories is when objects are
described through one or more numerical attributes. In that case, the granulation
of these continuous values could be performed via fuzzy sets (to account for the
vagueness and imprecision) and then the granulation of the objects themselves
could be conducted by using an RST indiscernibility relation (in order to detect
inconsistent information). As fuzzy sets or rough sets are combined, so-called fuzzy
rough sets or rough fuzzy sets have been developed and successfully applied to a
plethora of use cases. Additionally, other soft computing techniques can be
hybridized with FST and/or RST. For instance, fuzzy sets and genetic algorithms
(GAs) allow the generation of various computational methods, such as genetic
fuzzy systems. In the same way, fuzzy sets and artificial neural nets (ANNs) come
together in different ways to breed more powerful techniques, such as neuro-fuzzy
systems. ANNs have also been coupled with rough sets. For instance, RST-based
feature selection methods are used in the preprocessing stage of many ANN
models, as well as new neuron models have spawned (such as rough neurons) from
this profitable synergy.
The 2nd International Symposium on Fuzzy and Rough Sets (ISFUROS 2017)
was held from October 24–26, 2017, at the Meliá Marina Varadero hotel in
Varadero, Cuba, as a forum to present and discuss scientific results that contribute
toward theory and applications of fuzzy and rough set theories as well as their
hybridizations. ISFUROS 2017 took place under the umbrella of the First
International Scientific Convention organized by the Universidad Central de Las
Villas (UCLV), with over 20 concurrent events spread across five very intense and
fruitful days.
ISFUROS 2017 featured three keynote talks, two tutorial sessions, one panel
discussion, and 30 oral presentations out of the 55 submissions received. Out
of these, 20 accepted submissions were invited to prepare extended versions as
contributed book chapters to this Springer volume in the prestigious Studies in
Fuzziness and Soft Computing series. These 20 submissions encompass 62 authors
whose geographical distribution is as follows: Cuba (23), Spain (8), Canada (7),
Colombia (7), Finland (4), Peru (4), Belgium (3), Germany (2), Brazil (1), Italy (1),
Japan (1), and Poland (1).
This volume has been structured in three different parts. The first one is devoted
to theoretical advances and applications of fuzzy sets. The second one highlights
rough set theory and its applications, and the third one is dedicated to hybrid
systems.
Preface ix

In Part I, the reader will find new methods based on fuzzy sets to solve machine
learning problems, such as clustering, as well as optimization problems that borrow
FST elements into their formulation. Other contributions put forth new approaches
for decision making, including those featuring fuzzy cognitive maps. There are nine
chapters comprising this Part I.
Part II includes six chapters that enrich the state of the art in RST. Several papers
propose new algorithms for knowledge discovery and decision making using rough
sets.
In Part III, five hybrid methods are introduced. Fuzzy and rough sets are com-
bined in two of the chapters. In the rest, fuzzy sets are coupled with neural and Petri
nets, as well as with GAs.
The editors hope that the methods and applications presented in this volume will
help broaden the knowledge about granular computing, soft computing and two of
its most important building blocks: fuzzy and rough set theories.
The rest of this preface briefly expands on the content of each chapter so that the
reader may dive straight into those that captured her interest.

Part I: Fuzzy Sets: Theory and Applications

Chapter “A Proposal of Hybrid Fuzzy Clustering Algorithm with Application in

Condition Monitoring of Industrial Processes” introduces a fuzzy clustering algo-
rithm inspired by the Weighted Fuzzy C-Means (W-FCM) method that leans on
maximum entropy principles and kernel functions to better separate the clusters.
The proposed technique first aims at identifying and removing outlier points prior to
the clustering process. Its parameters are learned through the popular differential
evolution metaheuristic optimizer. The algorithm was applied to a fault diagnosis
scenario and enabled the online detection of new system faults.
Chapter “Solving a Fuzzy Tourist Trip Design Problem with Clustered Points of
Interest” introduces a route planning problem with applications in tourism. The goal
of the tourist trip design Problem is to maximize the number of points of interest to
visit. The authors proposed a new, more realistic formulation where (i) the points of
interest are clustered in various categories and (ii) the scores and travel time con-
straints are modeled through fuzzy logic. A fuzzy optimization approach and an
efficient greedy randomized adaptive search procedure (GRASP) implementation
were considered. The computational experiments indicate that the proposed tech-
nique is able to find significant solutions.
The Optimal Bucket Order Problem (OBOP) is a rank aggregation problem
where the resulting ranking may be partial, i.e., ties are allowed. Several algorithms
have been proposed to solve OBOP. However, their performance with respect to the
characteristics of the problem instances is not properly studied. Chapter
“Characterization of the Optimal Bucket Order Problem Instances and Algorithms
by Using Fuzzy Logic” describes different aspects of the OBOP instances (such as
the number of items to be ranked, distribution of the precedence values, and the
x Preface

utopicity), as well as the performance of several OBOP algorithms, from a fuzzy

logic standpoint. Based on this fuzzy characterization, several fuzzy relations
between instance characteristics and algorithmic performance have been
discovered.
Chapter “Uncertain Production Planning Using Fuzzy Simulation” applies fuzzy
logic to a production planning scenario with successful results. The goal is to
characterize the mean flow time of the system, namely the time by which a product
is finished and released to the customer. Other performance measures such as
production time and waiting time were modeled as fuzzy sets following a recently
proposed fuzzy random variable generation method.
Chapter “Fully Fuzzy Linear Programming Model for the Berth Allocation
Problem with Two Quays” investigates the berth allocation problem (BAP) for two
quays, where vessels can berth at any position within the limits of the quay and may
arrive at different times during the planning horizon. It is assumed that the arrival
time of the vessels is imprecise, meaning that vessels can actually be late or early up
to a certain threshold. Triangular fuzzy numbers represent the imprecision of the
vessel arrivals. Two models for this BAP scenario are unveiled. The first one is a
fuzzy mixed integer linear programming (MILP), which allows obtaining berthing
plans with different degrees of precision. The second one is a fully fuzzy linear
programming (FFLP) model that yields a fuzzy berthing plan that can adapt to
possible contingencies related to the vessels’ arrivals. The proposed models have
been implemented in CPLEX and evaluated in a synthetic scenario with a varying
number of vessels. The chapter concludes by suggesting the steps to be taken so as
to implement the FFLP BAP model in a maritime container terminal.
Chapter “Ideal Reference Method with Linguistic Labels: A Comparison with
LTOPSIS” is concerned with multicriteria decision making (MCDM). The building
blocks of an MCDM model are described, followed by a brief tour of the most
popular compensatory MCDM methods. In particular, the chapter points out the
limitations of the reference ideal method (RIM) to operate with linguistic labels.
Next, RIM’s basic concepts are described, and another variant is proposed to
determine the minimum distance to the reference ideal, as well as the normalization
function. The proposed scheme is illustrated by means of an example and compared
against the LTOPSIS method.
Fuzzy cognitive maps (FCMs) can be defined as recurrent neural networks that
allow modeling complex systems using concepts and causal relations. While this soft
computing technique has proven to be a valuable knowledge-based tool for building
decision support systems, further improvements related to its transparency are still
required. In Chapter “Comparative Analysis of Symbolic Reasoning Models for
Fuzzy Cognitive Maps,” the authors designed an FCM-based model where both the
causal weights and concepts’ activation values are described through linguistic terms
like low, medium, or high. Augmenting FCMs with the computing with words
(CWW) paradigm leads to cognitive models that are closer to human reasoning, thus
facilitating the understanding of the model’s output for decision makers. The sim-
ulations using a well-known case study related to simulation scenarios illustrate the
soundness and potential application of the proposed model.
Preface xi

Another success story showcasing FCMs is reported in Chapter “Fuzzy

Cognitive Maps for Evaluating Software Usability.” Software usability evaluation
is a highly complex process given the variety of criteria to consider and the lack of
consensus on the values to be used. The usability evaluation method proposed in
this chapter incorporates soft computing elements such as fuzzy logic and fuzzy
linguistic modeling. Furthermore, the use of FCMs allows adding the interrelation
between usability criteria and therefore obtaining a real global usability index.
A mobile application was developed to evaluate the usability of other mobile
applications based on the approach described here. The results obtained in a
real-world environment shows that the proposed technique is a feasible, reliable,
and easy-to-interpret solution for its use in industry.
Chapter entitled “Fuzzy Simulation of Human Behaviour in the Health-e-Living
System” elaborates on an application of fuzzy set theory to preventive health
support systems where adherence to medical treatment is an important measure to
promote health and reduce healthcare costs. Preventive healthcare information
technology system design includes ensuring adherence to treatment through
just-in-time adaptive interventions (JITAI). Determining the timing of the inter-
vention and the appropriate intervention strategy are two of the main difficulties
current systems face. In this chapter, a JITAI system called health-e-living (Heli)
was developed for a group of patients with type-2 diabetes. During Heli’s devel-
opment stages, it was verified that the state of each user is fuzzy and it is difficult to
identify the right moment to send a motivational message to the user without being
annoying. A fuzzy formula is proposed to measure the patients’ adherence to their
goals. As the adherence measurement needed more data, the Disco software toolset
was introduced to model the human behavior and the health action process
approach (HAPA) to simulate the interactions between users of the Heli system.
The effectiveness of interventions is essential in any JITAI system and the proposed
formula allows Heli to send motivational messages in correspondence with the
status of each user so as to evaluate the efficiency of any intervention strategy.

Part II: Rough Sets: Theory and Applications

Covering-based RST is an extension of Pawlak’s RST, and it was proposed to

expand the applications of the latter to more general contexts. In this extension, a
covering is used instead of a partition obtained through an equivalence relation.
Recently, many authors have studied the relationships between covering-based
rough sets, matroids, and submodular functions. In Chapter “Matroids and
Submodular Functions for Covering-Based Rough Sets,” the authors introduced
the matroidal structures obtained from different partitions and coverings of a
specific set. An extension of a matroidal structure for covering-based rough sets is
also unveiled. Finally, a partial order relation among the matroidal structures is
formulated via submodular functions, coverings, and their approximation operators.
xii Preface

Chapter “Similar Prototype Methods for Class Imbalanced Data Classification”

put forward four new methods for solving imbalanced classification problems based
on nearest prototypes. Using similarity relations for the granulation of the universe,
similarity classes are generated and a prototype is selected for each similarity class.
The novelty of the proposal lies in the marriage between RST, specifically the use
of the similarity quality measure, and classification concepts based on nearest
prototypes, to classify objects under these conditions. The implementation of this
RST metric allows creating a prototype that covers the objects whose decision value
is the majority class of the similarity class. Experimental results showed that the
performance of the proposed techniques is statistically superior to other imbalanced
classification methods.
For any educational project, it is important and challenging to know, at the time
of enrollment, whether a given student is likely to successfully pass the academic
year or not. This task is not simple at all because many factors contribute to failure
in an academic setting. Inferring how likely it is that an enrolled student struggles to
meet the program requirements is undoubtedly an interesting challenge for the areas
of data mining and education. In Chapter “Early Detection of Possible
Undergraduate Drop Out Using a New Method Based on Probabilistic Rough Set
Theory,” the authors proposed the use of data mining techniques in order to predict
how likely a student is to succeed in the academic year. Normally, there are more
students who succeed compared to those who fail, hence resulting in an imbalanced
data representation. To cope with imbalanced data, a new algorithm based on
probabilistic RST is introduced. This algorithm has two main drivers: (1) the use of
two different threshold values for the similarity between objects when dealing with
minority or majority class examples and (2) the combination of the original data
distribution with the probabilities predicted by the RST method. The experimental
analysis confirmed that better results are obtained in comparison to a number of
state-of-the-art algorithms.
Community detection is one of the most important problems in social network
analysis. This problem has been successfully addressed through multiobjective
evolutionary algorithms (MOEAs); however, most of the proposed MOEA-based
solutions only detect disjoint communities, although it has been shown that in most
real-world networks, nodes may belong to multiple communities. In Chapter
“Multiobjective Overlapping Community Detection Algorithms Using Granular
Computing,” three algorithms that build a set of overlapping communities from
different perspectives are introduced. These algorithms employ granular computing
principles and are rooted on a multiobjective optimization approach. The proposed
methods make use of highly cohesive information granules as initial expansion
seeds and employ the local properties of the network vertices in order to obtain
highly accurate overlapping communities structures.
Relational database systems are the predominant repositories to store
mission-critical information collected from industrial sensor devices, business
transactions and sourcing activities, among others. However, conventional
knowledge discovery processes require data to be transported to external mining
tools, which is a very challenging exercise in practice. To get over this dilemma,
Preface xiii

equipping databases with predictive capabilities are a promising direction. Using

rough set theory is particularly interesting for this subject, because it has the ability
to discover hidden patterns while being founded on a well-defined set of operations.
Unfortunately, existing implementations consider data to be static, which is a
prohibitive assumption in situations where data evolve over time and concepts tend
to drift. Therefore, Chapter “In-Database Rule Learning Under Uncertainty: A
Variable Precision Rough Set Approach” proposed an in-database rule learner for
non-stationary environments. The assessment under different scenarios with other
state-of-the-art rule inducers demonstrates that the proposed technique is compa-
rable to existing methods, yet superior in critical applications that anticipate further
confidence from the decision-making process.
Chapter “Facial Similarity Analysis: A Three-Way Decision Perspective”
describes a three-way classification of human judgments of similarity. In other
words, a pair of photographs is classified as similar, dissimilar, or undecidable. The
agreement of a set of participants leads to both a set of similar pairs and a set of
dissimilar pairs; their disagreement leads to undecidable pairs. Probabilistic rough
sets are used as the vehicle to induce three-way decisions. The authors put forth a
simple model and then a more refined model. Findings from this study may benefit
practical applications. For example, the selected photograph pairs in the similar,
dissimilar, and undecidable regions may provide a firm foundation for the devel-
opment of an understanding of the processes or strategies different people use to
judge facial similarity. The authors anticipate that it might be possible to use the
correct identification of strategy so as to create presentations of photographs that
would allow eyewitness identification to have improved accuracy and utility.

Part III: Hybrid Approaches

Rough cognitive ensembles (RCEs) can be defined as a multiclassifier system

composed of a set of Rough Cognitive Networks (RCNs), each operating at a
different granularity level. While this model is capable of outperforming several
traditional classifiers reported in the literature, there is still room for enhancing its
performance. In Chapter “Fuzzy Activation of Rough Cognitive Ensembles Using
OWA Operators,” the authors introduced a fuzzy strategy to activate the RCN input
neurons before performing the inference process. This fuzzy activation mechanism
essentially quantifies the extent to which an object belongs to the intersection
between its similarity class and each granular region in the RCN topology. To do
that, it is necessary to conduct an information aggregation process. An aggregation
technique based on the ordered weighted averaging operators (OWA) is developed
in this chapter. The numerical simulations have shown that the improved ensemble
classifier significantly outperforms the original RCE model for the datasets under
consideration. After comparing the proposed model to 14 well-known classifiers,
the experimental evidence confirms that the proposed scheme yields very promising
classification rates.
xiv Preface

In Chapter “Prediction by k-NN and MLP a New Approach Based on Fuzzy

Similarity Quality Measure. A Case Study,” the performance of the k-nearest
neighbors (k-NN) and multilayer perceptron (MLP) algorithms is used in a classical
task in the realm of Civil Engineering: predicting the behavior of the anchorage
of the railway’s fixations before the stud corrosion. The use of fuzzy similarity
quality measure for calculating the weights of the features that combine the uni-
variate marginal distribution algorithm (UMDA) enables both k-NN and MLP to
operate in the case of mixed data (i.e., nominal and numerical attributes).
Experimental results verified that the UMDA + RST + FUZZY approach in this
chapter is better than other methods utilized to calculate the feature weights.
Chapter “Scheduling in Queueing Systems and Networks Using ANFIS” is
concerned with a scheduling problem that appears in many real-world systems
where the customers must be waiting for a service known as queuing system.
Classical queueing systems are handled using probabilistic theories, mostly based
on asymptotic theory and/or sample analysis. The authors addressed a situation
where neither enough statistical data exists nor asymptotic behavior can be applied
to. This way, they proposed an adaptive neuro-fuzzy inference system (ANFIS)
method to derive scheduling rules of a queuing problem based on uncertain data.
They employed the utilization ratio and the work in process (WIP) of a queue to
train an ANFIS network to finally obtain the estimated cycle time of all tasks.
Multiple tasks and rework are considered into the problem, so it cannot be easily
modeled using classical probability theory. The experiment results through simu-
lation analysis demonstrated an improvement of the proposed ANFIS implemen-
tation across several performance measures compared to traditional scheduling
policies.
Chapter “Genetic Fuzzy System for Automating Maritime Risk Assessment”
employs genetic fuzzy systems (GFSs) to assess the risk level of maritime vessels
transmitting automatic identification system (AIS) data. Previous risk assessment
approaches based on fuzzy inference systems (FIS) relied on domain experts to
specify the FIS membership functions as well as the fuzzy rule base (FRB), a
burdensome and time-consuming process. This chapter aims to alleviate this load
by learning the membership functions and FRB for the FIS of an existing risk
management framework (RMF) directly from data. The proposed methodology is
tested with four different case studies in maritime risk analysis. Each case study
concerns a unique scenario involving a particular region: the Gulf of Guinea, the
Strait of Malacca, the Northern Atlantic during a storm, and the Northern Atlantic
during a period of calm seas. The experiments compare 14 GFS algorithms from the
KEEL software package and evaluate the resulting FRBs according to their accu-
racy and interpretability. The results indicate that IVTURS, LogitBoost, and NSLV
generate the most accurate rule bases while SGERD, GCCL, NSLV, and GBML
each generate interpretable rule bases. Finally, IVTURS, NSLV, and GBML
algorithms offer a reasonable compromise between accuracy and interpretability.
Generalized fuzzy Petri nets (GFP-nets) were recently proposed. Chapter “Fuzzy
Petri Nets and Interval Analysis Working Together” describes an extended class of
GFP-nets called type-2 generalized fuzzy Petri nets (T2GFP-nets). The new model
Preface xv

extends the existing generalized fuzzy Petri nets by introducing a triple of operators
ðIn; Out1 ; Out2 Þ in a T2GFP-net in the form of interval triangular norms, which are
supposed to function as substitute for the triangular norms in GFP-nets. Trying to
make GFP-nets more realistic with regard to the perception of physical reality, the
chapter establishes a connection between GFP-net and interval analysis. The link is
methodological, demonstrating the possible use of the interval analysis methodol-
ogy (to deal with incomplete information) to transform GFP-nets into a more
realistic model. The proposed approach can be used both for knowledge repre-
sentation and reasoning in knowledge-based systems.

Santa Clara, Cuba Rafael Bello

Ottawa, Canada Rafael Falcon
Granada, Spain José Luis Verdegay
July 2018
Acknowledgements

We want to express our sincere gratitude and appreciation to all those who made
ISFUROS 2017 and this Springer volume possible. In particular, we acknowledge
the support and direction provided by the ISFUROS 2017 Steering Committee and
the technical reviews and scientific insights contributed by all technical program
committee members, who generously devoted their time and efforts to provide
constructive and sound referee reports to evaluate the quality of all received
submissions.
Our gratitude also goes to the UCLV Convention organizers and the Meliá
Marina Varadero staff, who helped run the conference quite smoothly despite the
short notice to move the Convention to Varadero from its original venue in Santa
Maria Key after the catastrophic impact of hurricane Irma on the northern central
region of Cuba in September 2017. Editors are also indebted to the help received
from the project TIN2017-86647-P (funded by the Fondo Europeo de Desarrollo
Regional, FEDER) and the Asociación Universitaria Iberoamericana de Postgrado
(AUIP) research network iMODA. Special thanks go to Prof. Janusz Kacprzyk,
Gowrishankar Ayyasamy, and Leontina Di Cecco for their priceless support with
the publication of this Springer volume.

xvii
Contents

Part I Fuzzy Sets: Theory and Applications

A Proposal of Hybrid Fuzzy Clustering Algorithm with Application
in Condition Monitoring of Industrial Processes . . . . . . . . . . . . . . . . . . 3
Adrián Rodríguez-Ramos, Antônio José da Silva Neto
and Orestes Llanes-Santiago
Solving a Fuzzy Tourist Trip Design Problem with Clustered Points
of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Airam Expósito, Simona Mancini, Julio Brito and José A. Moreno
Characterization of the Optimal Bucket Order Problem Instances
and Algorithms by Using Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Juan A. Aledo, José A. Gámez, Orenia Lapeira and Alejandro Rosete
Uncertain Production Planning Using Fuzzy Simulation . . . . . . . . . . . . 71
Juan Carlos Figueroa-García, Eduyn-Ramiro López-Santana
and Germán-Jairo Hernández-Pérez
Fully Fuzzy Linear Programming Model for the Berth Allocation
Problem with Two Quays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Flabio Gutierrez, Edwar Lujan, Rafael Asmat and Edmundo Vergara
Ideal Reference Method with Linguistic Labels: A Comparison
with LTOPSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Elio H. Cables, María Teresa Lamata and José Luis Verdegay
Comparative Analysis of Symbolic Reasoning Models for Fuzzy
Cognitive Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Mabel Frias, Yaima Filiberto, Gonzalo Nápoles, Rafael Falcon,
Rafael Bello and Koen Vanhoof
Fuzzy Cognitive Maps for Evaluating Software Usability . . . . . . . . . . . 141
Yamilis Fernández Pérez, Carlos Cruz Corona and Ailyn Febles Estrada

xix
xx Contents

Fuzzy Simulation of Human Behaviour in the Health-e-Living

System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Remberto Martinez, Marcos Tong, Luis Diago, Timo Nummenmaa
and Jyrki Nummenmaa

Part II Rough Sets: Theory and Applications

Matroids and Submodular Functions for Covering-Based
Rough Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Mauricio Restrepo and John Fabio Aguilar
Similar Prototype Methods for Class Imbalanced Data
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Yanela Rodríguez Alvarez, Yailé Caballero Mota,
Yaima Filiberto Cabrera, Isabel García Hilarión,
Yumilka Fernández Hernández and Mabel Frias Dominguez
Early Detection of Possible Undergraduate Drop Out Using
a New Method Based on Probabilistic Rough Set Theory . . . . . . . . . . . 211
Enislay Ramentol, Julio Madera and Abdel Rodríguez
Multiobjective Overlapping Community Detection Algorithms
Using Granular Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Darian H. Grass-Boada, Airel Pérez-Suárez, Rafael Bello
and Alejandro Rosete
In-Database Rule Learning Under Uncertainty:
A Variable Precision Rough Set Approach . . . . . . . . . . . . . . . . . . . . . . 257
Frank Beer and Ulrich Bühler
Facial Similarity Analysis: A Three-Way Decision Perspective . . . . . . . 289
Daryl H. Hepting, Hadeel Hatim Bin Amer and Yiyu Yao

Part III Hybrid Approaches

Fuzzy Activation of Rough Cognitive Ensembles Using OWA
Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Marilyn Bello, Gonzalo Nápoles, Ivett Fuentes, Isel Grau, Rafael Falcon,
Rafael Bello and Koen Vanhoof
Prediction by k-NN and MLP a New Approach Based on Fuzzy
Similarity Quality Measure. A Case Study . . . . . . . . . . . . . . . . . . . . . . . 337
Yaima Filiberto, Rafael Bello, Wilfredo Martinez, Dianne Arias,
Ileana Cadenas and Mabel Frias
Contents xxi

Scheduling in Queueing Systems and Networks Using ANFIS . . . . . . . . 349

Eduyn López-Santana, Germán Méndez-Giraldo
and Juan Carlos Figueroa-García
Genetic Fuzzy System for Automating Maritime Risk Assessment . . . . . 373
Alexander Teske, Rafael Falcon, Rami Abielmona and Emil Petriu
Fuzzy Petri Nets and Interval Analysis Working Together . . . . . . . . . . 395
Zbigniew Suraj and Aboul Ella Hassanien
Contributors

Rami Abielmona School of Electrical Engineering and Computer Science,

University of Ottawa, Ottawa, Canada;
Research & Engineering Division, Larus Technologies Corporation, Ottawa,
Canada
John Fabio Aguilar Universidad Militar Nueva Granada, Bogotá, Colombia
Juan A. Aledo Universidad de Castilla-La Mancha, Albacete, Spain
Yanela Rodríguez Alvarez Departamento de Computación, Universidad de
Camagüey, Camagüey, Cuba
Dianne Arias Department of Computer Science, University of Camagüey,
Camagüey, Cuba
Rafael Asmat Department of Mathematics, National University of Trujillo,
Trujillo, Peru
Frank Beer University of Applied Sciences Fulda, Fulda, Germany
Marilyn Bello Department of Computer Science, Universidad Central “Marta
Abreu”, de Las Villas, Santa Clara, Cuba;
Faculty of Business Economics, Hasselt University, Hasselt, Belgium
Rafael Bello Department of Computer Science, Universidad Central “Marta
Abreu”, de Las Villas, Santa Clara, Cuba
Hadeel Hatim Bin Amer Department of Computer Science, University of Regina,
Regina, SK, Canada
Julio Brito Departamento de Ingeniería Informática y de Sistemas, Instituto
Universitario de Desarrollo Regional, Universidad de La Laguna, San Cristóbal de
La Laguna, Canary Islands, Spain
Ulrich Bühler University of Applied Sciences Fulda, Fulda, Germany

xxiii
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