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## Über dieses Buch

This book offers a timely snapshot of current soft-computing research and solutions to decision-making and optimization problems, which are ubiquitous in the current social and technological context, addressing fields including logistics, transportation and data analysis. Written by leading international experts from the United States, Brazil and Cuba, as well as the United Kingdom, France, Finland and Spain, it discusses theoretical developments in and practical applications of soft computing in fields where these methods are crucial to obtaining better models, including: intelligent transportation systems, maritime logistics, portfolio selection, decision- making, fuzzy cognitive maps, and fault detection. The book is dedicated to Professor José L. Verdegay, a pioneer who has been actively pursuing research in fuzzy sets theory and soft computing since 1982, in honor of his 65th birthday.

## Inhaltsverzeichnis

### A Review of Soft Computing Techniques in Maritime Logistics and Its Related Fields

The incessant increase in the world seaborne trade over the last few decades has encouraged maritime logistics has become a very attractive area of study for applying the general frameworks of soft computing. In this environment, there is a significant lack of efficient approaches aimed at obtaining exact solutions of a wide variety of optimization problems arisen in this field and which are classified as hard from the perspective of the complexity theory. These optimization problems demand increasingly new computational approaches able to report inexact solutions by exploiting extensively uncertainty, tolerance for imprecision, and partial truth to achieve tractability, among others. In the chapter at hand, we provide a review of the most highlighted soft computing techniques implemented in maritime logistics and its related fields and identify some opportunities to go further into depth on knowledge.
Christopher Expósito-Izquierdo, Belén Melián-Batista, J. Marcos Moreno-Vega

### Intelligent Data Analysis, Soft Computing and Imperfect Data

In different real problems the available information is not as precise or as accurate as we would like. Due to possible imperfection in the data (understanding that these contain data where not all the attributes are precisely known, such as missing, imprecise, uncertain, ambiguous, etc. values), tools provided by Soft Computing are quite adequate, and the hybridization of these tools with the Intelligent Data Analysis is a field that is gaining more importance. In this paper, first we present a brief overview of the different stages of Intelligent Data Analysis, focusing on two core stages: data preprocessing and data mining. Second, we perform an analysis of different hybridization approaches of the Intelligent Data Analysis with the Soft Computing for these two stages. The analysis is performed from two levels: If elements of Soft Computing are incorporated in the design of the method/model, or if they are also incorporated to be able to deal with imperfect information. Finally, in a third section, we present in more detail several methods which allow the use of imperfect data both for their learning phase and for the prediction.
Jose M. Cadenas, M. Carmen Garrido

### Soft Computing Methods in Transport and Logistics

The current economic context generates in supply chain management greater demands for flexibility and dynamism. In addition, there is an increase in uncertainty that adds more complexity to the problems associated with planning and management. Soft Computing offers a set of methodologies capable of responding to these challenges. This work provides an overview of transport and logistics problems, as well as the most representative combinatorial optimization models. Specifically, it focuses on the treatment of uncertainty through fuzzy optimization and metaheuristics methodologies. Promising results from the use of this approach suggest emerging areas of application, which are presented and described.
Julio Brito, Dagoberto Castellanos-Nieves, Airam Expósito, José. A. Moreno

### Applications of Soft Computing in Intelligent Transportation Systems

Intelligent Transportation Systems emerged to meet the increasing demand for more efficient, reliable and safer transportation systems. These systems combine electronic, communication and information technologies with traffic engineering to respond to the former challenges. The benefits of Intelligent Transportation Systems have been extensively proved in many different facets of transport and Soft Computing has played a major role in achieving these successful results. This book chapter aims at gathering and discussing some of the most relevant and recent advances of the application of Soft Computing in four important areas of Intelligent Transportation Systems as autonomous driving, traffic state prediction, vehicle route planning and vehicular ad hoc networks.
Antonio D. Masegosa, Enrique Onieva, Pedro Lopez-Garcia, Eneko Osaba

### Fuzzy Cognitive Maps Based Models for Pattern Classification: Advances and Challenges

Fuzzy Cognitive Maps (FCMs) have proven to be a suitable methodology for the design of knowledge-based systems. By combining both uncertainty depiction and cognitive mapping, this technique represents the knowledge of systems that are characterized by ambiguity and complexity. In short, FCMs can be defined as recurrent neural networks that include elements of fuzzy logic during the knowledge engineering phase. While the literature contains many studies claiming how this Soft Computing technique is able to model complex and dynamical systems, we explore another promising research field: the use of FCMs in solving pattern classification problems. This is motivated by the transparency of the decision model attached to these cognitive, neural networks. In this chapter, we revise some prominent advances in the area of FCM-based classifiers and open challenges to be confronted.
Gonzalo Nápoles, Maikel Leon Espinosa, Isel Grau, Koen Vanhoof, Rafael Bello

### A Proposal of On-Line Detection of New Faults and Automatic Learning in Fault Diagnosis

In this paper a new approach of automatic learning for a fault diagnosis system using fuzzy clustering techniques is presented. The proposal presents an off-line learning stage, for training the classifier to diagnose the initial known faults and the normal operation state. In this stage, the data are firstly pre-processed to eliminate outliers and reducing the confusion in the classification process by using the Density Objective Fuzzy C-Means (DOFCM) algorithm. Later on, the Kernel Fuzzy C-Means (KFCM) algorithm is used to achieve greater separability among the classes, and reducing the classification errors. Finally, a step is developed to optimize the two parameters used in the algorithms in the training stage using the Differential Evolution algorithm. After the training, the classifier is used on-line (recognition stage) in order to process every new sample taken from the process. In this stage, a novel fault detection algorithm is applied. The algorithm analyzes the observations which are not classified in the known classes and belonging to a window of time to determine if they constitute a new class, probably representative of a new fault or if they are noise. If a new class is identified, a procedure is developed to incorporate it to the known classes by the classifier. The approach proposed was validated using an illustrative example. The results obtained indicate the feasibility of the proposal.
Adrián Rodríguez Ramos, Alberto Prieto Moreno, Antônio José da Silva Neto, Orestes Llanes-Santiago

### Fuzzy Portfolio Selection Models for Dealing with Investor’s Preferences

This chapter provides an overview of the authors’ previous work about dealing with investor’s preferences in the portfolio selection problem. We propose a fuzzy model for dealing with the vagueness of investor preferences on the expected return and the assumed risk, and then we consider several modifications to include additional constraints and goals.
Clara Calvo, Carlos Ivorra, Vicente Liern

### On Fuzzy Convex Optimization to Portfolio Selection Problem

The goal of an investor is to maximize the required return in an investment by minimizing its risk. With this in mind, a set of securities are chosen according to the experience and knowledge of the investor, which subjective evaluations. Selecting these securities is defined as the portfolio selection problem and it can be classified as convex programming problems. These problems are of utmost importance in a variety of relevant practical fields. In addition, since ambiguity and vagueness are natural and ever-present in real-life situations requiring solutions, it makes perfect sense to attempt to address them using fuzzy convex programming technique. This work presents a fuzzy set based method that solves a class of convex programming problems with vagueness costs in the objective functions and/or order relation in the set of constraints. This method transforms a convex programming problem under fuzzy environment into a parametric convex multi-objective programming problem. The obtained efficient solutions to the transformed problem by satisfying an aspiration level defined by a decision maker. This proposed method is applied in a portfolio selection numerical example by using Bm&fBovespa data of some Brazilian securities.
Ricardo Coelho

### Digital Coaching for Real Options Support

Classical management science is making the transition to analytics, which has the same agenda to support managerial planning, problem solving and decision making in industrial and business contexts but is combining the classical models and algorithms with modern, advanced technology for handling data, information and knowledge. In work with managers in the forest industry, we found out that there is a growing interest to replace the classical net present value (NPV) with real options theory, especially for strategic issues and uncertain, dynamic environments. Uncertainty and dynamics motivate the use of soft computing, i.e. versions of the real options methods that use fuzzy numbers (intervals), macro heuristics, approximate reasoning and evolutionary algorithms. In general, managers can follow the logic of the real options theory but the methods require rather advanced levels of analytics; when the methods are implemented, they will be used by growing numbers of people with more of a business than analytics background. They find themselves in trouble pretty quickly as they need to master methods, they do not fully understand and details of which they forget from time to time. We propose that digital coaching is a way to guide and support users to give them better chances for effective and productive use of real options methods.
Christer Carlsson

### An Analysis of Decision Criteria for the Selection of Military Training Aircrafts

The Spanish Minister of Defense needs to replace the current military training aircrafts by other models to meet current training needs in the Spanish Air Force Academy. In order to know the main features that the candidate aircrafts should have, there is a need to take into account the knowledge and experience of experts in this specific field, such as trained test pilots and flight instructors. In this way, it will be possible to recognize the main technical criteria to consider. This study shows a case study that allowed obtaining not only the preferences of an expert’s group, but also the importance of the considered criteria. Given that the criteria information provided by the experts has different nature, with qualitative criteria (human factors, flying and handling qualities, etc.) coexisting with quantitative criteria (service ceiling, stalling speed, endurance, etc.), the joint use of linguistic labels and numerical values is needed. Therefore, a survey focused on the fuzzy AHP (Analytic Hierarchy Process) methodology is proposed to extract the knowledge from the experts group and finally obtain a unique set of weights for the criteria.
Juan M. Sánchez-Lozano, M. A. Socorro García-Cascales, María T. Lamata

### Participatory Search in Evolutionary Fuzzy Modeling

Search is one of the most useful procedures employed in numerous situations such as optimization, machine learning, information processing and retrieval. This chapter introduces participatory search, a class of population-based search algorithms constructed upon the participatory learning paradigm. Participatory search relies on search mechanisms that progress forming pools of compatible individuals. The individual that is the most compatible with the best individual is always kept in the current population. Random immigrants are added to complete the population at each algorithm step. Different types of recombination are possible. The first is a convex combination, arithmetic-like recombination modulated by the compatibility between individuals. The second is a recombination mechanism based on selective transfer. Mutation is an instance of differential variation modulated by compatibility between selected and recombined individuals. Applications concerning development of fuzzy rule-based models from actual data illustrate the potential of the algorithms. The performance of the models produced by participatory search algorithms are compared with a state of the art genetic fuzzy system. Experimental results show that the participatory search algorithm with arithmetic-like recombination performs better than the remaining ones.
Yi Ling Liu, Fernando Gomide

### But, What Is It Actually a Fuzzy Set?

Supported in a new view of meaning as a quantity in whatever universe of discourse, and for its possible use concerning plain language and ordinary reasoning in ‘Computing with Words’, the paper deals with the basic concept of a fuzzy set. That is, not only with the collective a linguistic label generates in language, but also with what membership functions reflect on it once ideally seen as measures of meaning.
Enric Trillas

### Gradual Numbers and Fuzzy Solutions to Fuzzy Optimization Problems

This short paper indicates that early examples of fuzzy elements in a fuzzy set, that is, entities that assign elements to membership values, in contrast with fuzzy sets that assign membership values to elements, can be found in papers by Verdegay in the early 1980, following a line of thought opened by Orlovsky. They are so-called fuzzy solutions to fuzzy optimization problems. The notion of fuzzy element, and more specifically gradual number sheds some light on the ambiguous notion of fuzzy number often viewed as generalizing a number while it generalizes intervals. The notion of fuzzy solution is in fact a parameterized solution, in the style of parametric programming. These considerations show the pioneering contributions of Verdegay to the development of fuzzy optimization.

### Using Fuzzy Measures to Construct Multi-criteria Decision Functions

We are interested in the formulation of multi-criteria decision functions based on the use of a measure over the space of criteria. Specifically the relationship between the criteria is expressed using a fuzzy measure. We then use the Choquet integral to construct decision functions based on the measure. We look at a number of different decision functions generated from specific classes of measures.
Ronald R. Yager

### A Modal Account of Preference in a Fuzzy Setting

In this paper we first consider the problem of extending fuzzy (weak and strict) preference relations, represented by fuzzy preorders on a set to a fuzzy preferences on subsets, and we characterise different possibilities. Based on their properties, we then semantically define and axiomatize several two-tiered graded modal logics to reason about the corresponding different notions of fuzzy preferences.
Francesc Esteva, Lluís Godo, Amanda Vidal

### On Possibilistic Dependencies: A Short Survey of Recent Developments

Carlsson and Fullér introduced the notions of possibilistic mean value and variance of fuzzy numbers. Fullér and Majlender introduced a measure of possibilistic covariance between marginal distributions of a joint possibility distribution as the average value of the interactivity relation between the level sets of its marginal distributions. Fullér et al. introduced the possibilistic correlation ratio, the possibilistic correlation coefficient and the possibilistic informational coefficient of correlation. In this paper we give a short survey of some later works which extend and develop these notions.
Robert Fullér, István Á. Harmati

### Penalty Function in Optimization Problems: A Review of Recent Developments

In this chapter we make a brief revision of some recent developments on the notion of penalty function as a tool for the fusion of information, including the most recently published definition as well as the extension of the concept to the lattice setting.
Humberto Bustince, Javier Fernandez, Pedro Burillo

### The Single Parameter Family of Gini Bonferroni Welfare Functions and the Binomial Decomposition, Transfer Sensitivity and Positional Transfer Sensitivity

We consider the binomial decomposition of generalized Gini welfare functions in terms of the binomial welfare functions $$C_j$$, $$j=1,\ldots ,n$$ and we examine the weighting structure of the latter, which progressively focus on the poorest part of the population. In relation with the generalized Gini welfare functions, we introduce measures of transfer sensitivity and positional transfer sensitivity and we illustrate the behaviour of the binomial welfare functions $$C_j$$, $$j=1,\ldots ,n$$ with respect to these measures. We investigate the binomial decomposition of the Gini Bonferroni welfare functions and we illustrate the dependence of the binomial decomposition coefficients in relation with the single parameter which describes the family. Moreover we examine the family of Gini Bonferroni welfare functions with respect to the transfer sensitivity and positional transfer sensitivity principles.
Silvia Bortot, Mario Fedrizzi, Ricardo Alberto Marques Pereira, Anastasia Stamatopoulou
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