In this paper, we will present a wider view on the relationship between interval-valued fuzzy sets and interval type-2 fuzzy sets, where we will show that interval-valued fuzzy sets are a particular ...case of the interval type-2 fuzzy sets. For this reason, both concepts should be treated in a different way. In addition, the view presented in this paper will allow a more general perspective of interval type-2 fuzzy sets, which will allow representing concepts that could not be presented by interval-valued fuzzy sets.
Classification problems involving multiple classes can be addressed in different ways. One of the most popular techniques consists in dividing the original data set into two-class subsets, learning a ...different binary model for each new subset. These techniques are known as binarization strategies.
In this work, we are interested in ensemble methods by binarization techniques; in particular, we focus on the well-known one-vs-one and one-vs-all decomposition strategies, paying special attention to the final step of the ensembles, the combination of the outputs of the binary classifiers. Our aim is to develop an empirical analysis of different aggregations to combine these outputs. To do so, we develop a double study: first, we use different base classifiers in order to observe the suitability and potential of each combination within each classifier. Then, we compare the performance of these ensemble techniques with the classifiers' themselves. Hence, we also analyse the improvement with respect to the classifiers that handle multiple classes inherently.
We carry out the experimental study with several well-known algorithms of the literature such as Support Vector Machines, Decision Trees, Instance Based Learning or Rule Based Systems. We will show, supported by several statistical analyses, the goodness of the binarization techniques with respect to the base classifiers and finally we will point out the most robust techniques within this framework.
► One-vs-one and one-vs-all are ensembles for multi-class problems. ► The confidence estimates and their aggregation are key factors of these ensembles. ► Aggregations based on voting and estimation of probabilities are the most robust. ► One-vs-one is more robust, one-vs-all has received less attention. ► Binarization is beneficial even when it is not necessary.
There are many real-world classification problems involving multiple classes, e.g., in bioinformatics, computer vision, or medicine. These problems are generally more difficult than their binary ...counterparts. In this scenario, decomposition strategies usually improve the performance of classifiers. Hence, in this paper, we aim to improve the behavior of fuzzy association rule-based classification model for high-dimensional problems (FARC-HD) fuzzy classifier in multiclass classification problems using decomposition strategies, and more specifically One-versus-One (OVO) and One-versus-All (OVA) strategies. However, when these strategies are applied on FARC-HD, a problem emerges due to the low-confidence values provided by the fuzzy reasoning method. This undesirable condition comes from the application of the product t-norm when computing the matching and association degrees, obtaining low values, which are also dependent on the number of antecedents of the fuzzy rules. As a result, robust aggregation strategies in OVO, such as the weighted voting obtain poor results with this fuzzy classifier. In order to solve these problems, we propose to adapt the inference system of FARC-HD replacing the product t-norm with overlap functions. To do so, we define n-dimensional overlap functions. The usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in OVO and OVA schemes. Furthermore, we propose a new aggregation strategy for OVO to deal with the problem of the weighted voting derived from the inappropriate confidences provided by FARC-HD for this aggregation method. The quality of our new approach is analyzed using 20 datasets and the conclusions are supported by a proper statistical analysis. In order to check the usefulness of our proposal, we carry out a comparison against some of the state-of-the-art fuzzy classifiers. Experimental results show the competitiveness of our method.
•A background and exhaustive survey on fingerprint matching methods in the literature is presented.•A taxonomy of fingerprint minutiae-based methods is proposed.•An extensive experimental study shows ...the performance of the state-of-the-art.
Fingerprint recognition has found a reliable application for verification or identification of people in biometrics. Globally, fingerprints can be viewed as valuable traits due to several perceptions observed by the experts; such as the distinctiveness and the permanence on humans and the performance in real applications. Among the main stages of fingerprint recognition, the automated matching phase has received much attention from the early years up to nowadays. This paper is devoted to review and categorize the vast number of fingerprint matching methods proposed in the specialized literature. In particular, we focus on local minutiae-based matching algorithms, which provide good performance with an excellent trade-off between efficacy and efficiency. We identify the main properties and differences of existing methods. Then, we include an experimental evaluation involving the most representative local minutiae-based matching models in both verification and evaluation tasks. The results obtained will be discussed in detail, supporting the description of future directions.
In this paper, we consider the concept of extended Choquet integral generalized by a copula, called
CC
-integral. In particular, we adopt a
CC
-integral that uses a copula defined by a parameter
α
, ...which behavior was tested in a previous work using different fixed values. In this contribution, we propose an extension of this method by learning the best value for the parameter
α
using a genetic algorithm. This new proposal is applied in the fuzzy reasoning method of fuzzy rule-based classification systems in such a way that, for each class, the most suitable value of the parameter
α
is obtained, which can lead to an improvement on the system’s performance. In the experimental study, we test the performance of 4 different so called
C
α
C
-integrals, comparing the results obtained when using fixed values for the parameter
α
against the results provided by our new evolutionary approach. From the obtained results, it is possible to conclude that the genetic learning of the parameter
α
is statistically superior than the fixed one for two copulas. Moreover, in general, the accuracy achieved in test is superior than that of the fixed approach in all functions. We also compare the quality of this approach with related approaches, showing that the methodology proposed in this work provides competitive results. Therefore, we demonstrate that
C
α
C
-integrals with
α
learned genetically can be considered as a good alternative to be used in fuzzy rule-based classification systems.
Overlap and grouping functions are important aggregation operators, especially in information fusion, classification and decision-making problems. However, when we do more in-depth application ...research (for example, non-commutative fuzzy reasoning, complex multi-attribute decision making and image processing), we find overlap functions as well as grouping functions are required to be commutative (or symmetric), which limit their wide applications. For the above reasons, this paper expands the original notions of overlap functions and grouping functions, and the new concepts of pseudo overlap functions and pseudo grouping functions are proposed on the basis of removing the commutativity of the original functions. Some examples and construction methods of pseudo overlap functions and pseudo grouping functions are presented, and the residuated implication (co-implication) operators derived from them are investigated. Not only that, some applications of pseudo overlap (grouping) functions in multi-attribute (group) decision-making, fuzzy mathematical morphology and image processing are discussed. Experimental results show that, in many application fields, pseudo overlap functions and pseudo grouping functions have greater flexibility and practicability.
Decision-makers’ subjective preferences can be well modeled using preference aggregation operators and related induced weights allocation mechanisms. However, when several different types of ...preferences occur in some decision environment with more complex uncertainties, repeated uses of preferences induced weights allocation sometimes become unsuitable or less reasonable. In this work, we discuss a common decision environment where several invited experts will offer their respective evaluation values for a certain object. There are three types of preferences which will significantly affect the weights allocations from experts. Instead of unsuitably performing preference induced weights allocation three times independently and then merging the results together using convex combination as some literatures recently did, in this work, we propose some organic and comprehensive rules-based screen method to first rule out some unqualified experts and then take preference induced weights allocation for the refined group of experts. A numerical example in business management and decision-making is presented to show the cognitive reasonability and practical feasibility.
In this paper, we present an approach to fully automate tumor delineation in positron emission tomography (PET) images. PET images play a major role in medicine for in vivo imaging in oncology (PET ...images are used to evaluate oncology patients, detecting emitted photons from a radiotracer localized in abnormal cells). PET image tumor delineation plays a vital role both in pre- and post-treatment stages. The low spatial resolution and high noise characteristics of PET images increase the challenge in PET image segmentation. Despite the difficulties and known limitations, several image segmentation approaches have been proposed. This paper introduces a new unsupervised approach to perform tumor delineation in PET images using Atanassov’s intuitionistic fuzzy sets (A-IFSs) and restricted dissimilarity functions. Moreover, the implementation of this methodology is presented and tested against other existing methodologies. The proposed algorithm increases the accuracy of tumor delineation in PET images, and the experimental results show that the proposed method outperformed all methods tested.
Aggregation operators are unvaluable tools when different pieces of information have to be taken into account with respect to the same object. They allow to obtain a unique outcome when different ...evaluations are available for the same element/object. In this contribution we assume that the opinions are not given in form of isolated values, but intervals. We depart from two “classical” aggregation functions and define a new operator for aggregating intervals based on the two original operators. We study under what circumstances this new function is well defined and we provide a general characterization for monotonicity. We also study the behaviour of this operator when the departing functions are the most common aggregation operators. We also provide an illustrative example demonstrating the practical application of the theoretical contribution to ensemble deep learning models.
•A new combination strategy for OVO is proposed by transforming the aggregation problem.•New instances are classified by the similarity of their outputs with respect to those of the training ...instances.•The possibility of carrying out pruning in OVO ensembles is introduced for the first time.•An exhaustive experimental study showing the existence of redundant (non-necessary) classifiers in OVO is developed.
The One-vs-One strategy is among the most used techniques to deal with multi-class problems in Machine Learning. This way, any binary classifier can be used to address the original problem, since one classifier is learned for each possible pair of classes. As in every ensemble method, classifier combination becomes a vital step in the classification process. Even though many combination models have been developed in the literature, none of them have dealt with the possibility of reducing the number of generated classifiers after the training phase, i.e., ensemble pruning, since every classifier is supposed to be necessary.
On this account, our objective in this paper is two-fold: (1) We propose a transformation of the aggregation step, which lead us to a new combination strategy where instances are classified on the basis of the similarities among score-matrices. (2) This fact allows us to introduce the possibility of reducing the number of binary classifiers without affecting the final accuracy. We will show that around 50% of classifiers can be removed (depending on the base learner and the specific problem) and that the confidence degrees obtained by these base classifiers have a strong influence on the improvement in the final accuracy.
A thorough experimental study is carried out in order to show the behavior of the proposed approach in comparison with the state-of-the-art combination models in the One-vs-One strategy. Different classifiers from various Machine Learning paradigms are considered as base classifiers and the results obtained are contrasted with the proper statistical analysis.
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