Open Access
Handling multicriteria fuzzy decision-making problems based on intuitionistic fuzzy sets
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
In this paper we present a new technique for handling multicriteria decision making problems based on intuitionistic fuzzy sets. In this new technique we use the degree of reliability and of non-reliability of each criterion in relation to a set of alternatives. We also present a new score function in order to evaluate the degree of suitability of the choice of a certain alternative.
Open Access
Co-occurrence of deep convolutional features for image search
(Elsevier, 2020) Forcén Carvalho, Juan Ignacio; Pagola Barrio, Miguel; Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
Image search can be tackled using deep features from pre-trained Convolutional Neural Networks (CNN). The feature map from the last convolutional layer of a CNN encodes descriptive information from which a discriminative global descriptor can be obtained. We propose a new representation of co-occurrences from deep convolutional features to extract additional relevant information from this last convolutional layer. Combining this co-occurrence map with the feature map, we achieve an improved image representation. We present two different methods to get the co-occurrence representation, the first one based on direct aggregation of activations, and the second one, based on a trainable co-occurrence representation. The image descriptors derived from our methodology improve the performance in very well-known image retrieval datasets as we prove in the experiments.
Open Access
Generalizing max pooling via (a, b)-grouping functions for convolutional neural networks
(Elsevier, 2023) Rodríguez Martínez, Iosu; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Herrera, Francisco; Takáč, Zdenko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Due to their high adaptability to varied settings and effective optimization algorithm, Convolutional Neural Networks (CNNs) have set the state-of-the-art on image processing jobs for the previous decade. CNNs work in a sequential fashion, alternating between extracting significant features from an input image and aggregating these features locally through ‘‘pooling" functions, in order to produce a more compact representation. Functions like the arithmetic mean or, more typically, the maximum are commonly used to perform this downsampling operation. Despite the fact that many studies have been devoted to the development of alternative pooling algorithms, in practice, ‘‘max-pooling" still equals or exceeds most of these possibilities, and has become the standard for CNN construction. In this paper we focus on the properties that make the maximum such an efficient solution in the context of CNN feature downsampling and propose its replacement by grouping functions, a family of functions that share those desirable properties. In order to adapt these functions to the context of CNNs, we present (𝑎, 𝑏)- grouping functions, an extension of grouping functions to work with real valued data. We present different construction methods for (𝑎, 𝑏)-grouping functions, and demonstrate their empirical applicability for replacing max-pooling by using them to replace the pooling function of many well-known CNN architectures, finding promising results.
Open Access
Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders
(Elsevier, 2020) Bustince Sola, Humberto; Marco Detchart, Cedric; Fernández Fernández, Francisco Javier; Wagner, Christian; Garibaldi, Jonathan M.; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this work we study a new class of similarity measures between interval-valued fuzzy sets. The novelty of our approach lays, firstly, on the fact that we develop all the notions with respect to total orders of intervals; and secondly, on that we consider the width of intervals so that the uncertainty of the output is strongly related to the uncertainty of the input. For constructing the new interval-valued similarity, interval valued aggregation functions and interval-valued restricted equivalence functions which take into account the width of the intervals are needed, so we firstly study these functions, both in line with the two above stated features. Finally, we provide an illustrative example which makes use of an interval-valued similarity measure in stereo image matching and we show that the results obtained with the proposed interval-valued similarity measures improve numerically (according to the most widely used measures in the literature) the results obtained with interval valued similarity measures which do not consider the width of the intervals.
Open Access
From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
(IEEE, 2019) Couso, Inés; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
We examine a broad collection of axiomatic definitions from various and diverse contexts, within the domain of fuzzy sets. We evaluate their respective extensions to the case of interval-valued fuzzy sets and intuitionistic fuzzy sets, from a purely formal point of view. We conclude that a large number of such extensions follow similar formal procedures This fact allows us to formulate a general procedure which encompasses all the reviewed extensions as particular cases of it. The new general formulation allows us to identify three different procedures to derive the corresponding extension to the field of interval-valued fuzzy sets or to the field of intuitionistic fuzzy sets from a specific real-valued measure in the context of fuzzy sets. These three processes agglutinate a multitude of particular constructions found in the literature.
Open Access
Type-2 fuzzy entropy-sets
(IEEE, 2017) Miguel Turullols, Laura de; Santos, Helida; Sesma Sara, Mikel; Bedregal, Benjamin; Jurío Munárriz, Aránzazu; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
The final goal of this study is to adapt the concept of fuzzy entropy of De Luca and Termini to deal with Type-2 Fuzzy Sets. We denote this concept Type-2 Fuzzy Entropy-Set. However, the construction of the notion of entropy measure on an infinite set, such us [0, 1], is not effortless. For this reason, we first introduce the concept of quasi-entropy of a Fuzzy Set on the universe [0, 1]. Furthermore, whenever the membership function of the considered Fuzzy Set in the universe [0, 1] is continuous, we prove that the quasi-entropy of that set is a fuzzy entropy in the sense of De Luca y Termini. Finally, we present an illustrative example where we use Type-2 Fuzzy Entropy-Sets instead of fuzzy entropies in a classical fuzzy algorithm.
Open Access
Interval subsethood measures with respect to uncertainty for the interval-valued fuzzy setting
(Atlantis Press, 2020) Pekala, Barbara; Bentkowska, Urszula; Sesma Sara, Mikel; Fernández Fernández, Francisco Javier; Lafuente López, Julio; Altalhi, A. H.; Knap, Maksymilian; Bustince Sola, Humberto; Pintor Borobia, Jesús María; Estatistika, Informatika eta Matematika; Ingeniaritza; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Ingeniería
In this paper, the problem of measuring the degree of subsethood in the interval-valued fuzzy setting is addressed. Taking into account the widths of the intervals, two types of interval subsethood measures are proposed. Additionally, their relation and main properties are studied. These developments are made both with respect to the regular partial order of intervals and with respect to admissible orders. Finally, some construction methods of the introduced interval subsethood measures with the use interval-valued aggregation functions are examined.
Open Access
A decision tree based approach with sampling techniques to predict the survival status of poly-trauma patients
(Atlantis Press, 2017) Sanz Delgado, José Antonio; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Gradín Purroy, Carlos; Belzunegui Otano, Tomás; Automatika eta Konputazioa; Osasun Zientziak; Institute of Smart Cities - ISC; Automática y Computación; Ciencias de la Salud; Gobierno de Navarra / Nafarroako Gobernua, PI-019/11
Survival prediction of poly-trauma patients measure the quality of emergency services by comparing their predictions with the real outcomes. The aim of this paper is to tackle this problem applying C4.5 since it achieves accurate results and it provides interpretable models. Furthermore, we use sampling techniques because, among the 378 patients treated at the Hospital of Navarre, the number of survivals excels that of deaths. Logistic regressions are used in the comparison, since they are an standard in this domain.
Open Access
A fuzzy association rule-based classifier for imbalanced classification problems
(Elsevier, 2021) Sanz Delgado, José Antonio; Sesma Sara, Mikel; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Imbalanced classification problems are attracting the attention of the research community because they are prevalent in real-world problems and they impose extra difficulties for learning methods. Fuzzy rule-based classification systems have been applied to cope with these problems, mostly together with sampling techniques. In this paper, we define a new fuzzy association rule-based classifier, named FARCI, to tackle directly imbalanced classification problems. Our new proposal belongs to the algorithm modification category, since it is constructed on the basis of the state-of-the-art fuzzy classifier FARC–HD. Specifically, we modify its three learning stages, aiming at boosting the number of fuzzy rules of the minority class as well as simplifying them and, for the sake of handling unequal fuzzy rule lengths, we also change the matching degree computation, which is a key step of the inference process and it is also involved in the learning process. In the experimental study, we analyze the effectiveness of each one of the new components in terms of performance, F-score, and rule base size. Moreover, we also show the superiority of the new method when compared versus FARC–HD alongside sampling techniques, another algorithm modification approach, two cost-sensitive methods and an ensemble.
Open Access
A framework for generalized monotonicity of fusion functions
(Elsevier, 2023) Sesma Sara, Mikel; Šeliga, Adam; Boczek, Michał; Jin, LeSheng; Kaluszka, Marek; Kalina, Martin; Bustince Sola, Humberto; Mesiar, Radko; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
The relaxation of the property of monotonicity is a trend in the theory of aggregation and fusion functions and several generalized forms of monotonicity have been introduced, most of which are based on the notion of directional monotonicity. In this paper, we propose a general framework for generalized monotonicity that encompasses the different forms of monotonicity that we can find in the literature. Additionally, we introduce various new forms of monotonicity that are not based on directional monotonicity. Specifically, we introduce dilative monotonicity, which requires that the function increases when the inputs have increased by a common factor, and a general form of monotonicity that is dependent on a function T and a subset of the domain Z. This two new generalized monotonicities are the basis to propose a set of different forms of monotonicity. We study the particularities of each of the new proposals and their links to the previous relaxed forms of monotonicity. We conclude that the introduction of dilative monotonicity complements the conditions of weak monotonicity for fusion functions and that (T,Z)-monotonicity yields a condition that is slightly stronger than weak monotonicity. Finally, we present an application of the introduced notions of monotonicity in sentiment analysis.