Javier Montero

Javier Montero
Complutense University of Madrid | UCM · Faculty of Mathematics

Ph.D. Mathematics

About

274
Publications
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5,196
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Publications

Publications (274)
Article
Full-text available
The majority of edge detection algorithms only deal with grayscale images, while their use with color images remains an open problem. This paper explores different approaches to aggregate color information of RGB and HSV images for edge extraction purposes through the usage of the Sobel operator and Canny algorithm. This paper makes use of Berkeley...
Chapter
Indexes are very used in social sciences. The construction of an index involves aggregating information about variables that sometimes cannot be ranked, being OWA operators the most appropriate alternative. The associated weights of OWA operators can be defined in different ways. In this paper we propose to use MOOWA aggregation operators (maximizi...
Chapter
This paper proposes a cluster validation procedure allowing to obtain the optimal number of clusters on a set of fuzzy partitions. Such a procedure is established considering fuzzy classification systems endowed with a dissimilarity function that, in turn, generates a dissimilarity matrix. Establishing a dissimilarity matrix for the case of a crisp...
Chapter
This paper presents an interesting particular instance of the Preference-Aversion (P-A) model, which combines the rich expressive capability allowed by the bipolar approach of that model with the simplicity resulting from imposing additive reciprocity constraints on the basic, positive/negative standard fuzzy preference structures from which the P-...
Chapter
Most edge detection algorithms only deal with grayscale images, while their use with color images remains an open problem. This paper explores different approaches to aggregating color information from RGB and HSV images for edge extraction purposes through the usage of the Canny algorithm. The Berkeley’s image data set is used to evaluate the perf...
Article
Full-text available
The idea of computable aggregation operators was introduced as a generalization of aggregation operators, allowing the replacement of the mathematical function usually considered for aggregation, by a program that performs the aggregation process. There are different reasons to justify this extension. One of them is the interest in exploring some c...
Article
Full-text available
In the last two decades, information entropy measures have been relevantly applied in fuzzy clustering problems in order to regularize solutions by avoiding the formation of partitions with excessively overlapping clusters. Following this idea, relative entropy or divergence measures have been similarly applied, particularly to enable that kind of...
Article
Fuzzy relations R:A2→[0,1] are widely used in decision-making in order to represent degrees of preference between alternatives in A. Examining fuzzy relations, this paper first reflects on an inherent incompatibility inside the domain of reciprocal fuzzy preference relations and preference structures. Aiming at clarifying the semantics of reciproca...
Chapter
In this paper, the notions of degree of global covering and degree of global redundancy on a fuzzy classification system are established and applied. Such notions are implemented in the evaluation of a fuzzy partition. In particular, the characterization of the financial solvency of an economic sector and the possible estimation of financial insolv...
Chapter
The measurement of polarization has been studied over the last thirty years. Despite the different applied approaches, since polarization concept is complex, we find a lack of consensus about how it should be measured. This paper proposes a new approach to the measurement of the polarization phenomenon based on fuzzy set. Fuzzy approach provides a...
Chapter
Traditionally, the term aggregation is associated with an aggregation function, implicitly assuming that any aggregation process can be represented by a function. However, the concept of computable aggregation considers that the core of the aggregation processes is the program that enables it. This new concept of aggregation introduces the scenario...
Article
This paper proposes a couple of criteria for evaluating the quality and relevance of a fuzzy partition. These criteria are established from a fuzzy classification system and its recursive De Morgan triplet. We propose a comparison process between the classes of a fuzzy partition, based on a translation invariant similarity relation. Therefore a cla...
Conference Paper
In this paper, different ways of aggregating color information in edge extraction task are explored. One of these approaches is based on a previous transformation of the RGB images into a new color space of 8 dimensions. This increases the number of dimensions, making differences between colors easier to detect, and in this way improving the perfor...
Article
Full-text available
Gröbner bases have been applied to a number of problems related to the verification of Knowledge-Based Systems (KBS) and other problems within graph theory. In particular, the authors have developed in previous papers algebraic approaches to decide whether a situation in a railway interlocking system is safe or not. These algebraic approaches stand...
Article
Inspired by the Zadeh approach to fuzzy connectives in fuzzy set theory and by some applications, we introduce and study set‐based extended functions, and in particular, set‐based extended aggregation functions. These functions reflect neither reordering nor repetition of input values, and, linking different arities, they introduce serious constrai...
Article
One of the most common techniques to find the adequate weights in ordered weighted averaging (OWA) operators is based on the orness concept, where the weights are determined by maximizing the entropy (variation) for a fixed orness value. But such an entropy represents a dispersion measure for nominal variables, while weights in an OWA operator are...
Chapter
In this paper, inspired by the Zadeh approach to the fuzzy connectives in fuzzy set theory and by some applications, we introduce and study set-based extended functions on different universes. After presenting some results for set-based extended functions on a general universe, we focus our investigation on set-based extended functions on some part...
Chapter
In this paper we propose an extension of the concept of pre-aggregation at two diferent levels. On the one hand, we extend the definition of pre-aggregation to a more general framework where the space [0, 1] is replaced by a totally ordered set with maximum and minimum value. On the other hand, since could be even discrete, we generalize the concep...
Chapter
In this paper we propose a comparison process that allows evaluating the relevance of a class in a fuzzy partition. This process starts by forming a commutative group structure based on a fuzzy classification system. On this structure, proximity relations are proposed to establish the comparison process. As our proposal is based on a fuzzy classifi...
Chapter
This paper examines the ambiguity of subjective judgments, which are represented by a system of pairwise preferences over a given set of alternatives. Such preferences are valued with respect to a set of reasons, in favor and against the alternatives, establishing a complete judgment, or viewpoint, on how to solve the decision problem. Hence, viewp...
Article
In this paper we extend the notion of stability of each aggregation function as presented in a previous paper of the authors, where an aggregation function was denominated Family of Aggregation Operators (FAO) in order to stress that aggregation operators within an aggregation function should be consistent. We will show that the previous definition...
Article
Full-text available
In this paper, a comparative assessment of the Image Divide and Link Algorithm (ID&L) in different color spaces is presented. This, in order to show the significance of choosing a specific color space when the algorithm computes the dissimilarity measure between adjacent pixels. Specifically, the algorithm procedure is based on treating a digital i...
Article
Full-text available
Traditionally, the last step of edge detection algorithms, which is called scaling-evaluation, produces the final output classifying each pixel as edge or non-edge. This last step is usually done based on local evaluation methods. The local evaluation makes this classification based on measures obtained for every pixel. By contrast, in this work, w...
Article
Full-text available
Most supervised classification algorithms produce a soft score (either a probability, a fuzzy degree, a possibility, a cost, etc.) assessing the strength of the association between items and classes. After that, each item is assigned to the class with the highest soft score. In this paper, we show that this last step can be improved through alterna...
Article
As a generalization of bivariate overlap functions, which measure the degree of overlapping (intersection for non-crisp sets) of n different classes, in this paper we introduce the concept of general overlap functions. We characterize the class of general overlap functions and include some construction methods by means of different aggregation and...
Chapter
This paper presents a study of the relevance property in a fuzzy partition from a fuzzy classification system. This study allows establishing a stopping criterion for the inclusion of a class in a fuzzy partition based on relevance. Such a criterion is constructed from a stable relationship on the commutative group formed by two new mappings (and t...
Conference Paper
This work extends the notion of consistency in terms of stability for Families of Aggregation Operators (FAO), as defined in previous works. The notion of stability proposed in this work, not only extends the previous one, but it can be applied to a wider set of FAOs, particularly, to those that we name here as Family of Improper Aggregation Operat...
Article
In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications.
Chapter
While classical image processing algorithms were designed for scalar-valued (binary or grayscale) images, new technologies have made it commonplace to work with vector-valued ones. These technologies can involve new types of sensors, as in remote sensing, but also mathematical models leading to an increased cardinality at each pixel. This work anal...
Article
In this paper, we introduce the concept of fuzzy interval-entropy. The main feature of this new entropy is that the provided value is a closed subinterval of [0, 1]. This fact has led us to define interval-valued fuzzy strong S-subsethood measures which we use to build fuzzy interval-entropies. As we require that the results of both measures are in...
Conference Paper
Edge detection problems try to identify those pixels that represent the boundaries of the objects in an image. The process for getting a solution is usually organized in several steps, producing at the end a set of pixels that could be edges (candidates to be edges). These pixels are then classified based on some local evaluation method, taking int...
Article
Full-text available
In this paper, we postulate computation as a key element in assuring the consistency of a family of aggregation functions so that such a family of operators can be considered an aggregation rule. In particular, we suggest that the concept of an aggregation rule should be defined from a computational point of view, focusing on the computational prop...
Chapter
In this paper we discuss about graph approach in image segmentation. In first place, some main image processing techniques are classified based upon the output these methods provide. Then, a fuzzy image segmentation definition is presented because in the literature review was found that it was not clearly defined. This definition of fuzzy image seg...
Article
This paper focuses on the representation of opposite concepts as paired fuzzy concepts, under a restricted setting for general paired structures. In particular, examining the notion of bipolarity and the semantics of bivariate scales, the proposed setting allows accomplishing a faithful knowledge representation by means of appropriate aggregation f...
Article
Preference semantics examine the meaning of the preference predicate, according to the way that alternatives can be understood and organized for decision making purposes. Through opposite-based semantics, preference structures can be characterized by their paired decomposition of preference into opposite poles, and their respective valuation of bin...
Article
The problem of missing data is common in real-world applications of supervised machine learning such as classification and regression. Such data often gives rise to the need for functions defined for varying dimension. Here we propose optimization methods for learning the weights of quasi-arithmetic means in the context of data with missing values....
Chapter
In this chapter, we show how the concepts of overlap function and overlap index can be used to define fuzzy measures which depend on the specific data of each considered problem.
Article
The aim of this paper is to apply and establish the advantages of using fuzzy classification systems in evaluating the quality of a fuzzy partition. The system is applied in a methodological proposal for the analysis of the business financial solvency in a specific sector. The sectorial analysis of the solvency is considered as an unsupervised fuzz...
Chapter
In this paper we show how uncertainty can be drastically reduced along our linguistic discourse. In particular, after discussing if the analysis of consistency in literature is a legitimate scientific question, from the linguistic analysis of the master piece of Miguel de Cervantes (1547–1616), “Don Quixote of La Mancha”, we will propose a procedur...
Chapter
Opposition-based models are a current hot-topic in knowledge representation. The point of this paper is to suggest that opposition can be in fact introduced at two different levels, those of the predicates of interest being represented (as short/tall) and of the logical references (true/false) used to evaluate the verification of the former. We stu...
Chapter
In this chapter we review several properties of Atanassov’s intuitionistic fuzzy relations, recalling the main concepts related to Atanassov’s intuitionistic fuzzy relations and the main properties that can be demanded to such conepts. We also consider the use of Atanassov’s operators over such relations.
Conference Paper
This paper proposes a method to evaluate hierarchical image segmentation procedures, in order to enable comparisons between different hierarchical algorithms and of these with other (non-hierarchical) segmentation techniques (as well as with edge detectors) to be made. The proposed method builds up on the edge-based segmentation evaluation approach...
Article
Full-text available
In this paper we discuss some main image processing techniques in order to propose a classification based upon the output these methods provide. Because despite a particular image analysis technique can be supervised or unsupervised, and can allow or not the existence of fuzzy information at some stage, each technique has been usually designed to f...
Article
One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n-dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the class...
Article
In this position paper we propose a consistent and unifying view to all those basic knowledge representation models that are based on the existence of two somehow opposite fuzzy concepts. A number of these basic models can be found in fuzzy logic and multi-valued logic literature. Here it is claimed that it is the semantic relationship between two...
Conference Paper
The aggregation operator have been considered from a computable point of view. The important condition that the computation is friendly when portions of data are inserted o deleted to the list of values to aggregate is considered.
Article
Making decisions by learning preferences requires to consider semantical aspects dealing with the meaning and use of the preference concept. Examining recent developments on bipolarity, where concepts are measured/verified regarding a pair of opposite poles, we focus on the dialectic process by which the meaning of concepts emerges. Our proposal is...
Article
Full-text available
In this paper we introduce the concept of Fuzzy Image Segmentation, providing an algorithm to build fuzzy boundaries based on the existing relations between the fuzzy boundary set problem and the (crisp) hierarchical image segmentation problem. In particular, since a crisp image segmentation can be characterized in terms of the set of edges that se...
Article
This paper introduces a hierarchical clustering algorithm in networks based upon a first divisive stage to break the graph and a second linking stage which is used to join nodes. As a particular case, this algorithm is applied to the specific problem of community detection in Social Networks, where a betweenness measure is considered for the divisi...
Article
In this work we introduce amethod for building interval-valued negations using the characterization theorem for strong negations which was proposed by Trillas in 1979. We also show that interval type-2 fuzzy sets are a three dimensional representation of interval-valued fuzzy sets and we analyze the problems to build complementation for such interv...
Article
This study introduces and develops a new approach to sequential aggregation of bags. It generalizes several related approaches known from the literature. The approach is based on a system of aggregation functions with property (SA) – a weakened form of symmetry. It generalizes symmetric associative aggregation. In the paper, several methods of cons...
Article
Full-text available
Providing emergency relief to the victims of natural disasters is a hugely complex process fraught with many challenging aspects: multiple uncertainties, little reliable information, scarcity of resources, a variety of involved entities, and so on. Nowadays there is a lot of information that could be used to improve decision-making in disaster mana...
Conference Paper
In this paper we develop a data-driven weight learning method for weighted quasi- arithmetic means where the observed data may vary in dimension.
Article
In 1979, Enric Trillas started to interest in in fuzzy connectives. His first paper on this topic was ”Funciones de negacin en la teora de subconjuntos difusos” ([9]) (Negation functions in the theory of fuzzy subsets), which appeared in Spanish in the Stochastica journal. This work, focused on the characterization of strong negations, has been so...
Article
In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.
Article
Many different kinds of sets have been defined within the framework of fuzzy sets . This paper focusses on those fuzzy set extensions that address the difficulties that experts find in order to build the membership values. In particular, we analyze type-2 fuzzy sets , interval-valued fuzzy sets , Atanassov’s intuitionistic fuzzy sets , or bipolar s...
Conference Paper
Full-text available
In this paper we present a new class of fuzzy sets, paired fuzzy sets, that tries to overcome any conflict between families of fuzzy sets that share a main characteristic: that they are generated from two basic opposite fuzzy sets. Hence, the first issue is to formalize the notion of opposition, that we will assume dependent on a specific negation,...
Conference Paper
The polarity of concepts and the dialectic process by which its meaning emerges has been subject of interest since the ancient Greeks. Recently, the term Bipolarity has been used in social and mathematical sciences, referring to the measurement of the meaning of concepts. It is claimed that the measuring process has to consider at least an associat...
Conference Paper
Full-text available
A crisp image segmentation can be characterized in terms of the set of edges that separates the adjacent regions of the segmentation. Based on these edges, an alternative way to define a fuzzy image segmentation is introduced in this paper. In this sense, the notion of fuzzy image segmentation is characterized by means of a fuzzy set over the set o...
Conference Paper
The evidence coming from cognitive psychology and linguistics shows that pairs of reference concepts (as e.g. good/bad, tall/short, nice/ugly, etc.) play a crucial role in the way we everyday use and understand natural languages in order to analyze reality and make decisions. Different situations and problems require different pairs of landmark con...
Article
In this paper, we want to stress that bipolar knowledge representation naturally allows a family of middle states which define as a consequence different kinds of bipolar structures. These bipolar structures are deeply related to the three types of bipolarity introduced by Dubois and Prade, but our approach offers a systematic explanation of how su...
Article
Fuzzy preference and aversion relations allow measuring in a gradual manner the attitude of the individual regarding some pair of alternatives. Following the Preference-Aversion (P-A) model, previously introduced for identifying the subjective cognitive state for some decision situation; here, we explore a methodology for learning relevance degrees...
Article
Full-text available
An aggregation operator [1, 5, 7, 8, 9, 12] is usually defined as a real function A n such that, from n data items x 1, …, x n in [0,1], produces an aggregated value A n (x 1,…,x n ) in [0,1] [4]. This definition can be extended to consider the whole family of operators for any n instead of a single operator for an specific n. This has led to the c...