BUSCADOR RECOLECTA

In this paper we introduce the concept of multiple bipolar fuzzy measures as a generalization of a bipolar fuzzy measure. We also propose a new definition of a group, which is based on the multidimensional bipolar fuzzy relations of its elements. Taking into account this information, we provide a novel procedure (based on the well-known Louvain algorithm) to deal with community detection problems. This new method considers the multidimensional bipolar information provided by multiple bipolar fuzzy measures, as well as the information provided by a graph. We also give some detailed computational tests, obtained from the application of this algorithm in several benchmark models.

In this paper, we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the risk of polarization. Particularly, we are interested in dealing with the problem of taking into account the polarization of nodes in the community detection problem. Adding this type of information to the community detection problem makes it more realistic, as a community is more likely to be defined if the corresponding elements are willing to maintain a peaceful dialogue. The polarization capacity is modeled by a fuzzy measure based on the JDJpol measure of polarization related to two poles. We also present an efficient algorithm for finding groups whose elements are no polarized. Hereafter, we work in a real case. It is a network obtained from Twitter, concerning the political position against the Spanish government taken by several influential users. We analyze how the partitions obtained change when some additional information related to how polarized that society is, is added to the problem.

Companies typically have to make relevant decisions regarding their clients’ fidelity and retention on the basis of analytical models developed to predict both their churn probability and Net Promoter Score (NPS). Although the predictive capability of these models is important, interpretability is a crucial factor to look for as well, because the decisions to be made from their results have to be properly justified. In this paper, a novel methodology to develop analytical models balancing predictive performance and interpretability is proposed, with the aim of enabling a better decision-making. It proceeds by fitting logistic regression models through a modified stepwise variable selection procedure, which automatically selects input variables while keeping their business logic, previously validated by an expert. In synergy with this procedure, a new method for transforming independent variables in order to better deal with ordinal targets and avoiding some logistic regression issues with outliers and missing data is also proposed. The combination of these two proposals with some competitive machine-learning methods earned the leading position in the NPS forecasting task of an international university talent challenge posed by a well-known global bank. The application of the proposed methodology and the results it obtained at this challenge are described as a case-study.

Traditionally, the last step of edge detection algorithms, which is called scaling-evaluation, produces the final output classifying each pixel as edge or nonedge. 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, we propose a global evaluation approach
based on the idea of edge list to produce a solution that suits more with the human perception. In particular, we propose a new evaluation method that can be combined with any classical edge detection algorithm in an easy way to produce a novel edge detection algorithm. The new global evaluation method is divided in four steps: in first place we build the edge lists, that we have called edge segments. In second place we extract the characteristics associated to each segment: length, intensity, location, and so on. In the third step we learn the characteristics that make a segment good enough to become an edge. At the fourth step, we apply the classification task. In this work we have built the ground truth of edge list necessary for the supervised classification. Finally, we test the effectiveness of this algorithm against other classical algorithms based on local evaluation approach.

In this work we introduce the notion of the weighted graph associated with a fuzzy measure. Having a finite set of elements between which there exists an affinity fuzzy relation, we propose the definition of a group based on that affinity fuzzy relation between the individuals. Then, we propose an algorithm based on the Louvain’s method to deal with community detection problems with additional information independent of the graph. We also provide a particular method to solve community detection problems over extended fuzzy graphs. Finally, we test the performance of our proposal by means of some detailed computational tests calculated in several benchmark models.

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., This work has been partially supported by the research projects S2013/ICE-2845, ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), TIN2015-66471-P (MINECO/ AEI-FEDER, UE), TIN2016-77356-P (MINECO/ AEI-FEDER, UE).

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 paired concepts what determines the emergence of different types of neutrality, namely indeterminacy, ambivalence and conflict, widely used under different frameworks (possibly under different names). It will be shown the potential relevance of paired structures, generated from two paired concepts together with their associated neutrality, all of them to be modeled as fuzzy sets. In this way, paired structures can be viewed as a standard basic model from which different models arise. This unifying view should therefore allow a deeper analysis of the relationships between several existing knowledge representation formalisms, providing a basis from which more expressive models can be later developed., This research has been partially supported by the Government of Spain (grants TIN2015-66471-P and TIN2013-40765-P), the Government of Madrid (grant S2013/ICCE-2845) and the UCM (Research Group 910149).

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 bivariate overlap functions. Finally, we apply general overlap functions to define a new matching degree in a classification problem. We deduce that the global behavior of these functions is slightly better than some other methods in the literature., The work has been supported by the Research Services of the Universidad Publica de Navarra, the
research projects TIN2016-77356-P (AEI/FEDER, UE) and TIN2015-66471-P from the Government of
Spain and by the Brazilian National Counsel of Technological and Scientific Development CNPq (Proc.
233950/2014-1, 306970/2013-9, 307781/2016-0) and by Caixa and Fundación Caja Navarra of Spain.

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., The work has been supported by projects TIN2013-40765-P and TIN2015-66471-P of the Spanish Ministry of Science, by grant VEGA 1/0420/15 and by grant VEGA 1/0419/13.

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.