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Since Arrow's main theorem showed the impossibility of a rational procedure in group decision making, many variations in restrictions and objectives have been introduced in order to find out the limits of such a negative result. But so far all those results are often presented as a proof of the great expected difficulties we always shall find pursuing a joint group decision from different individual opinions, if we pursue rational and ethical procedures. In this paper we shall review some of the alternative approaches fuzzy sets theory allows, showing among other things that the main assumption of Arrow's model, not being made explicit in his famous theorem, was its underlying binary logic (a crisp definition is implied in preferences, consistency, liberty, equality, consensus and every concept or piece of information). Moreover, we shall also point out that focusing the problem on the choice issue can be also misleading, at least when dealing with human behaviour., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

Supervised classification in remote sensing is a very complex problem and involves steps of different nature, including a serious data preprocessing. The final objective can be stated in terms of a classification of isolated pixels between classes, which can be either previously known or not (for example, different land uses), but with no particular shape nither well defined borders. Hence, a fuzzy approach seems natural in order to capture the structure of the image. In this paper we stress that some useful tools for a fuzzy classification can be derived from fuzzy coloring procedures, to be extended in a second stage to the complete non visible spectrum. In fact, the image is considered here as a fuzzy graph defined on the set of pixels, taking advantage of fuzzy numbers in order to summarize information. A fuzzy model is then presented, to be considered as a decision making aid tool. In this way we generalize the classical definition of fuzzy partition due to Ruspini, allowing in addition a first evaluation of the quality of the classification in this way obtained, in terms of three basic indexes (measuring covering, relevance and overlapping of our family of classes)., Universidad Complutense, University of California, Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

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 alternative procedures more sensible to the available soft information. To this aim, we propose a general fuzzy bipolar approach that enables learning how to take advantage of the soft information provided by many classification algorithms in order to enhance the generalization power and accuracy of the classifiers. To show the suitability of the proposed approach, we also present some computational experiences for binary classification problems, in which its application to some well-known classifiers as random forest, classification trees and neural networks produces a statistically significant improvement in the performance of the classifiers., Ministerio de Economía y Competitividad (MINECO), Ministerio de Educación y Ciencia (MEC), Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

The generation of test data for state-based specifications is a computationally expensive process. This problem is magnified if we consider that time constraints have to be taken into account to govern the transitions of the studied system. The main goal of this paper is to introduce a complete methodology, supported by tools, that addresses this issue by representing the test data generation problem as an optimization problem. We use heuristics to generate test cases. In order to assess the suitability of our approach we consider two different case studies: a communication protocol and the scientific application BIPS3D. We give details concerning how the test case generation problem can be presented as a search problem and automated. Genetic algorithms (GAs) and random search are used to generate test data and evaluate the approach. GAs outperform random search and seem to scale well as the problem size increases. It is worth to mention that we use a very simple fitness function that can be easily adapted to be used with other evolutionary search techniques., Spanish MEC project TESIS, UK EPSRC project Testing of Probabilistic and Stochastic Systems, Sección Deptal. de Sistemas Informáticos y Computación, Fac. de Ciencias Matemáticas, TRUE, pub