A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis

© 2014 Elsevier B.V. Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.Lynn D’eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765 and P10-TIC-6858, and by project PYR-2014-8 of the Genil Program of CEI BioTic GRANADA and Lluis Godo has been partially supported by the Spanish MINECO project EdeTRI TIN2012-39348-C02-01Peer Reviewe

Selección de prototipos basada en conjuntos rugosos difusos

En este trabajo abordamos uno de los principales problemas de k vecinos más cercanos (kNN): su sensibilidad al ruido. Llevamos a cabo Selección de Prototipos (SP), es decir, eliminamos instancias ruidosas para mejorar la calidad de la clasificación de k vecinos más cercanos. Concretamente, basándonos en un método existente de selección de instancias basada en conjuntos rugosos difusos, construimos un algoritmo de tipo envoltura que tiene en cuenta la granularidad óptima de la relación difusa de indiscernibilidad en cada conjunto de datos. Llamamos a este método Selección de Prototipos a base de Conjuntos Aproximados Difusos (SPCAD). La comparación del enfoque con el estado del arte en Selección de Prototipos confirma que nuestro método ofrece buenos resultados: supera a todos los métodos de selección de prototipos existentes con respeto a la precisión de la clasificación

Quality, Frequency and Similarity Based Fuzzy Nearest Neighbor Classification

This paper proposes an approach based on fuzzy rough set theory to improve nearest neighbor based classification. Six measures are introduced to evaluate the quality of the nearest neighbors. This quality is combined with the frequency at which classes occur among the nearest neighbors and the similarity w.r.t. the nearest neighbor, to decide which class to pick among the neighbor's classes. The importance of each aspect is weighted using optimized weights. An experimental study shows that our method, Quality, Frequency and Similarity based Fuzzy Nearest Neighbor (QFSNN), outperforms state-of-the-art nearest neighbor classifiers

Fuzzy Rough Positive Region based Nearest Neighbour Classification

Abstract—This paper proposes a classifier that uses fuzzy rough set theory to improve the Fuzzy Nearest Neighbour (FNN) classifier. We show that previous attempts to use fuzzy rough set theory to improve the FNN algorithm have some shortcomings and we overcome them by using the fuzzy positive region to measure the quality of the nearest neighbours in the FNN classifier. A preliminary experimental evaluation shows that the new approach generally improves upon existing methods. I

Implicator-Conjunctor Based Models of Fuzzy Rough Sets: Definitions and Properties

Ever since the first hybrid fuzzy rough set model was pro- posed in the early 1990¿s, many researchers have focused on the definition of the lower and upper approximation of a fuzzy set by means of a fuzzy relation. In this paper, we review those proposals which generalize the logical connectives and quantifiers present in the rough set approxima- tions by means of corresponding fuzzy logic operations. We introduce a general model which encapsulates all of these proposals, evaluate it w.r.t. a number of desirable properties, and refine the existing axiomatic approach to characterize lower and upper approximation operators. © 2013 Springer-Verlag.This work was partially supported by the Spanish Ministry of Science and Technology under Project TIN2011-28488. Lluis Godo has been partially supported by the MINECO Project TIN2012-39348-C02-01.Peer Reviewe

Trust and Distrust Aggregation Enhanced with Path Length Incorporation

Trust networks are social networks in which users can assign trust scores to each other. In order to estimate these scores for agents that are indirectly connected through the network, a range of trust score aggregators has been proposed. Currently, none of them takes into account the length of the paths that connect users; however, this appears to be a critical factor since longer paths generally contain less reliable information. In this paper, we introduce and evaluate several path length incorporating aggregation strategies in order to strike the right balance between generating more predictions on the one hand and maintaining a high prediction accuracy on the other hand.European Union (EU) TIN2010-17876; TIC-5299; TIC-05991FW