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Ordered weighted average based fuzzy rough sets

Traditionally, membership to the fuzzy-rough lower, resp. upper approximation is determined by looking only at the worst, resp. best performing object. Consequently, when applied to data analysis problems, these approximations are sensitive to noisy and/or outlying samples. In this paper, we advocate a mitigated approach, in which membership to the lower and upper approximation is determined by means of an aggregation process using ordered weighted average operators. In comparison to the previously introduced vaguely quantified rough set model, which is based on a similar rationale, our proposal has the advantage that the approximations are monotonous w.r.t. the used fuzzy indiscernibility relation. Initial experiments involving a feature selection application confirm the potential of the OWA-based model.

FRPS: A Fuzzy Rough Prototype Selection method

The k Nearest Neighbour (k NN) method is a widely used classification method that has proven to be very effective. The accuracy of k NN can be improved by means of Prototype Selection (PS), that is, we provide k NN with a reduced but reinforced dataset to pick its neighbours from. We use fuzzy rough set theory to express the quality of the instances, and use a wrapper approach to determine which instances to prune. We call this method Fuzzy Rough Prototype Selection (FRPS) and evaluate its effectiveness on a variety of datasets. A comparison of FRPS with state-of-the-art PS methods confirms that our method performs very well with respect to accuracy.

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.

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

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.

Enhancing the trust-based recommendation process with explicit distrust

When a Web application with a built-in recommender offers a social networking component which enables its users to form a trust network, it can generate more personalized recommendations by combining user ratings with information from the trust network. These are the so-called trust-enhanced recommendation systems. While research on the incorporation of trust for recommendations is thriving, the potential of explicitly stated distrust remains almost unexplored. In this article, we introduce a distrust-enhanced recommendation algorithm which has its roots in Golbecks trust-based weighted mean. Through experiments on a set of reviews from Epinions.com, we show that our new algorithm outperforms its standard trust-only counterpart with respect to accuracy, thereby demonstrating the positive effect that explicit distrust can have on trust-based recommendations.

IFROWANN: Imbalanced Fuzzy-Rough Ordered Weighted Average Nearest Neighbor Classification

Imbalanced classification deals with learning from data with a disproportional number of samples in its classes. Traditional classifiers exhibit poor behavior when facing this kind of data because they do not take into account the imbalanced class distribution. Four main kinds of solutions exist to solve this problem: modifying the data distribution, modifying the learning algorithm for considering the imbalance representation, including the use of costs for data samples, and ensemble methods. In this paper, we adopt the second type of solution and introduce a classification algorithm for imbalanced data that uses fuzzy rough set theory and ordered weighted average aggregation. The proposal considers different strategies to build a weight vector to take into account data imbalance. Our methods are validated by an extensive experimental study, showing statistically better results than 13 other state-of-the-art methods.

On the use of evolutionary feature selection for improving fuzzy rough set based prototype selection

The k-nearest neighbors classifier is a widely used classification method that has proven to be very effective in supervised learning tasks. In this paper, a fuzzy rough set method for prototype selection, focused on optimizing the behavior of this classifier, is presented. The hybridization with an evolutionary feature selection method is considered to further improve its performance, obtaining a competent data reduction algorithm for the 1-nearest neighbors classifier. This hybridization is performed in the training phase, by using the solution of each preprocessing technique as the starting condition of the other one, within a cycle. The results of the experimental study, which have been contrasted through nonparametric statistical tests, show that the new hybrid approach obtains very promising results with respect to classification accuracy and reduction of the size of the training set.

Preprocessing noisy imbalanced datasets using SMOTE enhanced with fuzzy rough prototype selection

The Synthetic Minority Over Sampling TEchnique (SMOTE) is a widely used technique to balance imbalanced data. In this paper we focus on improving SMOTE in the presence of class noise. Many improvements of SMOTE have been proposed, mostly cleaning or improving the data after applying SMOTE. Our approach differs from these approaches by the fact that it cleans the data before applying SMOTE, such that the quality of the generated instances is better. After applying SMOTE we also carry out data cleaning, such that instances (original or introduced by SMOTE) that badly fit in the new dataset are also removed. To this goal we propose two prototype selection techniques both based on fuzzy rough set theory. The first fuzzy rough prototype selection algorithm removes noisy instances from the imbalanced dataset, the second cleans the data generated by SMOTE. An experimental evaluation shows that our method improves existing preprocessing methods for imbalanced classification, especially in the presence of noise.

Multi-adjoint fuzzy rough sets: Definition, properties and attribute selection

This paper introduces a flexible extension of rough set theory: multi-adjoint fuzzy rough sets, in which a family of adjoint pairs are considered to compute the lower and upper approximations. This new setting increases the number of applications in which rough set theory can be used. An important feature of the presented framework is that the user may represent explicit preferences among the objects in a decision system, by associating a particular adjoint triple with any pair of objects. Moreover, we verify mathematical properties of the model, study its relationships to multi-adjoint property-oriented concept lattices and discuss attribute selection in this framework.

Fuzzy rough positive region based nearest neighbour classification

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.