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

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