A noise-tolerant approach to fuzzy-rough feature selection

In rough set based feature selection, the goal is to omit attributes (features) from decision systems such that objects in different decision classes can still be discerned. A popular way to evaluate attribute subsets with respect to this criterion is based on the notion of dependency degree. In the standard approach, attributes are expected to be qualitative; in the presence of quantitative attributes, the methodology can be generalized using fuzzy rough sets, to handle gradual (in) discernibility between attribute values more naturally. However, both the extended approach, as well as its crisp counterpart, exhibit a strong sensitivity to noise: a change in a single object may significantly influence the outcome of the reduction procedure. Therefore, in this paper, we consider a more flexible methodology based on the recently introduced vaguely quantified rough set (VQRS) model. The method can handle both crisp (discrete-valued) and fuzzy (real-valued) data, and encapsulates the existing noise-tolerant data reduction approach using variable precision rough sets (VPRS), as well as the traditional rough set model, as special cases.

I. Introduction

Fuzzy sets [1] and rough sets [2] address two important characteristics of imperfect data and knowledge: the former model vague information by expressing that objects belong to a set or relation to a given degree, while the latter provide approximations of concepts in the presence of incomplete information. To merge these notions into a joint theory that combines their mutual strengths has been the object of a hybridisation movement that emerged in the early 1990's with the seminal research of Dubois and Prade [3] and has flourished ever since [4]. Recently, cross-disciplinary research has also been boosted by the adoption of computing paradigms like granular computing (see e.g. [5]), with its focus on clustering information entities into granules in terms of similarity or indiscernibility, and soft computing [6], which has stressed the role of fuzzy sets and rough sets as partners, rather than as adversaries, within a panoply of practical applications.