The investigation of the Bayesian rough set model

AbstractThe original Rough Set model is concerned primarily with algebraic properties of approximately defined sets. The Variable Precision Rough Set (VPRS) model extends the basic rough set theory to incorporate probabilistic information. The article presents a non-parametric modification of the VPRS model called the Bayesian Rough Set (BRS) model, where the set approximations are defined by using the prior probability as a reference. Mathematical properties of BRS are investigated. It is shown that the quality of BRS models can be evaluated using probabilistic gain function, which is suitable for identification and elimination of redundant attributes

The investigation of the Bayesian rough set model

AbstractThe original Rough Set model is concerned primarily with algebraic properties of approximately defined sets. The Variable Precision Rough Set (VPRS) model extends the basic rough set theory to incorporate probabilistic information. The article presents a non-parametric modification of the VPRS model called the Bayesian Rough Set (BRS) model, where the set approximations are defined by using the prior probability as a reference. Mathematical properties of BRS are investigated. It is shown that the quality of BRS models can be evaluated using probabilistic gain function, which is suitable for identification and elimination of redundant attributes

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

Fuzzy-Rough Nearest Neighbour Classification and Prediction

AbstractNearest neighbour (NN) approaches are inspired by the way humans make decisions, comparing a test object to previously encountered samples. In this paper, we propose an NN algorithm that uses the lower and upper approximations from fuzzy-rough set theory in order to classify test objects, or predict their decision value. It is shown experimentally that our method outperforms other NN approaches (classical, fuzzy and fuzzy-rough ones) and that it is competitive with leading classification and prediction methods. Moreover, we show that the robustness of our methods against noise can be enhanced effectively by invoking the approximations of the Vaguely Quantified Rough Set (VQRS) model, which emulates the linguistic quantifiers “some” and “most” from natural language

Variable precision rough set theory decision support system: With an application to bank rating prediction

This dissertation considers, the Variable Precision Rough Sets (VPRS) model, and its development within a comprehensive software package (decision support system), incorporating methods of re sampling and classifier aggregation. The concept of /-reduct aggregation is introduced, as a novel approach to classifier aggregation within the VPRS framework. The software is applied to the credit rating prediction problem, in particularly, a full exposition of the prediction and classification of Fitch's Individual Bank Strength Ratings (FIBRs), to a number of banks from around the world is presented. The ethos of the developed software was to rely heavily on a simple 'point and click' interface, designed to make a VPRS analysis accessible to an analyst, who is not necessarily an expert in the field of VPRS or decision rule based systems. The development of the software has also benefited from consultations with managers from one of Europe's leading hedge funds, who gave valuable insight, advice and recommendations on what they considered as pertinent issues with regards to data mining, and what they would like to see from a modern data mining system. The elements within the developed software reflect each stage of the knowledge discovery process, namely, pre-processing, feature selection, data mining, interpretation and evaluation. The developed software encompasses three software packages, a pre-processing package incorporating some of the latest pre-processing and feature selection methods a VPRS data mining package, based on a novel "vein graph" interface, which presents the analyst with selectable /-reducts over the domain of / and a third more advanced VPRS data mining package, which essentially automates the vein graph interface for incorporation into a re-sampling environment, and also implements the introduced aggregated /-reduct, developed to optimise and stabilise the predictive accuracy of a set of decision rules induced from the aggregated /-reduct