New Measures of Uncertainty for Interval-Valued Data With Application to Attribute Reduction

Abstract

Uncertainty measurement (UM) gives a brand-new perspective on attribute reduction in an information system (IS). Interval-valued data is a kind of very vital data in rough set theory (RST). Rough set model based on tolerance relations can be considered to deal with interval-valued data. However, these kinds of tolerance relations have deficiencies when they are used in fuzzy rough computation. This paper studies new UM for an interval-valued information system (IVIS) and considers its attribute reduction. Firstly, a novel fuzzy symmetry relation on the object set of an IVIS is established based on "The similarity between information values that is fed back to the attribute set". Secondly, λ-information granules on the basis of a fuzzy symmetry relation are obtained. Then, four UMs for an IVIS are investigated. Next, numerical experiments and statistical tests are used to evaluate the performance of the proposed UMs. Moreover, attribute reduction in an IVIS is studied and the relevant algorithms are proposed. Finally, clustering analysis on the reduced IVIS is conducted. Experimental results indicate that the proposed algorithms are effective based on evaluation indicators of clustering performance. This paper provides a novel viewpoint for the establishment of fuzzy symmetry relation and attribute reduction algorithms.