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Brock TR # CS-02-02 Abstract

On model evaluation, indices of importance, and interaction values in rough set analysis.    [PDF]
Günther Gediga and Ivo Düntsch, May 2002.

As most data models, "Computing with words" uses a mix of methods to achieve its aims, including several measurement indices. In this paper we discuss some proposals for such indices in the context of rough set analysis and present some new ones. In the first part we investigate several classical approaches based on approximation quality and the drop of approximation quality when leaving out elements. We show that using the approximation quality index is sensible in terms of admissibility, and present additional indices for the usefulness and significance of an approximation. The analysis of a "drop" is reinterpreted in terms of model comparison, and a general framework for all these concepts is presented. In the second part of the paper we present an example how using similar nomenclature in the theory of Choquet-type aggregations of fuzzy measurements and rough set approximation quality, without regard to the fine structure of the underlying model assumptions, can suggest connections where there are none. On a more positive note, we show that so called qualitative power and interaction indices, which are structurally similar to quantitative Choquet-type aggregations can be used in the context of rough set analysis. Furthermore, we suggest a suitable entropy-based measure which enables the use of qualitative power and interaction indices as an approximation.