On Model Evaluation, Indexes of Importance, and Interaction Values in Rough Set Analysis

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 propose an entropy-based measure which allows the use of qualitative power and interaction indices as an approximation. Co-operation for this paper was supported by EU COST Action 274 “Theory and Applications of Relational Structures as Knowledge Instruments” (TARSKI), www.tarski.org Equal authorship is implied “Mesmerized by a single-purpose, mechanised ‘objective’ ritual in which we convert numbers into other numbers and get a yes-no answer, we have come to neglect close scrutiny of where the numbers come from”. [3]