Theoretical study on a new information entropy and its use in attribute reduction

The positive region in rough set framework and Shannon conditional entropy are two traditional uncertainty measurements, used usually as heuristic metrics in attribute reduction. In this paper first a new information entropy is systematically compared with Shannon entropy, which shows its competence of another new uncertainty measurement. Then given a decision system we theoretically analyze the variance of these three metrics under two reverse circumstances. Those are when condition (decision) granularities merge while decision (condition) granularities remain unchanged. The conditions that keep these measurements unchanged in the above different situations are also figured out. These results help us to give a new information view of attribute reduction and propose more clear understanding of the quantitative relations between these different views, defined by the above three uncertainty measurements. It shows that the requirement of reducing a condition attribute in new information view is more rigorous than the ones in the latter two views and these three views are equivalent in a consistent decision system.