Reduction of categorical and numerical attribute values for understandability of data and rules

In this paper, we discuss attribute-value reduction for raising up the understandability of data and rules. In the traditional "reduction" sense, the goal is to find the smallest number of attributes such that they enable us to discern each tuple or each decision class. However, once we pay attention also to the number of attribute values, that is, the size/resolution of each attribute domain, another goal appears. An interesting question is like, which one is better in the following two situations 1) we can discern individual tuples with a single attribute described in fine granularity, and 2) we can do this with a few attributes described in rough granularity. Such a question is related to understandability and Kansei expression of data as well as rules. We propose a criterion and an algorithm to find near-optimal solutions for the criterion. In addition, we show some illustrative results for some databases in UCI repository of machine learning databases.