Optimal Scale Selection in Multi-Scale Interval-Set Decision Tables

In traditional interval-set information systems (ISISs), each attribute is single-scale. However, processing and analyzing data at different scales is often necessary for practical applications. This paper introduces the granular information transformation into multi-scale interval-set information systems (MISISs), defines the similarity relation between objects in MISISs, and defines the rough approximation and correlation properties at different scales studied. Then, we propose the multi-scale interval-set decision table (MISDT) concept and discuss the monotonicity of scale variation of the positive region, generalized decision and positive complementarity conditional entropy. Then, we give three criteria for determining the optimal scales and discuss the relationship among the optimal scales of MISDTs. Finally, give heuristic algorithms and examples.