Stepwise optimal scale selection for multi-scale decision tables via attribute significance

Hierarchically structured data are very common or even unavoidable for data mining and knowledge discovering from the perspective of granular computing in real-life world. Based on this circumstance, multi-scale information system is introduced by Wu and Leung and extends the theory and application of information system. In such table, objects may take different values under the same attribute measured at different scales. Recently, scale selection is the main issue of multi-scale information system, and optimal scale selection is to choose a proper decision table for final decision making or classification. In this paper, we firstly propose the concept of multi-scale attribute significance, and, in the sense of binary classification, another two equivalent definitions are given. Then based on the concept of significance, this paper introduces a novel approach of stepwise optimal scale selection to obtain one optimal scale combination with less time cost compared with the lattice model. Specially, for inconsistent multi-scale decision tables, different types of consistence are considered with different requirements for optimal scale selection. Finally, five algorithms are designed and six numerical experiments are employed to illustrate the feasibility and efficiency of the proposed model. (C) 2017 Elsevier B.V. All rights reserved.