Rule acquisition and optimal scale selection in multi-scale formal decision contexts and their applications to smart city

In order to enrich the existing rule acquisition theory in formal decision contexts, this study puts forward three new types of rules: decision association rules, non-redundant decision association rules and simplest decision association rules. Then, we analyze the relationship among these three types of rules, and develop methods to acquire them from single-scale formal decision contexts. Some numerical experiments are also conducted to compare the performance of the method of acquiring the simplest decision association rules with that of the existing one of acquiring the non-redundant decision rules. Moreover, the new three types of rules are employed to introduce three types of consistencies in multi-scale formal decision contexts. In addition, the notion of an optimal scale is defined by each type of consistency, and how to select an optimal scale is investigated as well. Finally, two applications in smart city for the proposed rule acquisition and optimal scale selection methods are applied to smart city.