On possible rules and apriori algorithm in non-deterministic information systems

A framework of rule generation in Non-deterministic Infor-mation Systems (NISs), which follows rough sets based rule generation in Deterministic Information Systems (DISs), is presented. We have already coped with certain rules and minimal certain rules, which are characterized by the concept of consistency, in NISs. We also introduced discernibility functions into NISs. In this paper, possible rules in NISs are focused on. Because of the information incompleteness, huge number of possible rules may exist, and we introduce Min-Max strategy and Max-Max strategy into possible rule generation in NISs. Possible rules based on these strategies are characterized by the criteria minimum support, maximum support, minimum accuracy and maximum accuracy, and Apriori based algorithm is applied.