Roughnon-deterministicinformation analysis is a framework for handling the rough sets based concepts, which are defined in not only DISs (DeterministicInformation Systems) but also NISs (Non-deterministicInformation Systems), on computers. NISs were proposed for dealing with information incompleteness in DISs. In this paper, two modalities, i.e., the certainty and the possibility, are defined for each concept like the definability of a set, the consistency of an object, data dependency, rule generation, reduction of attributes, criterion of rules support, accuracy and coverage. Then, each algorithm for computing two modalities is investigated. An important problem is how to compute two modalities depending upon all derived DISs. A simple method, such that two modalities are sequentially computed in all derived DISs, is not suitable. Because the number of all derived DISs increases in exponential order. This problem is uniformly solved by means of applying either inf and sup information or possibleequivalence relations. An information analysis tool for NISs is also presented.
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