On Computing Extensions and Restrictions of Information Systems Noting Some Order Properties
Fundamenta Informaticae - Concurrency Specification and Programming (CS&P)
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In the paper, we consider the extensions of information systems from the rough set perspective. A consistent extension of a given information system includes only objects corresponding to the known attribute values which satisfy all minimal rules extracted from the original information system. A partially consistent extension of a given information system includes objects corresponding to the known attribute values which are consistent, to a certain degree with the knowledge represented by all minimal rules extracted from the original information system. Using adequately defined lower approximations of sets of objects in the original information system we can test membership of a new object added to the system to its consistent extension without computing any rules. If a given object does not belong to a consistent extension, then we can calculate a degree of the partial membership of the object to the consistent extension. This degree is expressed by the so-called consistency factor. Consistent and partially consistent extensions of information systems are useful in discovering or predicting new states of concurrent systems described by information systems.