## On definability in the nondeterministic information system.(English)Zbl 0677.68110

Summary: We introduce several approximation operations \b{E}$${}_ i$$ in the space (U,E), where E is a cover of a set U. In particular when E is a partition of U, they are reduced to the operations \b{X} and $$\bar X$$ of Pawlak. We investigate the properties of the operations \b{E}$${}_ i$$, the relations among them and their connections with set-theoretical oprations $$\cup$$, -, $$\cap$$. We examine the notions of definability with respect to the introduced operations. We apply the results obtained to the nondeterministic information systems, but the scope of applications may be extended.

### MSC:

 68P20 Information storage and retrieval of data 93A99 General systems theory