Abstract: The covering decision information system is one of the research focuses. However, there is little research on the covering decision information system which the decision is a covering. In this paper, a characteristic function is used to transform the decision expressed by covering into a formal context composed of 0 and 1. Furthermore, the definition of a multi-decision covering information system is given. In the multi-decision covering information system, two kinds of covering reduction are discussed by constructing a corresponding discernibility matrix. And the relation between the covering consistent set corresponding to these two kinds of reductions and the upper approximation consistent set in the covering decision information system is studied.

Key words: multi-decision covering information system, discernibility matrix, covering reduction