On Two Definitions of Reduct

This paper studies the relationship between the two most common definitions of reduct. Although there are other definitions, almost all the literature published in the framework of the Theory of Rough Sets, uses one of the two definitions we study here. However, there is an ambiguity in the use of these definitions and often authors do not previously declare what definition they refer to. Moreover, there are no publications where the relation between these two definitions is widely discussed, just that is what this paper addresses. We enunciate and demonstrate several properties expressing relations between both definitions including some illustrative examples.