In this paper we introduce the concept of valued tolerance as an extension of the usual concept of indiscernibility (which is a crisp equivalence relation) in rough sets theory. Some specific properties of the approach are discussed in the paper. Further on the problem of inducing rules from such a knowledge is addressed. In this case a "credibility degree" is associated to each rule. Properties of such a degree are analysed in the paper and its use in classification problems is discussed.