Decision trees are one of the most popular data-mining techniques for knowledge discovery. Many approaches for induction of decision trees often deal with the continuous data and missing values in information systems. However, they do not perform well in real situations. This paper presents a new algorithm, decision tree construction based on the Cloud transform and Rough set theory under the characteristic relation (CR), for mining classification knowledge from a given data set. The continuous data is transformed into discrete qualitative concepts via the cloud transformation and then the attribute with the smallest weighted mean roughness under the characteristic relation is selected as the current splitting node. Experimental evaluation shows the decision trees constructed by the CR algorithm tend to have a simpler structure, much higher classification accuracy and more understandable rules than those by C5.0 in most cases.