This paper proposes an algorithm that uses inductive learning and rough set theory (ILRS) to analyze the clinical data available in a patient file (records). A typical patient file has unstructured (both descriptive and quantitative) information that is also uncertain and sometimes incomplete. Successful clinical treatments depend on correct medical diagnosis which determines the correct set of variables or features causing a certain pathology. Clinical applications are by no means the only applications that require decision-making with reasoning from a large and incomplete amount of information. We show that the proposed ILRS technique is able to reduce the available number of features into a smaller core set that precisely describes the information system. We can also quantitatively evaluate the level of dependence of the considered pathology, or decision feature, on a given set of condition features or attributes. Moreover, we show that the proposed algorithm is able to cope with uncertain and incomplete information. We consider a case study of an incomplete information system obtained during cannulation of radial and dorsalis pelis arteries. We show how ILRS succeeds to remove redundancy and determine the most significant condition attributes for a given set of decision attributes from contaminated data with uncertainty. A multi-class classification with preference relations is presented through a set of decision rules. Unlike statistical analysis of clinical data, the reliability of the proposed ILRS algorithm is independent of the data size.