Fault diagnosis has become an important component in intelligent systems, such as intelligent control systems and intelligent elearning systems. Reiter's diagnosis theory, described by first-order sentences, has been attracting much attention in this field. However, descriptions and observations of most real-world situations are related to fuzziness because of the incompleteness and the uncertainty of knowledge, e.g., the fault diagnosis of student behaviors in the elearning processes. In this paper, an extension of Reiter's consistency-based diagnosis methodology, fuzzy diagnosis, has been proposed, which is able to deal with incomplete or fuzzy knowledge. A number of important properties of the fuzzy diagnoses schemes have also been established. The computing of fuzzy diagnoses is mapped to solving a system of inequalities. Some special cases, abstracted from real-world situations, have been discussed. In particular, the fuzzy diagnosis problem, in which fuzzy observations are represented by clause-style fuzzy theories, has been presented and its solving method has also been given. A student fault diagnostic problem abstracted from a simplified real-world elearning case is described to demonstrate the application of our diagnostic framework.