Case-Based Reasoning: A Fuzzy Approach

This paper is an attempt at providing a fuzzy set-based formalization of case-based reasoning. The proposed approach assumes a principle stating that “the more similar are the problem description attributes, the more similar are the outcome attributes”. If this principle is accepted it induces constraints on the fuzzy similarity relations which are acceptable with respect to the cases stored in the memory. The idea of having cases in the memory with different levels of typicality is also discussed. A weaker form of this principle concluding only on the graded possibility of the similarity of the outcome attributes, is also considered. These two forms of the case-based reasoning principle are modelled in terms of fuzzy rules. Then an approximate reasoning machinery taking advantage of this principle enables us to apply the information stored in the memory of previous cases to the current problem. Extensions of the proposed approach in order to handle incomplete or fuzzy descriptions is also considered and studied. The paper does not take into account the learning aspects of casebased reasoning.