Using fuzzy integral to modeling case based reasoning with feature interaction

The guiding principle of case-based reasoning (CBR) is the CBR-hypothesis which assumes that "similar problems have similar solutions". This principle requires a model to compute the problem-similarity in terms of individual features. One frequently used model is to consider the weighted average of feature-similarities as an overall similarity measure. Due to some inherent interaction among diverse features, the weighted average model does not work well in many real-world problems. This paper proposes using a non-linear integral tool to address such a problem. Five fuzzy integrals with respect to a fuzzy measure or a nonadditive set function are discussed in this paper. The interaction among the features is considered to be reflected in the non-additive set function, and the overall similarity is computed by using the integral model instead of using the weighted average model. Because the weighted average can be regarded as a special case of nonlinear integral, this paper to some extent generalizes the application scope of traditional CBR techniques based on similarity.