Optimal Cascade Linguistic Attribute Hierarchies for Information Propagation

A hierarchical approach, in which a high- dimensional model is decomposed into series of low-dimensional sub-models connected in cascade, has been shown to be an effec- tive way to overcome the 'curse of dimensionality' problem. The upwards propagation of information through a cascade hierar- chy of Linguistic Decision Trees (LDTs) based on label semantics forms a process of cascade decision making. In order to exam- ine how a cascade hierarchy of LDTs works compared with a single LDT for multiple attribute decision making, we developed genetic algorithm with linguistic ID3 in wrapper to find optimal cascade hierarchies. Experiments have been carried out on the two benchmark databases, Pima Diabetes and Wisconsin Breast Cancer databases from the UCI Machine Learning Repository. It is shown that an optimal cascade hierarchy of LDTs has better performance than a single LDT. The use of attribute hierarchies also greatly reduces the number of rules when the relationship between a goal variable and input attributes is highly uncertain and nonlinear. Moreover, the cascade linguistic attribute hierar- chy presents cascade transparent linguistic rules, which will be useful for analyzing the effect of different attributes on the de ci- sion making as a reference in a special application.