Optimal Cascade Linguistic Attribute Hierarchies for Information Propagation

A hierarchical approach, in which a highdimensional model is decomposed into series of low-dimensional sub-models connected in cascade, has been shown to be an effective way to overcome the ‘curse of dimensionality’ problem. The upwards propagation of information through a cascade hierarchy of Linguistic Decision Trees (LDTs) based on label semantics forms a process of cascade decision making. In order to examine 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 hierarchy presents cascade transparent linguistic rules, which will be useful for analyzing the effect of different attributes on the decision making as a reference in a special application.