Some learning paradigms for granular computing

I. HIERARCHICAL ARCHITECTURE FOR FUZZY MODELING HE basic approach used in fuzzy logic for the modeling of complex relationships is called fuzzy systems modeling. This approach has been used in many of the successful applications of fuzzy logic [1]. It allows for rapid and inexpensive development of systems by greatly reducing the number of rules needed in the modeling process. It also contributes to reductions in the time consuming task of knowledge engineering by allowing the capturing of expert knowledge in a manner easy for the expert to articulate by providing a bridge between human linguistic expression and the types of formal models needed for computer processing and manipulation. We describe an extension of this basic fuzzy systems model which uses a hierarchical organization of the rules. This framework, called a Hierarchical Prioritized Structure (HPS) [2-9], allows for the modeling of more complex relationships and can be used in the construction of large scale fuzzy systems models. The HPS has a number of features that can further contribute to reduction in the costs associated with the task of knowledge engineering. One feature is its ability to allow the modeling of default rules. There are a number of benefits associated with models that allow for the inclusion of default rules. The use of default rules contribute to affordable systems development by further reducing the number of rules needed. They also give the synthetic entities a robustness to operate in situations in which they have not been explicitly programmed or trained. It allows for modularity by enabling the modeling of common sense. Another important feature of this HPS structure is that it provides a framework in which model adaption can naturally take place by allowing rules and knowledge to move between different levels of the hierarchy. This allows for the inclusion of new knowledge without the complete repudiation of old knowledge by just moving the old knowledge to a lower level. This allows for the modeling of more sophisticated and human-like learning mechanisms.