A hierarchical structure for representing and learning fuzzy rules

Abstract

Yager provides an example in which the flat representation of fuzzy if-then rules leads to unsatisfactory results. Consider a rule base consisting to two rules: if U is 12 the V is 29; if U is (10-15) the V is (25-30). If U = 12 we would get V is G where G = (25-30). The application of the defuzzification process leads to a selection of V = 27.5. Thus we see that the very specific instruction was not followed. The problem with the technique used is that the most specific information was swamped by the less specific information. In this paper we shall provide for a new structure for the representation of fuzzy if-then rules. The representational form introduced here is called a Hierarchical Prioritized Structure (HPS) representation. Most importantly in addition to overcoming the problem illustrated in the previous example this HPS representation has an inherent capability to emulate the learning of general rules and provides a reasonable accurate cognitive mapping of how human beings store information.