Fuzzy Decision Diagrams for the Representation, Analysis and Optimization of Rule Bases

When no expert knowledge is available, fuzzy if-then rules may be extracted from examples of performance of a system. For this, an a priori decision on the number of linguistic terms of the linguistic variables may be required. This may induce a “rigid granularity“, usually finer than that actually required by the system. Fuzzy Decision Diagrams are introduced as an efficient data structure to represent fuzzy rule bases and to systematically check their completeness and consistency. Moreover if the hypothesis of rigid granularity holds, reordering of the variables of a Fuzzy Decision Diagram may lead to a compacter and more precise rule base. The concept of reconvergent subgraphs is introduced to support the search for effective reorderings.