Dealing with Complexity in Large Scale and Structured Fuzzy Systems

Fuzzy inference engines must always deal with the complexity involved in an exponentially increasing number of rules. Sometimes in complex problems, it is difficult to have expert knowledge at one’s disposal to design the whole rule set. Nevertheless, experts can guide the rule design by defining the variables involved and giving guidelines about their behavior. A dependence relationship (DR) is a set of rules defined by a group of related inputs and outputs. In order to make the design and evaluation of DRs automatic, two properties called type and intensity are introduced. The DR type identifies the output membership functions shifting the neutral selection to the right or to the left. The DR intensity qualifies the final output membership function selection admitting the existence of nuances in rule fulfillment. Applying these properties, DR rules can be automatically designed and appropriately interpreted by the fuzzy inference engine in complex systems.