Crossing unordered sets of rules in evolutionary fuzzy controllers

In recent years the use of Genetic or Evolutionary techniques has produced interesting results on the automatic generation of Knowledge Bases for Fuzzy Logic Controllers. Three diierent representations of the rule base have been considered: list of rules, relational matrix and decision table. The use of lists of rules reduces the dimension of the rule base but presents some handicaps for crossover since usually requires some kind of ordering of the list before applying the operator. A new crossover operator, working with lists (sets) of rules, is designed in such a way that maintaining the advantage of working with a reduced set of rules, incorporates the characteristic of an easy crossover by using a virtual structure of decision table. Fuzzy Controllers 1] (FCs) can be considered as knowledge-based systems, incorporating human knowledge into their Knowledge Base through Fuzzy Rules and Fuzzy Membership Functions (among other information elements). The deen-ition of these Fuzzy Rules and Fuzzy Membership Functions is actually aaected by subjective decisions , having a great innuence over the performance of the FC. In recent years the use of Genetic or Evolutionary techniques has produced interesting results on the automatic generation of Knowledge Bases for Fuzzy Controllers. The term evolutionary computation usually refers to the design of adaptive systems using evolutionary principles. The algorithms applied in evolutionary computation are population-based search methods that employ some kind of selection process to bias the search toward good solutions. The idea of an evolutionary fuzzy controller is that of a fuzzy controller with learning, where the main role on learning is played by genetic algorithms or evolutionary computation. The keys of such a process are: to maintain a population of potential solutions for the problem to be solved, to design a set of evolution operators that search for new and/or better potential solutions and to deene an adequate performance index to drive the selection process. The basic evolution operators are three: selection , crossover and mutation. The evolution operators work with a code (called chromosome) representing the KB. The selection operator creates a mating pool where chromosomes copied from the population await the action of crossover and mutation. Those chromosomes with a higher tness value obtain a larger number of copies in the mating pool. The crossover operator provides a mechanism for KBs (represented by chromosomes) to mix attributes through a random process. This operator is applied to pairs of individuals from …