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from the training set. Before ACOs are run to nd rules describing the next class, the full training set is reinstated. A simpli ed version of the algorithm is to run just one ACO algorithm for each class, the assumption being that one rule is suf cient to describe a class. Further developments allow FRANTIC to induce rules sequentially. In the simpli ed form one ACO algorithm is also run for each class. However, instead of running the ACOs in succession, they are run in parallel (in principle; i.e., this is not as yet a true parallel implementation running on multiple processors), with each maintaining its own problem graph, pheromone levels, and heuristic values. After each class has had its rules created for a particular iteration, all possible combinations of rules (one from each class) are formed into a ruleset, and this is tested on the training set. The rules in the best-performing ruleset are used to update the pheromone levels, with the rule describing a speci c class being used to update the pheromone levels of the associated ACO. When creating a rule antecedent, an ant traverses a problem graph where each node represents a term that may be added. In the case of constructing rules with negated terms, the graph has double the number of nodes one extra for each original linguistic term. The choice of the next node to visit depends on both a heuristic value and the pheromone level associated with the node. It is made probabilistically but is biased toward terms that have relatively higher heuristic and pheromone values. However, after selection and before a term is added to a rule antecedent, a check is made; this ensures that the resultant rule antecedent covers a minimum number of the appropriate class instances from the training set, and is a way of avoiding over tting to the training data. Here a fuzzy rule describing a speci c class is said to cover or match a fuzzy instance if the rule and instance belong to the same class, and if the degree of match between the condition parts of rule and instance is equal to or greater than a pre-de ned threshold value. For simple propositional rules, or rules with negated terms, if an ant adds a term to its rule antecedent, then it will not consider other linguistic terms belonging to the same linguistic variable. If this restriction is removed, then it is possible for ants to add more than one linguistic term from each variable, with the interpretation being of a disjunctive operator between the terms added. The heuristic used to guide ants when selecting terms is based on fuzzy subsethood values (see Section 3.2.2.1), giving a degree to which one fuzzy set is a subset of another fuzzy set. At the start of an ACO run, all nodes in the graph have an equal amount of pheromone, which is set to the inverse of the number of nodes. The pheromone level of individual nodes, however, changes between iterations. Toward the end of each iteration, rules created by all ants are evaluated. This is done by assessing how accurate it is in classifying the training instances. However, in standard FRANTIC-IRL each rule is evaluated individually, without taking into account how it may interact with other rules describing other classes, while in FRANTIC-SRL [109] a rule forms part of a ruleset that is evaluated as a whole. For rule evaluation the tness function combines a measure of the sensitivity
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of a rule (its accuracy among instances of the same class as the rule) with a measure of the speci city of the rule (its accuracy among instances of different classes).
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