YAILS uses a hill-climbing search strategy. This search is controlled by an evaluation function which gives each point in the search space a specific value. The evaluation function should in some way express our ideas of what is a good rule. YAILS uses two properties of a complex to characterize it. These two properties are then combined using some function that will be described bellow and from this combination it results what I call the quality (Q) of a rule.
The properties observed by YAILS to characterize a rule are its consistency and completeness. The consistency ratio tries to capture in some way the probable percentage of correct answers given by the rule based on the previous experience. Completeness tries to illustrate how general (relatively to to concept of the rule) is the assertion made by its conditions (i.e. a completeness ratio near 1 means that almost the examples of the same concept satisfied the rule). Bellow I present a more formal definition of these two properties (see appendix A for definitions of sub-concepts presented in the formulas):
Knowing the properties desirable for a rule the next step would be their combination into a single function which would enable to obtain a quantitative measure to evaluate each point in the search space. For the construction of such function I started with the assumption that consistency was more important than completeness. Of course you want general rules (high completeness) but first of all we don't want do mistakes in classification. With that goal in mind the chose combination function was the following :
The meaning of this function is that consistency has a flexible weight between the range 0.5..0.75, depending on the value of consistency in it self. Inversely completeness can have a weight between 0.25..0.5, again depending on the value of consistency. With such function rules with poor generality can have reasonable quality as long as they have excellent consistency (this is the case of rules that capture rare cases). It should be stated that this is a heuristic combination function and results only from feelings of the author on this matter thus having no theoretical support. Nevertheless the results obtained with this function seem to be quite satisfactory. Anyway one of the future tasks will be the comparison with other approaches such as the use of m-probabilities.