A distance measure for the mutation of fuzzy rules
A. Krone, T. Slawinski · OpenGrey (Institut de l'Information Scientifique et Technique) · 2000
A common approach in the field of EA design is to translate the real-world problem into a standard representation. A disadvantage of this mapping between the phenotype and genotype is that the effects of genetic operators on the phenotype space are difficult to determine and that problem knowledge is not considered. Another approach is to use the concept of the Metric Based Evolutionary Algorithm (MBEA) [1]. The domain knowledge is expressed by a metric on the phenotype space, such that similar individuals according to the metric have similar fitness values. The metric on the phenotype space is preserved by the coding function for the genotype space. The genetic operators (mutation, recombination) are designed in consideration of a set of formal requirements (bias free operation, locality, reachability, feature preservation). In the field of fuzzy modelling an appropriate metric for the distance between fuzzy rules is a difficult problem, especially if rules of different length are used. A first approach has been made by heuristic assumptions about the effect of modifications of a fuzzy rule [5, 6]. The disadvantage of this approach is that the spatial position of the rules is neglected and that the defined distance measure is not directly utilized for the mutation operator. In this paper, a distance measure is described that considers the spatial situation and can be much better exploited for the design of the mutation operator. It is developed for the evolutionary rule search in the Fuzzy-ROSA method [2-4]. In Section 2, the elements of the search space are defined and the problem of finding an appropriate distance measure is discussed. In Section 3, the distance measure is defined by a relation vector and a cumulating distance value. Figures illustrate the distance measure. How this distance measure can be used for the mutation operator is explained in Section 4. Section 5 gives a conclusion. (orig.)