Towards a Linguistic Description of Dependencies in Data

The problem of a linguistic description of dependencies in data by a set of rules Rk: “If X is Tk then Y is Sk” is considered, where Tk’s are linguistic terms like SMALL, BETWEEN 5 AND 7 describing some fuzzy intervals Ak. Sk’s are linguistic terms like DECREASING and QUICKLY INCREASING describing the slopes pk of linear functions yk = pkx + qk approximating data on Ak. The decision of this problem is obtained as a result of a fuzzy partition of the domain X on fuzzy intervals Ak, approximation of given data {xi, yi}, i = 1, . . . , n by linear functions yk = pkx + qk on these intervals and by re-translation of the obtained results into linguistic form. The properties of the genetic algorithm used for construction of the optimal partition and several methods of data re-translation are described. The methods are illustrated by examples, and potential applications of the proposed methods are discussed.