Elements of Fuzzy Logic in Solving Clustering Problems

Abstract

To structure data, developers of decision support systems are increasingly using “Data Mining” methods and models, including data clustering algorithms. In this paper, the author proposes a clustering algorithm based on the graph theory and fuzzy logic methodology. Unlike the well-known clustering algorithms, where the division of a set of input vectors into groups (clusters) subject to the object similarity principle is determined by measuring the distance to a certain center(s), the formation of clusters is proposed to be done following the principle of pairwise distance of objects from each other by a value not exceeding that set by the decision-maker. The clustering problem key parameters include the distance between the objects and the number of objects in one cluster. The clear and fuzzy approaches to data cluster formation are implemented. In case of the fuzzy approach, the measure of the sample objects’ similarity is determined by the decision-maker based on the fuzzy logic tools. Intended input parameters of this measure depend on the objective function of the problem. The construction of clusters of the required configuration in the fuzzy interpretation of the data clustering issue relies on the decision maker’s (DM) empirical choice of the α-slice in a fuzzy set of the distance between the objects.