Fuzzy Cluster Analysis: Pseudometrics and Fuzzy Clusters

Introduction. Clustering problems arise in various spheres of human activity. In cases where there are no initial data sufficient for statistical analysis or information obtained from experts is used, fuzzy models proposed that take into account different types uncertainty and more argumentatively reflect real situations model systems purposes. Particular attention drawn to invariance with measured scales according the classification S. Stevens. It known when solving cluster using transitive closure operation respect equivalence obtained, such connections between objects as similarity dissimilarity changed. Therefore, it necessary problem adequacy developing algorithms analysis. The purpose paper an analyzing results on introduction metrics pseudometrics sets presence several qualitative quantitative characteristics objects. Propose approach ensures pseudometrics, is, provides permissible transformations values features, also division classes without distorting distance them. Results. Axiomatic definitions a α level proposed, which introduced elements similar certain given set, if condition met: ratio must be invariant pseudometric. This ensured by use linguistic correlation coefficient calculating relations dissimilarity. Based definition threshold conorm, clusters determined. Conclusions. can basis development problems. meaningful interpretation clusters, possibility clarifying further studies their structure. Keywords: metric, pseudometric, relation, cluster.