Інтервальна нечітка кластеризація на основі альтернативних критеріїв якості

Abstract

The paper studies several clustering validity indices (Kwon index, Xie-Beni index, partition index) in view of the fuzzy parameter. We reveal the pattern of change in indices being researched against the fuzzy parameter change. We introduce an interval type-2 fuzzy clustering method based on combination of three validity indices. The membership values are presented as intervals. It allows preserving completeness of information on a set of their possible values, as well as reducing the influence of each specific index on uncertainty reflected in the result. The latter is achieved by detecting the intersection area of intervals of fuzzy parameter values based on every studied index. The solutions tol-erance of results’ abnormal observations is achieved by using the PCM robust clustering method. We analyze the widths of intervals of membership values obtained using the proposed approach in the case of noisy data or data containing abnormalities. Using the proposed approach the countries of the world are clustered relying on their human development characteristics.