Principal Component Analysis for Fuzzy Interval-Valued Data

Abstract

In the field of fuzzy data analysis, a method of expressing the uncertainty of human thinking by using fuzzy interval data and applying principal component analysis has been proposed. In addition, from the standpoint of statistical learning theory, principal component analysis for interval-valued data has been proposed in the field of symbolic data analysis. Fuzzy interval data has been applied to these methods and their properties investigated. However, the data to be investigated is a data structure under specific restrictions, so various data structures have not been investigated. In addition, performance surveys using evaluation values concerning explainable power of the data have not been conducted. Therefore, in this paper, we purpose a method to investigate the applicability of fuzzy interval data to the interval-valued data principal component analysis proposed in the symbolic data analysis by using reproducibility, visualization, and evaluation values of the principal component analysis.