Principal Component Analysis and Factor Analysis for an Atanassov IF Data Set

The present contribution is devoted to the theory of fuzzy sets, especially Atanassov Intuitionistic Fuzzy sets (IF sets) and their use in practice. We define the correlation between IF sets and the correlation coefficient, and we bring a new perspective to solving the problem of data file reduction in case sets where the input data come from IF sets. We present specific applications of the two best-known methods, the Principal Component Analysis and Factor Analysis, used to solve the problem of reducing the size of a data file. We examine input data from IF sets from three perspectives: through membership function, non-membership function and hesitation margin. This examination better reflects the character of the input data and also better captures and preserves the information that the input data carries. In the article, we also present and solve a specific example from practice where we show the behavior of these methods on data from IF sets. The example is solved using R programming language, which is useful for statistical analysis of data and their graphical representation.

Automated summary

This article focuses on the theory of fuzzy sets, specifically Atanassov Intuitionistic Fuzzy sets (IF sets) and their practical applications. It defines the correlation between IF sets and introduces a new perspective for reducing data files when input data are from IF sets. The article also presents specific applications of Principal Component Analysis and Factor Analysis for reducing data file size, as well as a detailed examination of input data from IF sets from three different perspectives.