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

Author

Listed:
  • Viliam Ďuriš

    (Department of Mathematics, Constantine the Philosopher University in Nitra, Tr. A. Hlinku 1, 94974 Nitra, Slovakia)

  • Renáta Bartková

    (Podravka International s.r.o., Janka Jesenského 1486, 96001 Zvolen, Slovakia)

  • Anna Tirpáková

    (Department of Mathematics, Constantine the Philosopher University in Nitra, Tr. A. Hlinku 1, 94974 Nitra, Slovakia
    Department of School Education, Faculty of Humanities, Tomas Bata University in Zlín, Štefánikova 5670, 76000 Zlín, Czech Republic)

Abstract

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.

Suggested Citation

  • Viliam Ďuriš & Renáta Bartková & Anna Tirpáková, 2021. "Principal Component Analysis and Factor Analysis for an Atanassov IF Data Set," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2067-:d:622954
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