Principal component analysis based on intuitionistic fuzzy random variables

  • Gholamreza HesamianEmail author
  • Mohammad Ghasem Akbari


This paper suggests a principal component analysis for intuitionistic fuzzy data. For this purpose, first a notion of intuitionistic fuzzy random variable was introduced and discussed. The concept of correlation and its natural estimator between two intuitionistic fuzzy random variables was also developed and the main properties of the proposed correlation criteria were investigated. Then, the conventional principal component analysis was extended for intuitionistic fuzzy random variables. In this regard, score and loading plots were extended to analyze the first and the second principle components. A possible application of the proposed method was also illustrated via an practical psychology-relevant example.


Intuitionistic fuzzy random variable Principal component Covariance Correlation Eigenvalue Loading plot Score plot 

Mathematics Subject Classification

62A86 62H25 



The authors would like to thank the editor and anonymous reviewers for their constructive suggestions and comments, which improved the presentation of this work.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of StatisticsPayame Noor UniversityTehranIran
  2. 2.Department of StatisticsUniversity of BirjandBirjandIran

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