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Principal component analysis based on intuitionistic fuzzy random variables

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Statistics, Payame Noor University, Tehran, 19395-3697, Iran

    Gholamreza Hesamian

  2. Department of Statistics, University of Birjand, Birjand, 615-97175, Iran

    Mohammad Ghasem Akbari

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  1. Gholamreza Hesamian
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  2. Mohammad Ghasem Akbari
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Correspondence to Gholamreza Hesamian.

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Communicated by Vasily E. Tarasov.

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Hesamian, G., Akbari, M.G. Principal component analysis based on intuitionistic fuzzy random variables. Comp. Appl. Math. 38, 158 (2019). https://doi.org/10.1007/s40314-019-0939-9

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  • DOI: https://doi.org/10.1007/s40314-019-0939-9

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