Principal component analysis based on intuitionistic fuzzy random variables
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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.
KeywordsIntuitionistic fuzzy random variable Principal component Covariance Correlation Eigenvalue Loading plot Score plot
Mathematics Subject Classification62A86 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.
- Abhishek K, Chatterjee S, Datta S, Mahapatra SS (2017) Integrating principal component analysis. Fuzzy linguistic reasoning and Taguchi philosophy for quality-productivity optimization. Mater Today Proc 4(2), Part A:1772–1777Google Scholar
- Guo J, Li W (2007) Principal component analysis based on error theory and its application. Appl Stat Manag 26(4):636–640Google Scholar
- Lauro NC, Verde R, Irpino A (2008) Principal component analysis of symbolic data described by intervals, chapter 15. In: Diday E, Noirhomme-Fraiture M (eds) Symbolic data analysis and the SODAS software. Wiley, New York, pp 279–311Google Scholar
- Narasimhulu GV, Jilani SAK (2012) Fuzzy principal component analysis based gait recognition. Int J Comput Sci Inf Technol 3(3):4015–4020Google Scholar
- Szmidt E, Kacprzyk J (2012) A new approach to principal component analysis for intuitionistic fuzzy data sets. In: Greco S, Bouchon-Meunier B, Coletti G, Fedrizzi M, Matarazzo B, Yager RR (eds) IPMU 2012, Part II. CCIS, vol 298. Springer, Heidelberg, pp 529–538Google Scholar
- Yabuuchi Y, Watada J, Nakamori Y (1997) Fuzzy principal component analysis for fuzzy data. In: The 6th IEEE international conference on fuzzy systems, Barcelona, pp 83–92Google Scholar
- Zair M, Rahmoune C, Benazzouz D (2018) Multi-fault diagnosis of rolling bearing using fuzzy entropy of empirical mode decomposition, principal component analysis, and SOM neural network. In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering ScienceGoogle Scholar