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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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References

  • 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:1772–1777

  • Akbari MG, Hesamian G (2018a) Record value based on intuitionistic fuzzy random variables. Int J Syst Sci 48(15):3305–3315

    Article  MathSciNet  Google Scholar 

  • Akbari MG, Hesamian G (2018b) Linear model with exact inputs and interval-valued fuzzy outputs. IEEE Trans Fuzzy Syst 26:518–530

    Article  Google Scholar 

  • Ammiche M, Kouadri A, Bensmail A (2018) A modified moving window dynamic PCA with fuzzy logic filter and application to fault detection. Chemom Intell Lab Syst 177:100–113

    Article  Google Scholar 

  • Anderberg MR (1973) Cluster analysis for applications. Academic Press, New York

    MATH  Google Scholar 

  • Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  Google Scholar 

  • Chen SM, Tan JM (1994) Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 67:163–172

    Article  MathSciNet  Google Scholar 

  • Chen FC, Tzeng YF, Hsu MH, Chen WR (2011) Combining Taguchi method, principal component analysis and fuzzy logic to the tolerance design of a dual-purpose six-bar mechanism. Trans Can Soc Mech Eng 34(2):277–293

    Article  Google Scholar 

  • Darvishi S, Fatemi A, Faroughi P (2015) Introduce a novel PCA method for intuitionistic fuzzy sets based on cross entropy. Appl Math 6:990–995

    Article  Google Scholar 

  • De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst 117:209–213

    Article  Google Scholar 

  • Denoeux T, Masson M (2004) Principal component analysis of fuzzy data using autoassociative neural networks. IEEE Trans Fuzzy Syst 12:336–349

    Article  Google Scholar 

  • Douzal-Chouakria A, Billard L, Diday E (2011) Principal component analysis for interval-valued observations. Stat Anal Data Min 4:229–246

    Article  MathSciNet  Google Scholar 

  • D’Urso P, Giordania P (2004) A least squares approach to principal component analysis for interval valued data. Chemom Intell Lab Syst 70(2):179–192

    Article  Google Scholar 

  • Dzulkalnine MF, Sallehuddin R, Yusoff Y, Radzi NHM, Mustaffa NH (2018) Fuzzy PCA and support vector machines for breast cancer classification. Int J Eng Technol 7:62–64

    Article  Google Scholar 

  • Gioia F, Lauro CN (2006) Principal component analysis on interval data. Comput Stat 21:343–363

    Article  MathSciNet  Google Scholar 

  • Giordania P, Kiersb AL (2006) A comparison of three methods for principal component analysis of fuzzy interval data. Comput Stat Data Anal 51(1):379–397

    Article  MathSciNet  Google Scholar 

  • Guo J, Li W (2007) Principal component analysis based on error theory and its application. Appl Stat Manag 26(4):636–640

    Google Scholar 

  • Hesamian G, Shams M (2016) Parametric testing statistical hypotheses for fuzzy random variables. Soft Comput 20:1537–1548

    Article  Google Scholar 

  • Kwakernaak H (1978) Fuzzy random variables, part I: definitions and theorems. Inf Sci 19:1–15

    Article  Google 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 279–311

    Google Scholar 

  • Lee KH (2005) First course on fuzzy theory and applications. Springer, Berlin

    MATH  Google Scholar 

  • Li C, Jin J (2018) A scalar expected value of intuitionistic fuzzy random individuals and its application to risk evaluation in insurance companies. Math Probl Eng 2018:1–18

    MathSciNet  Google Scholar 

  • Liu B, Shen Y, Chen WZX, Wang X (2015) An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making. Eur J Oper Res 245(1):209–225

    Article  MathSciNet  Google Scholar 

  • Luukka P (2009) PCA for fuzzy data and similarity classifier in building recognition system for post-operative patient data. Expert Syst Appl 36(2):1222–1228

    Article  Google Scholar 

  • Mishra R, Mishra ON (2018) A hybrid PCA-AHP-multi-grade fuzzy approach to assess marketing-based flexibility. Mark Intell Plan 36:213–229

    Article  Google Scholar 

  • Narasimhulu GV, Jilani SAK (2012) Fuzzy principal component analysis based gait recognition. Int J Comput Sci Inf Technol 3(3):4015–4020

    Google Scholar 

  • Parsaie A, Emamgholizadeh S, Azamathulla HM, Haghiabi AH (2018) ANFIS-based PCA to predict the longitudinal dispersion coefficient in rivers. Int J Hydrol Sci Technol 8:410–424

    Article  Google Scholar 

  • Parvathi R, Radhika C (2015) Intuitionistic fuzzy random variable. Notes Intuit Fuzzy Sets 21(1):69–80

    MATH  Google Scholar 

  • Pei Z (2015) Intuitionistic fuzzy variables: concepts and applications in decision making. Expert Syst Appl 42(22):9033–9045

    Article  Google Scholar 

  • Polat K, Gnes S (2008) Principles component analysis fuzzy weighting preprocessing and artificial immune recognition system based diagnostic system for diagnosis of lung cancer. Expert Syst Appl 34(1):214–221

    Article  Google Scholar 

  • Pu Y, Apel D, Xu H (2018) A principal component analysis/fuzzy comprehensive evaluation for rockburst potential in kimberlite. Pure Appl Geophys 175:2141–2151

    Article  Google Scholar 

  • Sârbu C, Pop HF (2016) Principal component analysis versus fuzzy principal component analysis, a case study: the quality of Danube water (1985–1996). J Talanta 65:1215–1220

    Article  Google Scholar 

  • Sugeno M (1985) An introductory survey of fuzzy control. Inf Sci 36:59–83

    Article  MathSciNet  Google Scholar 

  • Szmidt E, Kacprzyk J (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31:1037–1053

    MATH  Google 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 529–538

    Google Scholar 

  • Tao AX, Chang BR, Li CC, Wang DR, Liu ER (2017) Density-sensitive robust fuzzy kernel principal component analysis technique. Neurocomputing 329:210–226

    Article  Google 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 83–92

  • Velasquez RMA, Lara JVM (2017) Principal components analysis and adaptive decision system based on fuzzy logic for power transformer. Fuzzy Inf Eng 9:493–514

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–356

    Article  Google 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 Science

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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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