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Soft Computing

, Volume 18, Issue 11, pp 2149–2160 | Cite as

A complex multi-attribute large-group decision making method based on the interval-valued intuitionistic fuzzy principal component analysis model

  • Bingsheng Liu
  • Yuan ChenEmail author
  • Yinghua Shen
  • Hui Sun
  • Xuanhua Xu
Methodologies and Application

Abstract

In the complex multi-attribute large-group decision making (CMALGDM) problems where attribute values are interval-valued intuitionistic fuzzy numbers (IVIFNs), the number of decision attributes is often large and their correlation degrees are high, which increase the difficulty of decision making and thus influence the accuracy of the result. To solve this problem, this paper proposes the interval-valued intuitionistic fuzzy principal component analysis (IVIF-PCA) model. This model represents major information of original attributes, effectively reduces dimensions of attribute space, and synthesizes original attributes into several relatively independent principal components (PCs). The basic thought of this model is as follows: first, we use thoughts of ‘equivalency’ and ‘order invariance’ to transform IVIFN samples into interval number samples; subsequently, we use the ‘error theory’ to replace interval numbers with their middle points, and combine the middle points with the traditional PCA to obtain the PC scores of interval number samples; finally, we adopt the thought of ‘equivalency’ to obtain the PC scores of IVIFN samples. Moreover, based on the IVIF-PCA model, we give a decision making method for the CMALGDM problem. The feasibility and validity of the decision making method is investigated through a numerical example.

Keywords

Complex multi-attribute large-group decision making (CMALGDM) Interval-valued intuitionistic fuzzy principal component analysis (IVIF-PCA) Error theory Score function Weighted arithmetic average operator 

Notes

Acknowledgments

We would like to thank the two anonymous reviewers for their constructive comments that have helped to improve the presentation and quality of the paper. This paper was supported by the National Natural Science Foundation of China (No. 71102072, No. 71271143, No. 71171141, and No. 71171202).

Supplementary material

500_2013_1190_MOESM1_ESM.pdf (333 kb)
Supplementary material 1 (pdf 332 KB)

References

  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96MathSciNetCrossRefzbMATHGoogle Scholar
  2. Atanassov KT, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349MathSciNetCrossRefzbMATHGoogle Scholar
  3. Cazes P, Chouakria A, Diday E, Schektman Y (1997) Extension de l’analyse en composantes principales à des données de type intervalle. Revuede Statistique Appliquée 45:5–24Google Scholar
  4. Chen XH (2009) Complex large-group decision making methods and application. Science Press, Beijing (in Chinese)Google Scholar
  5. Chen TY, Li CH (2010) Determining objective weights with intuitionistic fuzzy entropy measures: a comparative analysis. Inf Sci 180:4207–4222CrossRefGoogle Scholar
  6. Chen Q, Xu ZS, Liu SS, Yu XH (2010) A method based on interval-valued intuitionistic fuzzy entropy for multiple attribute decision making. Inf Tokyo 13:67–77Google Scholar
  7. Chen ZP, Yang W (2011) Appl Math Model 35:4424–4437MathSciNetCrossRefzbMATHGoogle Scholar
  8. Douzal-Chouakria A, Billard L, Diday E (2011) Principal component analysis for interval-valued observations. Stat Anal Data Min 4:229–246MathSciNetCrossRefGoogle Scholar
  9. Guo JP, Li WH (2007) Principal component analysis based on error theory and its application. Appl Stat Manag 26:636–640 (in Chinese)Google Scholar
  10. Herrera F, Herrera-Viedma E, Martínez L (2008) A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans Fuzzy Syst 16:354–370CrossRefGoogle Scholar
  11. Jolliffe I (2002) Principal component analysis. Springer, New YorkzbMATHGoogle Scholar
  12. Khaleie S, Fasanghari M (2012) An intuitionistic fuzzy group decision making method using entropy and association coefficient. Soft Comput 16:1197–1211CrossRefGoogle Scholar
  13. Kim SH, Choi SH, Kim JK (1999) An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach. Eur J Oper Res 118:139–152CrossRefzbMATHGoogle Scholar
  14. Lauro NC, Palumbo F (2000) Principal components analysis of interval data: a symbolic data analysis approach. Computation Stat 15:73–87CrossRefzbMATHGoogle Scholar
  15. Li DF (2010a) TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 18:299–311Google Scholar
  16. Li DF (2010b) Linear programming method for MADM with interval-valued intuitionistic fuzzy sets. Expert Syst Appl 37:5939–5945 Google Scholar
  17. Liu BS et al. (2013) A partial binary tree DEA-DA cyclic classification model for decision makers in complex multi-attribute large-group interval-valued intuitionistic fuzzy decision-making problems. Inform Fusion. http://dx.doi.org/10.1016/j.inffus.2013.06.004
  18. Merigó JM (2011) A unified model between the weighted average and the induced OWA operator. Expert Syst Appl 38:11560–11572CrossRefGoogle Scholar
  19. Merigó JM, Lobato-Carral C, Carrilero-Castillo A (2012) Decision making in the European Union under risk and uncertainty. Eur J Int Manag 6:590–609CrossRefGoogle Scholar
  20. Moore RE (1966) Interval Analysis. Prentice-Hall, Englewood CliffsGoogle Scholar
  21. Nayagam VLG, Muralikrishnan S, Sivaraman G (2011) Multicriteria decision-making method based on interval-valued intuitionistic fuzzy sets. Expert Syst Appl 38:1464–1467CrossRefGoogle Scholar
  22. Palumbo F, Lauro NC (2003) A PCA for interval-valued data based on midpoints and radii. In: Yanai H, Okada A, Shigemasu K, Kano Y, Meulman J (eds) New developments in psychometrics. Springer, Tokyo, pp 641–648CrossRefGoogle Scholar
  23. Tan CQ, Chen XH (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37:149–157CrossRefGoogle Scholar
  24. Wang ZJ, Li KV, Wang WZ (2009) An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Inf Sci 179:3026–3040CrossRefzbMATHGoogle Scholar
  25. Wei GW, Merigó JM (2012) Methods for strategic decision making problems with immediate probabilities in intuitionistic fuzzy setting. Sci Iran E 19:1936–1946CrossRefGoogle Scholar
  26. Xia MM, Xu ZS (2010) Generalized point operators for aggregating intuitionistic fuzzy information. Int J Intell Syst 25:1061–1080zbMATHGoogle Scholar
  27. Xu XH, Chen XH, Wang HW (2009) A kind of large group decision making method oriented utility valued preference information. Control Decis 24:440–446 (in Chinese)MathSciNetGoogle Scholar
  28. Xu XH, Yong YF (2011) Improved ants-clustering algorithm and its application in multi-attribute large group decision making. J Syst Eng Electron 33:346–349 (in Chinese)zbMATHGoogle Scholar
  29. Xu ZS (2007a) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRefGoogle Scholar
  30. Xu ZS (2007b) A method for multiple attribute decision making with incomplete weight information in linguistic setting. Knowl Based Syst 20:719–725CrossRefGoogle Scholar
  31. Xu ZS (2007c) Models for multiple attribute decision making with intuitionistic fuzzy information. Int J Uncertain Fuzz 15:285–297CrossRefzbMATHGoogle Scholar
  32. Xu ZS (2007d) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22:215–219 (in Chinese)Google Scholar
  33. Xu ZS (2010a) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negotiat 19:57–76CrossRefGoogle Scholar
  34. Xu ZS (2010b) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf Sci 180:181–190CrossRefzbMATHGoogle Scholar
  35. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433MathSciNetCrossRefzbMATHGoogle Scholar
  36. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bingsheng Liu
    • 1
  • Yuan Chen
    • 1
    Email author
  • Yinghua Shen
    • 2
  • Hui Sun
    • 1
  • Xuanhua Xu
    • 3
  1. 1.College of Management and EconomicsTianjin UniversityTianjinPeople’s Republic of China
  2. 2.School of BusinessHohai UniversityNanjingPeople’s Republic of China
  3. 3.School of BusinessCentral South UniversityChangshaPeople’s Republic of China

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