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Introduce a Novel PCA Method for Intuitionistic Fuzzy Sets Based on Cross Entropy

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DOI: 10.4236/am.2015.66091    3,281 Downloads   3,756 Views   Citations

ABSTRACT

In this paper, a new method for Principal Component Analysis in intuitionistic fuzzy situations has been proposed. This approach is based on cross entropy as an information index. This new method is a useful method for data reduction for situations in which data are not exact. The inexactness in the situations assumed here is due to fuzziness and missing data information, so that we have two functions (membership and non-membership). Thus, method proposed here is suitable for Atanasov’s Intuitionistic Fuzzy Sets (A-IFSs) in which we have an uncertainty due to a mixture of fuzziness and missing data information. For the demonstration of the application of the method, we have used an example and have presented a conclusion.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Darvishi, S. , Fatemi, A. and Faroughi, P. (2015) Introduce a Novel PCA Method for Intuitionistic Fuzzy Sets Based on Cross Entropy. Applied Mathematics, 6, 990-995. doi: 10.4236/am.2015.66091.

References

[1] Atanassov, K.T. (1983) Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 20, 87-96.
http://dx.doi.org/10.1016/S0165-0114(86)80034-3
[2] Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353.
http://dx.doi.org/10.1016/S0019-9958(65)90241-X
[3] Li, D.-F. (2014) Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Sets. In: Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, 308, 75-151.
http://dx.doi.org/10.1007/978-3-642-40712-3_3
[4] Li, D.-F. (2014) Multiattribute Group Decision-Making Methods with Intuitionistic Fuzzy Sets. In: Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, 308, 251-288.
http://dx.doi.org/10.1007/978-3-642-40712-3_6
[5] Szmidt, E., Kacprzyk, J. and Bujnowski, P. (2013) The Kendall Rank Correlation between Intuitionistic Fuzzy Sets: An Extended Analysis. Soft Computing: State of the Art Theory and Novel Applications, 291, 39-54. http://dx.doi.org/10.1007/978-3-642-34922-5_4
[6] Zhang, X., Deng, Y., Chan, F.T.S., Xu, P., Mahadevan, S. and Hu, Y. (2013) IFSJSP: A Novel Methodology for the Job-Shop Scheduling Problem Based on Intuitionistic Fuzzy Sets. International Journal of Production Research, 51, 5100-5119. http://dx.doi.org/10.1080/00207543.2013.793425
[7] Szmidt, E. and Kacprzyk, J. (2012) A New Approach to Principal Component Analysis for Intuitionistic Fuzzy Data Sets. Advances in Computational Intelligence. Communications in Computer and Information Science, 298, 529-538.
[8] Feng, H., Yuan, M. and Fan, X. (2012) PCA Based on Mutual Information for Acoustic Environment Classification. Paper Presented at the International Conference on Audio, Language and Image Processing (ICALIP), Shanghai Ac- oustics Laboratory, Shanghai, 16-18.
[9] Fatemi, A. (2011) Entropy of Stochastic Intuitionistic Fuzzy Sets. Journal of Applied Sciences, 11, 748-751. http://dx.doi.org/10.3923/jas.2011.748.751
[10] Shang, X.G. and Jiang, W.S. (1997) A Note on Fuzzy Information Measures. Pattern Recognition Letters, 18, 425-432. http://dx.doi.org/10.1016/S0167-8655(97)00028-7
[11] Valchos, I.K. and Sergiadis, G.D. (2007) Intuitionistic Fuzzy Information—Applications to Pattern Recognition. Pattern Recognition Letters, 28, 197-206. http://dx.doi.org/10.1016/j.patrec.2006.07.004
[12] Quinland, J.R. (1986) Induction of Decisions Trees. Machine Learning, 1, 81-106.
http://dx.doi.org/10.1007/BF00116251

  
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