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

Sonia Darvishi; Adel Fatemi; Pouya Faroughi

doi:10.4236/am.2015.66091

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AM> Vol.6 No.6, June 2015

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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 3,460 Downloads 4,030 Views Citations

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Sonia Darvishi¹, Adel Fatemi², Pouya Faroughi^2*

Affiliation(s)

¹Department of Statistics, North Tehran Branch, Islamic Azad University, Tehran, Iran.
²Department of Statistics, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran.

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.

KEYWORDS

PCA, Cross Entropy, Intuitionistic Fuzzy Sets, Discrimination Information Measure, A-IFSs

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.

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