Applied Mathematics, 2015, 6, 990-995 Published Online June 2015 in SciRes. http://www.scirp.org/journal/am http://dx.doi.org/10.4236/am.2015.66091 How to 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. http://dx.doi.org/10.4236/am.2015.66091 Introduce a Novel PCA Method for Intuitionistic Fuzzy Sets Based on Cross Entropy Sonia Darvishi 1 , Adel Fatemi 2 , Pouya Faroughi 2* 1 Department of Statistics, North Tehran Branch, Islamic Azad University, Tehran, Iran 2 Department of Statistics, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran Email: soniadarvishi@yahoo.com , fatemi@iausdj.ac.ir , * pouyafaroughi@iausdj.ac.ir Received 5 April 2015; accepted 1 June 2015; published 4 June 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ 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 me- thod is a useful method for data reduction for situations in which data are not exact. The inexact- ness 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 1. Introduction This study can be very significant for statistical analyzes, since in many situations of data collection not only the data are recorded inexactly, but also they might be incomplete due to data missing. In other words, since this study applies to intuistionistic fuzzy situation, which is a generalized form of the fuzzy situation, it will have significant implications for all fuzzy situations. Intuitionistic fuzzy set [1] is a generalization of fuzzy sets [2]. Due to the significance of intuistionistic fuzzy sets as a generalized fuzzy situation, many scholars have devoted attention to the subject and have applied the results of their studies to different fields, especially statistical anal- * Corresponding author.