Abstract
This chapter compares type 1 and type 2 fuzzy principal component analysis which are based on type 1 and type 2 fuzzy C-means algorithms, respectively. The two clustering methods are the combination of k-means clustering algorithm and type 1 and type 2 fuzzy logic, respectively.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Change history
19 July 2024
A correction has been published.
References
Jolliffe, I.T.: Principal Component Analysis, 2nd Edn. Springer Series in Statistics (2002)
Zadeh, L.A.: Fuzzy Sets (1965) Information and Control, vol. 8, pp. 338–353 (1965)
Heoa, G., Gadera, P., Frigui, H.: RKF-PCA: robust kernel fuzzy PCA. Neural Netw. 22, 642–650 (2009). (Elsevier)
Elbanby, Gh., El Madbouly, E., Abdalla, A.: Fuzzy principal component analysis for sensor fusion. In: The 11th International Conference on Information Sciences, Signal Processing and their Applications: Main Tracks
Gueorguieva, N., Valova, I., Georgiev, G.: Fuzzyfication of principle component analysis for data dimensionalty reduction. In: IEEE International Conference on Fuzzy Systems FUZZ-IEEE 2016. Published online 2016, pp. 1818–1825 (2016)
Pop, H.F., Einax, J.W., Sârbu, C.: Classical and fuzzy principal component analysis of some environmental samples concerning the pollution with heavy metals. Chemom. Intell. Lab. Syst. 97, 25–32 (2009). (Elsevier)
Zimmermann, H.-J.: Fuzzy set theory. In: Advanced Review, WIREs Computational Statistics, vol. 2, no. 3, pp. 317–332 (2010). (May/June 2010)
Khanmirza, E., Nazarahari, M., Mousavi, A.: Identification of piecewise affine systems based on fuzzy PCA-guided robust clustering technique. EURASIP J. Adv. Signal Process (2016)
Salgado, P., Gonçalves, L., Igrejas, G.: Sliding PCA fuzzy clustering algorithm. In: AIP Conference Proceedings, vol. 1389, pp. 1992 (2011)
Hadri, A., Chougdali, K., Touahni, R.: Intrusion detection system using PCA and Fuzzy PCA techniques. In: International Conference on Advanced Communication Systems and Information Security (ACOSIS) (2016)
Cundari, T.R., Sarbu, C., Pop, H.F.: Robust fuzzy principal component analysis (FPCA). A comparative study concerning interaction of carbon-hydrogen bonds with molybdenum-oxo bonds. J. Chem. Inf. Comput. Sci. 42(6), 1363–1369 (2002). (Nov 2002)
Xiaohong, W., Jianjiang, Z.: Fuzzy principal component analysis and its kernel-based model. J. Electron. (China) 24, 772–775 (2007)
Nascimento, S., Mirkin, B., Moura-Pires, F.: A fuzzy clustering model of data and fuzzy c-means. In: Ninth IEEE International Conference on Fuzzy Systems. FUZZ-IEEE 2000 (2000)
Zhai, D., Mendel, J.M.: Uncertainty measures for general Type-2 fuzzy sets. Inf. Sci. 181, 503–518 (2011). (Elsevier)
Mendel, J.M.: Type 2 fuzzy sets and systems: an overview. IEEE Comput. Intell. Mag. (2007). (Feb 2007)
Mendel, J., John, R.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2) (2002). (Apr 2002)
Nie, M., Tan, W.W.: Modeling capability of type-1 fuzzy set and interval type-2 fuzzy set. IEEE World Congress Comput. Intell. (2012). (10–15 Jun 2012)
Kim, E., Oh, S., Pedrycz, W.: Design of reinforced interval type-2 fuzzy c-means-based fuzzy classifier. IEEE Trans. Fuzzy Syst. 1063–6706 (c) (2017)
Fathy, E.: A new method for solving the linear programming problem in an interval-valued intuitionistic fuzzy environment. Alexandria Eng. J. 61(12), 10419–10432 (2022)
Singh, V., Verma, N.K., Cui, Y.: Type-2 fuzzy PCA Approach in extracting salient features for molecular cancer diagnostics and prognostics. IEEE Trans. Nanobioscience 18(3), 482–489 (2019)
Taghikhani, S., Baroughi, F., Alizadeh, B.: A generalized interval type-2 fuzzy random variable based algorithm under mean chance value at risk criterion for inverse 1-median location problems on tree networks with uncertain costs. J. Comput. Appl. Math. 408, 114104 (2022)
Hwang, Ch., Chung-Hoon Rhee, F.: Uncertain fuzzy clustering: interval type-2 fuzzy approach to C-means. IEEE Trans. Fuzzy Syst. 15(1) (2007). (Feb 2007)
Linda, O., Manic, M.: General type-2 fuzzy c-means algorithm for uncertain fuzzy clustering. IEEE Trans. Fuzzy Syst. 20(5) (2012). (Oct 2012)
Aminifar, S.: Uncertainty avoider interval type II defuzzification method. Math. Probl. Eng. (2020)
Ding, W., Abdel-Basset, M., Hawash, H., Mostafa, N.: Interval type-2 fuzzy temporal convolutional autoencoder for gait-based human identification and authentication. Inf. Sci. (Ny) 597, 144–165 (2022)
Gölcük, I.: An interval type-2 fuzzy axiomatic design method: a case study for evaluating blockchain deployment projects in supply chain. Inf. Sci. (Ny) 602, 159–183 (2022)
Hefaidh, H., Mébarek, D.: Using fuzzy-improved principal component analysis (PCA-IF) for ranking of major accident scenarios. Arab. J. Sci. Eng. 45(3), 2235–2245 (2020)
Rajati, M.R., Mendel, J.M.: Uncertain knowledge representation and reasoning with linguistic belief structures. Inf Sci (Ny) 585, 471–497 (2022)
Singh, V., Verma, N.K., Cu, Y.: Type-2 Fuzzy PCA approach in extracting salient features for molecular cancer diagnostics and prognostics. IEEE Trans. Nanobioscience 18(3) (2019). (July 2019)
Wang, Y., Chen, L., Zhou, J., Li, T., Chen, C.L.P.: Interval type-2 outlier-robust picture fuzzy clustering and its application in medical image segmentation. Appl. Soft. Comput. 122, 108891 (2022)
Wu, L., Qian, F., Wang, L., Ma, X.: An improved type-reduction algorithm for general type-2 fuzzy sets. Inf. Sci. (Ny). 593, 99–120 (2022)
Yan, S.R., Alattas, K.A., Bakouri, M., et al.: Generalized type-2 fuzzy control for type-I diabetes: analytical robust system. Mathematics 10(5), 1–20 (2022)
Chiao, K.P.: The general type 1 and interval type 2 fuzzy sets addition based on the Yager T-norms with entropy as degree of fuzziness. In: 2019 International Conference Fuzzy Theory its Application iFUZZY 2019. Published online, vol. 2019, pp. 214–219 (2019)
Mendel, J.M.: On KM algorithms for solving type-2 fuzzy set problems. IEEE Trans. Fuzzy Syst. 21(3) (2013). (June 2013)
Karnik, N.N., Mendel, J.M.: Centroid of a type-2 fuzzy set. Inf. Sci. 132(2001), 195–220 (2001). (Elsevier)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Bouchra, D., Hassania, H., Gouiouez, M. (2023). Extension of Fuzzy Principal Component Analysis to Type-2 Fuzzy Principal Component Analysis. In: Castillo, O., Kumar, A. (eds) Recent Trends on Type-2 Fuzzy Logic Systems: Theory, Methodology and Applications. Studies in Fuzziness and Soft Computing, vol 425. Springer, Cham. https://doi.org/10.1007/978-3-031-26332-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-031-26332-3_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-26331-6
Online ISBN: 978-3-031-26332-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)