Mathematics and Statistics Vol. 8(5), pp. 559 - 565
DOI: 10.13189/ms.2020.080509
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Integration of Cluster Centers and Gaussian Distributions in Fuzzy C-Means for the Construction of Trapezoidal Membership Function

Siti Hajar Khairuddin ^*, Mohd Hilmi Hasan , Manzoor Ahmed Hashmani
Department of Computer and Information Sciences, Universiti Teknologi PETRONAS, Perak, Malaysia

ABSTRACT

Fuzzy C-Means (FCM) is one of the mostly used techniques for fuzzy clustering and proven to be robust and more efficient based on various applications. Image segmentation, stock market and web analytics are examples of popular applications which use FCM. One limitation of FCM is that it only produces Gaussian membership function (MF). The literature shows that different types of membership functions may perform better than other types based on the data used. This means that, by only having Gaussian membership function as an option, it limits the capability of fuzzy systems to produce accurate outcomes. Hence, this paper presents a method to generate another popular shape of MF, the trapezoidal shape (trapMF) from FCM to allow more flexibility to FCM in producing outputs. The construction of trapMF is using mathematical theory of Gaussian distributions, confidence interval and inflection points. The cluster centers or mean (μ) and standard deviation (σ) from the Gaussian output are fully used to determine four trapezoidal parameters; lower limit a, upper limit d, lower support limit b, and upper support limit c with the assistance of function trapmf() in Matlab fuzzy toolbox. The result shows that the mathematical theory of Gaussian distributions can be applied to generate trapMF from FCM.

KEYWORDS
Fuzzy C Means, Gaussian Distribution, Normal Distribution Membership Function, Trapezoidal MF

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Siti Hajar Khairuddin , Mohd Hilmi Hasan , Manzoor Ahmed Hashmani , "Integration of Cluster Centers and Gaussian Distributions in Fuzzy C-Means for the Construction of Trapezoidal Membership Function," Mathematics and Statistics, Vol. 8, No. 5, pp. 559 - 565, 2020. DOI: 10.13189/ms.2020.080509.

(b). APA Format:
Siti Hajar Khairuddin , Mohd Hilmi Hasan , Manzoor Ahmed Hashmani (2020). Integration of Cluster Centers and Gaussian Distributions in Fuzzy C-Means for the Construction of Trapezoidal Membership Function. Mathematics and Statistics, 8(5), 559 - 565. DOI: 10.13189/ms.2020.080509.