Paper:

# An Efficient Solution of Real-Time Fuzzy Regression Analysis to Information Granules Problem

## Azizul Azhar Ramli^{*1,*2}, Junzo Watada^{*2},

and Witold Pedrycz^{*3,*4}

^{*1}Faculty of Computer Science and Information Technology, Universiti Tun Hussein Onn Malaysia, Parit Raja, Batu Pahat 86400, Johor Darul Takzim, Malaysia

^{*2}Graduate School of Information, Production and Systems, Waseda University, 2-7 Hibikino, Wakamatsu-ku, Kita Kyushu-shi 808-0135, Japan

^{*3}Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, T6G 2V4, Canada

^{*4}Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

Regression models are well known and widely used as one of the important categories of models in system modeling. In this paper, we extend the concept of fuzzy regression in order to handle real-time implementation of data analysis of information granules. An ultimate objective of this study is to develop a hybrid of a genetically-guided clustering algorithm called genetic algorithm-based Fuzzy C-Means (GAFCM) and a convex hull-based regression approach being regarded as a potential solution to the formation of information granules. It is shown that a setting of Granular Computing helps us reduce the computing time, especially in case of real-time data analysis, as well as an overall computational complexity. We propose an efficient real-time information granules regression analysis based on the convex hull approach in which a Beneath-Beyond algorithm is employed to design sub-convex hulls as well as a main convex hull structure. In the proposed design setting, we emphasize a pivotal role of the convex hull approach or more specifically the Beneath-Beyond algorithm, which becomes crucial in alleviating limitations of linear programming manifesting in system modeling.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.16, No.2, pp. 199-209, 2012.

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