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.

and Witold Pedrycz, “An Efficient Solution of Real-Time Fuzzy Regression Analysis to Information Granules Problem,”

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

- [1] A. Bargiela and W. Pedrycz, “Granular Computing: An Introduction,” Kluwer Academic Publishers, 2003.
- [2] D. Shifei, X. Li, Z. Hong, and Z. Liwen, “Research And Progress of Cluster Algorithms Based on Granular Computing,” Int. J. of Digital Content Technology and its Applications, Vol.4, No.5, pp. 96-104, 2010.
- [3] L. O. Hall, I. B. Ozyurt, and J. C. Bezdek, “Clustering with a Genetically Optimized Approach,” IEEE Trans. on Evolutionary Computation, Vol.3, Issue 2, pp. 103-112, 1999.
- [4] A. Bargiela and W. Pedrycz, “Toward a Theory of Granular Computing for Humancentered Information Processing,” IEEE Trans. on Fuzzy Systems, Vol.16, Issue 16, pp. 320-330, 2008.
- [5] B. Chen, P. C. Tai, R. Harrison, and Y. Pan, “FIKModel: Novel Efficient Granular Computing Model for Protein Sequence Motifs and Structure Information Discovery,” Sixth IEEE Int. Symposium on BioInformatics and BioEngineering (BIBE 2006), Arlington, Virginia, USA, pp. 20-26, 2006.
- [6] A. A. Ramli, J. Watada, and W. Pedrycz, “Real-Time Fuzzy Regression Analysis: A Convex Hull Approach,” European J. of Operational Research, Vol.210, Issue 3, pp. 606-617, 2011.
- [7] A. A. Ramli and J. Watada, “New Perspectives of Fuzzy Performance Assessment of Manufacturing Enterprises,” The 5th Int. Conf. on Intelligent Manufacturing and Logistics Systems (IML 2009), Waseda University, Kitakyushu, Japan, pp. 16-18, 2009.
- [8] P.-S. Yu, S.-T. Chena, and I.-F. Changa, “Support Vector Regression for Real-Time Flood Stage Forecasting,” J. of Hydrology, Vol.328, Issues 3-4, pp. 704-716, 2006.
- [9] W. Wang, S. Chena, and G. Qu, “Incident Detection Algorithm based on Partial Least Squares Regression,” Transportation Research Part C: Emerging Technologies, Vol.16, Issue 1, pp. 54-70, 2008.
- [10] W. Pedrycz and G. Vulcovich, “Representation and Propagation of Information Granules in Rule-based Computing,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.4, No.1, pp. 102-110, 2000.
- [11] F. Höppner and F. Klawonn, “Systems of Information Granules. In Handbook of Granular Computing,” in W. Pedrycz, A. Skowron, and V. Kreinovich (Eds.), John Wiley & Sons, Ltd, Chichester, UK, doi: 10.1002/9780470724163.ch9, 2008.
- [12] B. Chen, J. Hu, L. Duan, and Y. Gu, “Network Administrator Assistance System Based on Fuzzy C-means Analysis,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.13, No.2, pp. 91-96, 2009.
- [13] S. Nascimento, B.Mirkin, and F.Moura-Pires, “A Fuzzy Clustering Model of Data and Fuzzy C-Means,” IEEE Conf. on Fuzzy Systems (FUZZ-IEEE2000), San Antonio, Texes, USA, pp. 302-307, 2000.
- [14] M. Alata, M. Molhim, and A. Ramini, “Optimizing of Fuzzy CMeans Clustering Algorithm using GA,” World Academy of Science, Engineering and Technology, pp. 224-229, 2008.
- [15] Y. Yabuuchi and J.Watada, “Possibilistic Forecasting Model and Its Application to Analyze The Economy in Japan,” Lecture Notes in Computer Science, Springer Berlin/Heidelberg, Vol.3215, pp. 151-158, 2004.
- [16] H. J. Lin, F.W. Yang, and Y. T. Kao, “An Efficient GA-Based Clustering Technique,” Tamkang J. of Science and Engineering, Vol.8, No.2, pp. 113-122, 2005.
- [17] Y.Wang, “Fuzzy Clustering Analysis by using Genetic Algorithm,” ICIC Express Letters, Vol.2, No.4, pp. 331-337, 2008.
- [18] Z. Emiris, “A Complete Implementation for Computing General Dimensional Convex Hulls,” Int. J. of Computing Geometry and Applications, Vol.8, No.2, pp. 223-249, 1998.
- [19] B. Barber, D. P. Dobki, and H. Hupdanpaa, “The Quickhull Algorithm for Convex Hull,” ACM Trans. on Mathematical Software, Vol.22, No.4, pp. 469-483, 1996.
- [20] H.-F. Wang and R.-C. Tsaur, “Insight of a Possibilistic Regression Model,” Fuzzy Sets and Systems, Vol.112, Issues 3, pp. 355-369, 2000.
- [21] J.Watada and W. Pedrycz, “A Possibilistic Regression Approach to Acquisition of Linguistic Rules,” in W. Pedrycz, A. Skowron, and V. Kreinovich (Eds.), Handbook on Granular Commutation, John Wiley and Sons Ltd., Chapter 32, pp. 719-740, 2008.
- [22] H. Tanaka, S. Uejima, and K. Asai, “Linear Regression Analysis with Fuzzy Model,” IEEE Trans. Systems, Man and Cybernetics, Vol.12, No.6, pp. 903-907, 1982.
- [23] A. A. Ramli, J.Watada, andW. Pedrycz, “Real-Time Fuzzy Switching Regression Analysis: A Convex Hull Approach,” 11th Int. Conf. on Information Integration and Web-based Applications and Services (iiWAS2009), Kuala Lumpur, Malaysia, pp. 284-291, 2009.
- [24] A. Frank and A. Asuncion, “UCI Machine Learning Repository,” Irvine, CA: University of California, School of Information and Computer Science, 2010.

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