Sains Malaysiana 43(11)(2014): 1781–1790

 

Multivariate Relationship Modeling using Nested Fuzzy Cognitive Map

(Model Hubungan Multivariasi Menggunakan Peta Kognitif Kabur Tersarang)

 

 

O. MOTLAGH1*, E.I. PAPAGEORGIOU2, S.H. TANG3 & ZAMBERI JAMALUDIN1

 

1Robotics and Atomation, Universiti Teknikal Malaysia Melaka, 76100 Durian Tunggal, Melaka

Malaysia

 

2Informatics and Computer Tech., Technological Education Institute (TEI), Lamia, 654 04 Kavala

Greece

 

3Mechanical and Manufacturing Department, Universiti Putra Malaysia, 43400 Serdang, Selangor

Malaysia

 

Diserahkan: 7 Jun 2013/Diterima: 11 Mac 2014

 

ABSTRACT

Soft computing is an alternative to hard and classic math models especially when it comes to uncertain and incomplete data. This includes regression and relationship modeling of highly interrelated variables with applications in curve fitting, interpolation, classification, supervised learning, generalization, unsupervised learning and forecast. Fuzzy cognitive map (FCM) is a recurrent neural structure that encompasses all possible connections including relationships among inputs, inputs to outputs and feedbacks. This article examines a new methods for nonlinear multivariate regression using fuzzy cognitive map. The main contribution is the application of nested FCM structure to define edge weights in form of meaningful functions rather than crisp values. There are example cases in this article which serve as a platform to modelling even more complex engineering systems. The obtained results, analysis and comparison with similar techniques are included to show the robustness and accuracy of the developed method in multivariate regression, along with future lines of research.

 

Keywords: Nested fuzzy cognitive map; neural activation; regression

 

ABSTRAK

Pengiraan lembut adalah alternatif kepada model matematik klasik dan sukar terutama apabila ia melibatkan data yang tidak menentu dan tidak lengkap. Ini termasuk regresi dan pemodelan hubungan pemboleh ubah yang sangat berkait dengan aplikasi dalam penyesuaian lengkung, interpolasi, pengelasan, pembelajaran yang diselia, generalisasi, pembelajaran tanpa penyeliaan dan ramalan. Peta kognitif kabur (FCM) merupakan struktur neural berulang yang merangkumi semua kemungkinan sambungan termasuk hubungan antara input, input kepada output dan maklum balas. Artikel ini mengkaji kaedah baru untuk regresi multivariasi tak linear menggunakan peta kognitif kabur. Penyumbang utama adalah penggunaan struktur FCM bersarang untuk menentukan kelebihan pemberat dalam bentuk fungsi bermakna dan bukannya nilai-nilai bersih. Terdapat kes-kes contoh dalam artikel ini yang berfungsi sebagai satu platform untuk pemodelan sistem kejuruteraan yang lebih kompleks. Keputusan yang diperoleh, analisis dan perbandingan dengan teknik yang sama disertakan untuk menunjukkan keberkesanan dan ketepatan kaedah yang dibangunkan dalam regresi multivariasi bersama-sama dengan hala tuju untuk penyelidikan yang akan datang.

 

Kata kunci: pengaktifan neural; peta kognitif kabur tersarang; regresi

 

RUJUKAN

 

Abraham, A. & Nath, B. 2001. A neuro-fuzzy approach for modelling electricity demand in Victoria. Applied Soft Computing 1(2): 127-138.

Bartkiewicz, W. 2000. Neuro-fuzzy approaches to short-term electrical load forecasting. Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. 6: 229-234.

Bianco, V., Manca, O. & Nardini, S. 2009. Electricity consumption forecasting in Italy using linear regression models. Energy 34(9): 1413-1421.

Chang, P-C., Fan, C-Y. & Lin, J-J. 2011. Monthly electricity demand forecasting based on a weighted evolving fuzzy neural network approach. International Journal of Electrical Power and Energy Systems 33(1): 17-27.

Connor, J.T. 1996. A robust neural network filter for electricity demand prediction. Journal of Forecasting 15(6): 437-458.

Cottet, R. & Smith, M. 2003. Bayesian modeling and forecasting of intraday electricity load. Journal of the American Statistical Association 98(464): 839-849.

Darbellay, G.A. & Slama, M. 2000. Forecasting the short-term demand for electricity: Do neural networks stand a better chance. International Journal of Forecasting 16(1): 71-83.

Dickerson, J.A. & Kosko, B. 1994. Virtual worlds as fuzzy cognitive maps. Presence 3(2): 173-189.

Erdogdu, E. 2007. Electricity demand analysis using cointegration and ARIMA modelling: A case study of Turkey. Energy Policy 35(2): 1129-1146.

Espey, J.A. & Espey, M. 2004. Turning on the lights: A meta- analysis of residential electricity demand elasticities. Journal of Agricultural and Applied Economics 36(1): 65-81.

Gulsen, M., Smith, A.E. & Tate, D.M. 1995. A genetic algorithm approach to curve fitting. International Journal of Production Research 33(7): 1911-1923.

Historical demand data. 2013. Historical demand data from 2004 to date. http://www.nemweb.com.au/REPORTS/Archive/ HistDemand/. Accessed on 10 November 2013.

Karr, C.L., Weck, B., Massart, D.L. & Vankeerberghen, P. 1995. Least median squares curve fitting using a genetic algorithm. Engineering Applications of Artificial Intelligence 8(2): 177-189.

Khan, M.R. & Ondrůšek, Č. 2001. The Hopfield model for short-term load prediction, 2nd Spring International Power Engineering Conference. UVEE, FEI, Brno University of Technology, Czech Republic. pp. 81-85.

Kosko, B. 1996. Fuzzy Engineering. Upper Saddle River, NJ: Prentice-Hall Inc.

Motlagh, O., Jamaludin, Z., Tang, S.H. & Khaksar, W. 2013. An agile FCM for real-time modeling of dynamic and real-life systems, evolving systems: Special issue on temporal aspects in fuzzy cognitive maps. DOI: 10.1007/s12530-013-9077-6.

Motlagh, O., Tang, S.H., Maslan, M.N., Jafar, F.A. & Maslita, A.A. 2013a. A novel graph computation technique for multi-dimensional curve fitting. Connection Science 25(2- 3): 129-138.

Motlagh, O., Tang, S.H., Ismail, N. & Ramli, A.R. 2012. An expert fuzzy cognitive map for reactive navigation of mobile robots. Fuzzy Sets and Systems 201: 105-121.

Motlagh, O., Tang, S.H., Khaksar, W. & Ismail, N. 2012a. An alternative approach to FCM activation for modeling dynamic systems. Applied Artificial Intelligence 26(8): 733-742.

Negnevitsky, M. 2005. Artificial Intelligence: A Guide to Intelligent Systems. England: Pearson Education Ltd.

Pai, P-F. & Hong, W-C. 2005. Forecasting regional electricity load based on recurrent support vector machines with genetic algorithms. Electric Power Systems Research 74(3): 417-425.

Papageorgiou, E.I. & Salmeron, J.L. 2012. Learning fuzzy grey cognitive maps using non-linear Hebbian. International Journal of Approximate Reasoning 53(1): 54-65.

Pappas, S.Sp., Ekonomou, L., Karampelas, P., Karamousantas, D.C., Katsikas, S.K., Chatzarakis, G.E. & Skafidas, P.D. 2010. Electricity demand load forecasting of the Hellenic power system using an ARMA model. Electric Power Systems Research 80(3): 256-264.

Papageorgiou, E.I., Stylios, C.D. & Groumpos, P.P. 2004. Active Hebbian learning algorithm to train fuzzy cognitive maps. Int. Journal of Approximate Reasoning 37(3): 219-247.

Papageorgiou, E.I., Stylios, C.D. & Groumpos, P.P. 2003. Fuzzy cognitive map learning based on nonlinear Hebbian rule. Australian Conf. on Artificial Intelligence. pp. 256-268.

Santin, O.G. 2011. Behavioural patterns and user profiles related to energy consumption for heating. Energy and Buildings 43(10): 2662-2672.

Stach, W., Kurgan, L., Pedrycz, W. & Reformat, M. 2005. Genetic learning of fuzzy cognitive maps. Fuzzy Sets and Systems 153: 371-401.

Taylor, J.W., de Menezes, L.M. & McSharry, P.E. 2006. A comparison of univariate methods for forecasting electricity demand up to a day ahead. International Journal of Forecasting 22(1): 1-16.

Thatcher, M.J. 2007. Modelling changes to electricity demand load duration curves as a consequence of predicted climate change for Australia. Energy 32: 1647-1659.

Vazquez, A. 2002. A balanced differential learning algorithm in fuzzy cognitive maps, Technical Report, Departament de Lenguatges I Sistemes Informatics, Universitat Politecnica de Catalunya (UPC).

Yao, A.W.L., Chi, S.C. & Chen, J.H. 2003. An improved Grey-based approach for electricity demand forecasting. Electric Power Systems Research 67(3): 217-224.

 

 

*Pengarang untuk surat-menyurat; email: omid@utem.edu.my

 

 

 

sebelumnya