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

Received: 7 June 2013/Accepted: 11 March 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

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*Corresponding author; email: omid@utem.edu.my