NCFS: new chaotic fuzzy system as a general function approximator

Abstract

Conventional fuzzy systems (type-1 and type-2) are universal approximators. The goal of this paper is to design and implement a new chaotic fuzzy system (NCFS) based on the Lee oscillator for function approximation and chaotic modelling. NCFS incorporates fuzzy reasoning of the fuzzy systems, self-adaptation of the neural networks, and chaotic signal generation in a unique structure. These features enable the structure to handle uncertainties by generating new information or by chaotic search among prior knowledge. The fusion of chaotic structure into the neurons of the membership layer of a conventional fuzzy system makes the NCFS more capable of confronting nonlinear problems. Based on the GFA and Stone-Weierstrass theorems, we show that the proposed model has the function approximation property. The NCFS performance is investigated by applying it to the problem of chaotic modelling. Simulation results are demonstrated to illustrate the concept of function approximation.

KEYWORDS:

• Chaotic fuzzy system
• function approximation
• chaotic neural network
• oscillatory neuron

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Membership Functions.

2 Type-1 Fuzzy Neural Network.

3 Interval Type-2 Fuzzy Neural Network.

4 Chaotic Fuzzy System.

Additional information

Notes on contributors

Hamid Abbasi

Hamid Abbasi received the B.Sc. degree in Computer hardware Engineering, M.Sc. in Artificial Intelligence from IAU, Mashhad Branch, in 2005 and 2008, respectively. He is currently a Ph.D. candidate in Artificial Intelligence in IAU, Science and Research Branch, Tehran, Iran. He is also Faculty member of computer department of DIAU. He is the author or a co-author of more than 15 papers that have appeared in various journals and conference proceedings. His research interests are Neuro Fuzzy systems, chaotic systems, evolutionary algorithms.

Mahdi Yaghoobi

Mahdi Yaghoobi received the B.S. degree and M.S degree in electrical engineering from Ferdowsi University, Mashhad, 1989 and 1993, respectively, the PhD from Science and Research Branch, Islamic Azad University, Tehran, Iran. At present he is associate professor of Electrical Engineering Department in Islamic Azad University of Mashhad. His area of research is chaos theory and applications, predictive control, fuzzy control and evolutionary algorithms.

Arash Sharifi

Arash Sharifi received the B.S. degree in computer hardware engineering from IAU South Tehran Branch, M.S degree and Ph.D. degree in artificial intelligence from IAU science and research branch, in 2007 and 2012 respectively. He is currently head of computer engineering department of SRBIAU. His current research interests include image processing, machine learning and deep learning.

Mohammad Teshnehlab

Mohammad Teshnehlab received the B.Sc. degree from Stony Brook University, USA, in 1980, the M.Sc. degree from Oita University, Japan, in 1990, and the Ph.D. degree from Saga University, Japan, in 1994. He is currently a Faculty Member of the Electrical Engineering Department, K. N. Toosi University of Technology. His research areas are artificial rough and deep neural networks, fuzzy systems and neural nets, optimisation, and expert systems. He is a member of the Industrial Control Center of Excellence and the Founder of the Intelligent Systems Laboratory (ISLab). He is also a Co-Founder and a member of the Intelligent Systems Scientific Society of Iran (ISSSI) and a member of the Editorial Board of the Iranian Journal of Fuzzy Systems (IJFS), the International Journal of Information and Communication Technology Research (IJICTR), and the Scientific Journal of Computational Intelligence in Electrical Engineering.