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Mathematical Problems in Engineering
Volume 2014, Article ID 735310, 19 pages
Research Article

An Interval Type-2 Fuzzy System with a Species-Based Hybrid Algorithm for Nonlinear System Control Design

1Department of Electrical Engineering, Yuan Ze University, Taiwan
2Department of Mechanical Engineering, National Chung Hsing University, Taiwan

Received 9 December 2013; Accepted 18 March 2014; Published 24 April 2014

Academic Editor: Jianming Zhan

Copyright © 2014 Chung-Ta Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a species-based hybrid of the electromagnetism-like mechanism (EM) and back-propagation algorithms (SEMBP) for an interval type-2 fuzzy neural system with asymmetric membership functions (AIT2FNS) design. The interval type-2 asymmetric fuzzy membership functions (IT2 AFMFs) and the TSK-type consequent part are adopted to implement the network structure in AIT2FNS. In addition, the type reduction procedure is integrated into an adaptive network structure to reduce computational complexity. Hence, the AIT2FNS can enhance the approximation accuracy effectively by using less fuzzy rules. The AIT2FNS is trained by the SEMBP algorithm, which contains the steps of uniform initialization, species determination, local search, total force calculation, movement, and evaluation. It combines the advantages of EM and back-propagation (BP) algorithms to attain a faster convergence and a lower computational complexity. The proposed SEMBP algorithm adopts the uniform method (which evenly scatters solution agents over the feasible solution region) and the species technique to improve the algorithm’s ability to find the global optimum. Finally, two illustrative examples of nonlinear systems control are presented to demonstrate the performance and the effectiveness of the proposed AIT2FNS with the SEMBP algorithm.