Applied Soft Computing 18 (2014) 302–313 Contents lists available at ScienceDirect Applied Soft Computing j ourna l ho me page: www.elsevier.com/locate /asoc A type-2 neural fuzzy system learned through type-1 fuzzy rules and its FPGA-based hardware implementation Chia-Feng Juang ∗ , Wen-Sheng Jang Department of Electrical Engineering, National Chung Hsing University, Taichung 402, Taiwan, ROC a r t i c l e i n f o Article history: Received 10 April 2013 Received in revised form 2 October 2013 Accepted 7 January 2014 Available online 23 January 2014 Keywords: Type-2 fuzzy systems Fuzzy neural networks Neural fuzzy systems Fuzzy chips Fuzzy hardware a b s t r a c t This paper first proposes a type-2 neural fuzzy system (NFS) learned through its type-1 counterpart (T2NFS-T1) and then implements the built IT2NFS-T1 in a field-programmable gate array (FPGA) chip. The antecedent part of each fuzzy rule in the T2NFS-T1 uses interval type-2 fuzzy sets, while the consequent part uses a Takagi-Sugeno-Kang (TSK) type with interval combination weights. The T2NFS-T1 uses a simplified type-reduction operation to reduce system training time and hardware implementation cost. Given a training data set, a TSK type-1 NFS is first learned through structure and parameter learning. The built type-1 fuzzy logic system (FLS) is then extended to a type-2 FLS, where highly overlapped type-1 fuzzy sets are merged into interval type-2 fuzzy sets to reduce the total number of fuzzy sets. Finally, the rule consequent and antecedent parameters in the T2NFS-T1 are tuned using a hybrid of the gradient descent and rule-ordered recursive least square (RLS) algorithms. Simulation results and comparisons with various type-1 and type-2 FLSs verify the effectiveness and efficiency of the T2NFS-T1 for system modeling and prediction problems. A new hardware circuit using both parallel-processing and pipeline techniques is proposed to implement the learned T2NFS-T1 in an FPGA chip. The T2NFS-T1 chip reduces the hardware implementation cost in comparison to other type-2 fuzzy chips. © 2014 Elsevier B.V. All rights reserved. 1. Introduction The neural-fuzzy approach to data-based modeling and predic- tion has drawn much research attention in the last two decades. While many neural fuzzy systems (NFSs) have been proposed, most studies have used type-1 fuzzy logic systems (FLSs) [1–4]. In recent years, studies on the theory and applications of interval type-2 FLSs have become a research focus. Interval type-2 FLSs are exten- sions of type-1 FLSs, where the membership value of an interval type-2 fuzzy set (FS) is an interval type-1 FS. Several advantages of using interval type-2 FLSs over their type-1 counterparts have been reported [5–7]. However, the footprint of uncertainty and operations with interval values in an interval type-2 FLS also lead to greater complexity in computing system outputs and assigning proper system parameters. To automate the design of interval type-2 FLSs, several inter- val type-2 NFSs have been proposed with claimed superiority over the type-1 NFSs used for comparison [7–16]. Parameter learning of interval type-2 FLSs using a gradient descent algorithm was proposed in [7]. The approach does not use structure learning to determine the number of rules and FSs. In other words, the struc- ture is fixed and should be assigned in advance. Several studies ∗ Corresponding author. Tel.: +886 4 22840688x806; fax: +886 4 22851410. E-mail address: cfjuang@dragon.nchu.edu.tw (C.-F. Juang). on structure learning of interval type-2 FLSs have been proposed [8–16]. These studies use the idea of clustering to generate type- 2 fuzzy rules. The general approach is using the maximum value of centers of interval firing strengths as a rule generation criterion for each incoming datum [9–11,13–16]. Because structure learn- ing is easier when using type-1 fuzzy rules than type-2 fuzzy rules, type-1 NFSs with structure learning ability have been extensively studied. This paper proposes a new method that builds a type-2 NFS via extending a built type-1 NFS (T2NFS-T1). For previous inter- val type-2 NFSs [8–15], the type-reduction outputs are computed using an iterative procedure, such as the Karnik–Mendel proce- dure [5], which is computationally expensive. For this problem, the T2NFS-T1 uses a simple weighted sum operation [17] to sim- plify the type-reduction operation, which reduces both software training time and hardware implementation cost. In learning, the T2NFS-T1 can be used to convert well-trained type-1 NFSs learned through different types of learning algorithms to type-2 NFSs with- out regeneration of the type-2 rules from an empty set. This is different from previous type-2 NFSs that generate type-2 fuzzy rules from an empty set [9–16], which do not make good use of the learning results in extensively studied type-1 NFSs. Given a training data set, a TSK type-1 NFS is first learned through struc- ture and parameter learning. The T2NFS-T1 is then initialized from extending the built type-1 FLS to its type-2 counterpart. The gen- eral approach to the learning of an interval type-2 FLS from a type-1 FLS is by extending all type-1 FSs to interval type-2 FSs. In this 1568-4946/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2014.01.006