I. Introduction
The MARRIAGE of fuzzy logic systems (FLSs) and neural networks (NNs) has drawn considerable attention in recent years. So-called fuzzy neural networks (FNNs) [1]–[8], [40]–[42], [51]–[53] inherit their learning ability from NNs, and much of their inference technology from fuzzy systems, which are widely used in robotics, temperature control, system identification, bioengineering, and many others. Some FNNs, including, for example, the adaptive network-based fuzzy inference system (ANFIS) [1], the fuzzy adaptive learning control network [3] and the self-constructing neural fuzzy inference network (SONFIN) [4], are well known. ANFIS uses a fixed structure, with all parameters turned by a hybrid learning algorithm. For the consequent part of their fuzzy rule, ANFIS and SONFIN use the Takagi–Sugeno–Kang (TSK) type and Mamdani-type, respectively. Many studies [1], [2], [4], [5] indicate that TSK-type FNNs achieve superior learning accuracy than Mamdani-type FNNs.