An interval type-2 neural fuzzy inference system (IT2NFIS) with compensatory operator

In this paper, an interval type-2 neural fuzzy system (IT2NFIS) with compensatory operator is proposed for system modeling. The IT2NFIS uses type-2 fuzzy sets in the premise clause in order to effectively handle the uncertainties in terms of data and information. The premise part of each compensatory fuzzy rule is an interval type-2 fuzzy set in the IT2NFIS, where compensatory operation is able to adaptively adjust fuzzy membership functions and to dynamically optimize fuzzy operations. The consequent part in the IT2NFIS consists of the Takagi-Sugeno-Kang (TSK) type that is a linear combination of exogenous input variables. Initially the rule base in the IT2NFIS is empty. All rules generated are based on on-line type-2 fuzzy clustering. All free weights are learned by a gradient descent algorithm to improve the learning performance. Simulation results show that our approach yields smaller root mean squared errors than its rivals.