Abstract-This paper presents a novel application of a hybrid learning approach to the optimisation of membership and non-membership functions of a newly developed interval type-2 intuitionistic fuzzy logic system (IT2 IFLS) of a TakagiSugeno-Kang (TSK) fuzzy inference system with neural network learning capability. The hybrid algorithms consisting of decoupled extended Kalman filter (DEKF) and gradient descent (GD) are used to tune the parameters of the IT2 IFLS for the first time. The DEKF is used to tune the consequent parameters in the forward pass while the GD method is used to tune the antecedents parts during the backward pass of the hybrid learning. The hybrid algorithm is described and evaluated, prediction and identification results together with the runtime are compared with similar existing studies in the literature. Performance comparison is made between the proposed hybrid learning model of IT2 IFLS, a TSK-type-1 intuitionistic fuzzy logic system (IFLS-TSK) and a TSK-type interval type-2 fuzzy logic system (IT2 FLS-TSK) on two instances of the datasets under investigation. The empirical comparison is made on the designed systems using three artificially generated datasets and three real world datasets. Analysis of results reveal that IT2 IFLS outperforms its type-1 variants, IT2 FLS and most of the existing models in the literature. Moreover, the minimal run time of the proposed hybrid learning model for IT2 IFLS also puts this model forward as a good candidate for application in real time systems.Index Terms-Interval type-2 intuitionistic fuzzy logic system; Decoupled extended Kalman filter; Gradient descent algorithm.

Abstract-This paper presents an approach to prediction based on a new interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of Takagi-Sugeno-Kang (TSK) fuzzy inference. The gradient descent algorithm (GDA) is used to adapt the parameters of the IT2IFLS. The empirical comparison is made on the designed system using two synthetic datasets. Analysis of our results reveal that the presence of additional degrees of freedom in terms of non-membership functions and hesitation indexes in IT2IFLS tend to reduce the root mean square error (RMSE) of the system compared to a type-1 fuzzy logic approach and some interval type-2 fuzzy systems.

This paper presents an approach to prediction based on a new interval type-2 Atanassov-intuitionistic fuzzy logic system (IT2AIFLS) of Takagi-Sugeno-Kang (TSK) fuzzy inference with neural network learning capability. The gradient descent (GD) algorithm is used to adapt the parameters of the IT2AIFLS. The empirical comparison is made on the designed system using some benchmark regression problems -both artificial and real world datasets. Analyses of our results reveal that IT2AIFLS outperforms its type-1 variant, other type-1 fuzzy logic approaches and some type-2 fuzzy systems in the regression tasks. The reason for the improved performance of the proposed framework of IT2AIFLS is because of the introduction of nonmembership functions and intuitionistic fuzzy indices into the classical IT2FLS model. This increases the level of fuzziness in the proposed IT2AIFLS framework, thus providing more accurate approximations than AIFLS, classical type-1 and interval type-2 fuzzy logic systems.

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