  In this paper, a new interval type-2 fuzzy neural network able to construct
non-separable fuzzy rules with adaptive shapes is introduced. To reflect the
uncertainty, the shape of fuzzy sets considered to be uncertain. Therefore, a
new form of interval type-2 fuzzy sets based on a general Gaussian model able
to construct different shapes (including triangular, bell-shaped, trapezoidal)
is proposed. To consider the interactions among input variables, input vectors
are transformed to new feature spaces with uncorrelated variables proper for
defining each fuzzy rule. Next, the new features are fed to a fuzzification
layer using proposed interval type-2 fuzzy sets with adaptive shape.
Consequently, interval type-2 non-separable fuzzy rules with proper shapes,
considering the local interactions of variables and the uncertainty are formed.
For type reduction the contribution of the upper and lower firing strengths of
each fuzzy rule are adaptively selected separately. To train different
parameters of the network, the Levenberg-Marquadt optimization method is
utilized. The performance of the proposed method is investigated on clean and
noisy datasets to show the ability to consider the uncertainty. Moreover, the
proposed paradigm, is successfully applied to real-world time-series
predictions, regression problems, and nonlinear system identification.
According to the experimental results, the performance of our proposed model
outperforms other methods with a more parsimonious structure.
