  An important constraint of Fuzzy Inference Systems (FIS) is their structured
rules defined based on evaluating all input variables. Indeed, the length of
all fuzzy rules and the number of input variables are equal. However, in many
decision-making problems evaluating some conditions on a limited set of input
variables is sufficient to decide properly (unstructured rules). Therefore,
this constraint limits the performance, generalization, and interpretability of
the FIS. To address this issue, this paper presents a neuro-fuzzy inference
system for classification applications that can select different sets of input
variables for constructing each fuzzy rule. To realize this capability, a new
fuzzy selector neuron with an adaptive parameter is proposed that can select
input variables in the antecedent part of each fuzzy rule. Moreover, in this
paper, the consequent part of the Takagi-Sugeno-Kang FIS is also changed
properly to consider only the selected set of input variables. To learn the
parameters of the proposed architecture, a trust-region-based learning method
(General quasi-Levenberg-Marquardt (GqLM)) is proposed to minimize
cross-entropy in multiclass problems. The performance of the proposed method is
compared with some related previous approaches in some real-world
classification problems. Based on these comparisons the proposed method has
better or very close performance with a parsimonious structure consisting of
unstructured fuzzy.
