  This paper provides an in-depth review of the optimal design of type-1 and
type-2 fuzzy inference systems (FIS) using five well known computational
frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS),
hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and
multi-objective fuzzy systems (MFS), which is in view that some of them are
linked to each other. The heuristic design of GFS uses evolutionary algorithms
for optimizing both Mamdani-type and Takagi-Sugeno-Kang-type fuzzy systems.
Whereas, the NFS combines the FIS with neural network learning systems to
improve the approximation ability. An HFS combines two or more low-dimensional
fuzzy logic units in a hierarchical design to overcome the curse of
dimensionality. An EFS solves the data streaming issues by evolving the system
incrementally, and an MFS solves the multi-objective trade-offs like the
simultaneous maximization of both interpretability and accuracy. This paper
offers a synthesis of these dimensions and explores their potentials,
challenges, and opportunities in FIS research. This review also examines the
complex relations among these dimensions and the possibilities of combining one
or more computational frameworks adding another dimension: deep fuzzy systems.
