Multiobjective Programming for Type-2 Hierarchical Fuzzy Inference Trees
  This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An
HFIT produces an optimum treelike structure, i.e., a natural hierarchical
structure that accommodates simplicity by combining several low-dimensional
fuzzy inference systems (FISs). Such a natural hierarchical structure provides
a high degree of approximation accuracy. The construction of HFIT takes place
in two phases. Firstly, a nondominated sorting based multiobjective genetic
programming (MOGP) is applied to obtain a simple tree structure (a low
complexity model) with a high accuracy. Secondly, the differential evolution
algorithm is applied to optimize the obtained tree's parameters. In the derived
tree, each node acquires a different input's combination, where the
evolutionary process governs the input's combination. Hence, HFIT nodes are
heterogeneous in nature, which leads to a high diversity among the rules
generated by the HFIT. Additionally, the HFIT provides an automatic feature
selection because it uses MOGP for the tree's structural optimization that
accepts inputs only relevant to the knowledge contained in data. The HFIT was
studied in the context of both type-1 and type-2 FISs, and its performance was
evaluated through six application problems. Moreover, the proposed
multiobjective HFIT was compared both theoretically and empirically with
recently proposed FISs methods from the literature, such as McIT2FIS,
TSCIT2FNN, SIT2FNN, RIT2FNS-WB, eT2FIS, MRIT2NFS, IT2FNN-SVR, etc. From the
obtained results, it was found that the HFIT provided less complex and highly
accurate models compared to the models produced by the most of other methods.
Hence, the proposed HFIT is an efficient and competitive alternative to the
other FISs for function approximation and feature selection.
