Heuristic design of fuzzy inference systems: A review of three decades of research

TL;DR

This review comprehensively analyzes three decades of research on heuristic design of fuzzy inference systems, covering five computational frameworks and their integration, challenges, and future directions.

Contribution

It synthesizes developments in heuristic fuzzy system design over 30 years, highlighting the interrelations and potential of combining multiple frameworks including deep fuzzy systems.

Findings

Genetic-fuzzy systems optimize fuzzy models using evolutionary algorithms.

Neuro-fuzzy systems enhance approximation through neural network integration.

Hierarchical fuzzy systems address high-dimensionality challenges.

Abstract

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.