Extreme learning machine with fuzzy input and fuzzy output for fuzzy regression

Abstract

It is practically and theoretically significant to approximate and simulate a system with fuzzy inputs and fuzzy outputs. This paper proposes a extreme learning machine (ELM)-based fuzzy regression model ( $${{\rm FR}}_{{{\rm ELM}}}$$ ) in which both inputs and outputs are triangular fuzzy numbers. Algorithm for training $${{\rm FR}}_{{{\rm ELM}}}$$ is designed, and its computational complexity is analyzed. Furthermore, the convergence and error estimation for $${{\rm FR}}_{{{\rm ELM}}}$$ are discussed. Numerical simulations show that the proposed $${{\rm FR}}_{{{\rm ELM}}}$$ can effectively approximate a fuzzy input and fuzzy output system.