Multiple Function Approximation — A New Approach Using Asymmetric Complex Fuzzy Inference System

Abstract

This paper proposes an asymmetric complex fuzzy inference system (ACFIS) that improves a conventional fuzzy inference system (FIS) in two ways. First, the proposed model uses the novel neural-net-like aim–object parts, making the model flexible, in terms of model size of parameters and terse asymmetric structure. Second, the enhanced complex fuzzy sets (ECFSs) are used to expand membership degree from a single real-valued state to complex-valued vector state. Hence, the ACFIS can have the ability to predict multiple targets simultaneously. In addition, a hybrid learning algorithm, combining the particle swarm optimization (PSO) and the recursive least-square estimator (RLSE), is utilized to optimize the proposed model. To test the proposed approach, we did experimentation on four-function approximation using one single model only with 10 repeated trails. Based on the experimental results, the ACFIS has shown excellent performance.

Keywords

• multi-target prediction
• aim–object part
• asymmetric complex fuzzy inference system
• complex fuzzy set
• function approximation