Complex neural fuzzy system and its application on multi-class prediction — A novel approach using complex fuzzy sets, IIM and multi-swarm learning

In this paper, we present a novel complex neural fuzzy approach to multi-class prediction. The complex neural fuzzy system (CNFS) is proposed using complex fuzzy sets (CFSs), fuzzy causalities and multi-swarm machine learning. In general, CFSs are regarded as advanced fuzzy sets with membership degrees defined in the unit disk of the complex plane, in contrast to regular fuzzy sets with membership degrees in the real-valued unit interval [0,1]. The proposed model is composed of the premises designed by CFSs, the consequences designed by Takagi–Sugeno linear functions, and a fuzzy causality layer connecting the premises toward the consequences, and it is able to perform prediction of multiple targets. The usage of fuzzy causality in the proposed model makes difference to traditional fuzzy models using If-Then rules, and gives the freedom and flexibility for model construction. To optimize the proposed CNFS, we present a hybrid learning scheme using the particle swarm optimization with multiple swarms (denoted as PSO_msw) and the Kalman filtering algorithm (denoted as KFA). In the hybrid learning method, the KFA updates the consequence parameters while the PSO_msw evolves the rest parameters of the model. The proposed approach has been tested with experiments using several real-world stock market datasets. Compared with other methods, the proposed approach has shown excellent performance.