An improved structure learning algorithm of Bayesian Network based on the hesitant fuzzy information flow

Abstract The Bayesian Network (BN) is one of the most effective theoretical models in the fields of uncertain reasoning. With the nonlinear evolution of events and the complexity of practical problems, there will be massive data with uncertainty, bringing more challenges to the application of the BN. In this paper, by combining the advantages of the hesitant fuzzy set (HFS) in depicting uncertain information and the advantages of information flow (IF) in the causal analysis of nonlinear systems, an improved Particle Swarm Optimization (PSO) algorithm for the structure learning of the BN based on the hesitant fuzzy information flow (HFIF) is proposed. First, a new physical notion called HFIF is defined to depict the causal relationship between two intensive hesitant fuzzy variable sequences. Then the global causal analysis based on HFIF is conducted. By constructing an unconstrained optimization model, the initial structure and the optimized search space with the most significant causality are obtained, based on which, the approximate optimal structure by the PSO algorithm and the directions of the arcs by HFIF are determined at the same time. A specific implementation process of the structure learning based on the improved PSO algorithm under hesitant fuzzy environment is also presented. Moreover, the proposed algorithm is applied to the structure learning of ASIA network and BOBLO network. Comparisons between the proposed algorithm and traditional algorithms are conducted to demonstrate the effectiveness and advantages of the proposed algorithm in structure learning under hesitant fuzzy environment.