Hierarchical Flexible Beta Fuzzy Design by a Multi-Objective Evolutionary Hybrid Approach

This paper introduces a novel evolutionary approach for the automated modeling of efficient hierarchical or multilevel fuzzy systems. The proposed approach is formed by two principal learning stages: the first stage consists of using a proposed multi-objective algorithm called the multi-objective extended immune programming algorithm in order to evolve the architecture of the hierarchical fuzzy system. The use of such a step aims to optimize the structure of the hierarchical fuzzy system and to generate in the same time an accurate and an interpretable fuzzy system with a few number of fuzzy rules. In the second stage, the parameters of beta membership function parameters and the consequent parts of rules are tuned by applying the hybrid artificial bee colony algorithm. The proposed hybrid approach interleaves these two learning phases for the architecture learning and the parameter tuning until a near optimum hierarchical fuzzy system is generated. The efficiency of the methodology is evaluated through some well-known benchmark time-series problems, a nonlinear plant identification problem, and some high-dimensional classification data sets. Compared with other existing works, the proposed system proves its superiority in terms of reaching high accuracy, smaller rule-base, and good convergence speed.