A simplified implementation of hierarchical fuzzy systems

This paper aims to propose a simplified implementation of hierarchical fuzzy systems. A well-known problem for fuzzy logic systems (FLS) is that although the fuzzy logic system can be applied to model or to control a complex nonlinear system, the rules increase exponentially with the increase in the number of variables. To cope with this rule-explosion problem, a popular strategy is to hierarchically decompose a fuzzy system into a number of low-dimensional fuzzy systems, i.e., to build a hierarchical fuzzy system. In this paper, a simplified defuzzification–fuzzification algorithm is proposed to reduce the computational complexity in conventional hierarchical fuzzy systems. Based on the proposed algorithm, the middle-layer FLS in the hierarchical structure only needs an inference engine and the fuzzifier and defuzzifier can be eliminated. From simulation results, it can be seen that the feasibility of the modified hierarchical fuzzy logic algorithm can be ensured. Moreover, the computational efficiency can be improved by the proposed simplified defuzzification–fuzzification algorithm.