A New Rule Reduction Method for Fuzzy Modeling

The Takagi-Sugeno fuzzy model (T-S fuzzy model) has been successfully applied to a wide range of problems due to its accurate modeling ability. However, its rule redundancy and dimension disaster remain an open and unsolved issue. In this article, a novel fuzzy modeling method is proposed to reduce the fuzzy rule number without a loss in modeling accuracy. It includes two novel mechanisms: the rule fusion mechanism and the space projection mechanism. The rule fusion mechanism is developed to merge several rules into one according to similarity. In this way, the number of rules will greatly decrease. After the rules are merged, the relationship of data is strongly nonlinear, which renders the local linear model ineffective. In order to alleviate this difficulty, the space projection mechanism is then proposed to project the low-dimensional feature space to a high-dimension space. In this high-dimension space, the relation of data is linear and easily represented by a linear model. In this way, the traditional fuzzy inference is still applicative. With the help of these two mechanisms, a fuzzy model with few rules is constructed, which enables reconstruction of the nonlinear system. A solving method is then developed to determine the optimal parameters of the fuzzy model. Additional analysis and proof show that the proposed method exhibits the uniform approximation ability for strongly nonlinear systems. Case studies not only demonstrate the effectiveness of the proposed method, but also demonstrate its superior modeling performance in comparison to several conventional fuzzy modeling methods, even with the use of fewer rules.