Improving the interpretability of Takagi-Sugeno fuzzy model by using linguistic modifiers and a multiple objective learning scheme

We present a new Tagaki-Sugeno (TS) type model whose membership functions (MFs) are characterized by linguistic modifiers. As a result, during adaptation, the trained local models tend to become the tangents of the global model, leading to good model interpretability. In order to prevent the global approximation ability from being degraded, an index of fuzziness is proposed to evaluate linguistic modification for MFs with adjustable crossover points. A new learning scheme is also developed, which uses the combination of global approximation error and the fuzziness index as its objective function. By minimizing the multiple objective performance measure, a tradeoff between the global approximation and local model interpretation can be achieved. Experimental results show that by the proposed method, good interpretation of local models and transparency of input space partitioning can be obtained for the TS model, while at the same time the global approximation ability is still preserved.