Subdivision methods for decreasing excess fuzziness of fuzzy arithmetic in fuzzified neural networks

When a fuzzy input vector is presented to a multi-layer feedforward neural network, the corresponding fuzzy output vector is calculated by fuzzy arithmetic. It is well known that fuzzy arithmetic involves excess fuzziness; we employ subdivision methods of interval input vectors for decreasing excess fuzziness included in fuzzy outputs from neural networks. First we examine a simple subdivision method where each level set of a fuzzy input vector is subdivided into many cells with the same size by uniformly subdividing all elements of the level set into multiple intervals. Next we examine a hierarchical subdivision method where each level set is subdivided into many cells with different sizes by iteratively subdividing a single element of a cell into two intervals. Finally we modify the hierarchical subdivision method for efficiently decreasing excess fuzziness.