Interpolation of fuzzy if-then rules by neural networks

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A number of approaches have been proposed for implementing fuzzy if-then rules with trainable multilayer feedforward neural networks. In these approaches, learning of neural networks is performed for fuzzy inputs and fuzzy targets. Because the standard back-propagation (BP) algorithm cannot be directly applied to fuzzy data, transformation of fuzzy data into non-fuzzy data or modification of the learning algorithm is required. Therefore the approaches for implementing fuzzy if-then rules can be classified into two main categories: introduction of preprocessors of fuzzy data and modification of the learning algorithm. In the first category, the standard BP algorithm can be employed after generating non-fuzzy data from fuzzy data by preprocessors. Two kinds of preprocessors based on membership values and level sets are examined in this paper. In the second category, the standard BP algorithm is modified to directly handle the level sets (i.e., intervals) of fuzzy data. This paper examines the ability of each approach to interpolate sparse fuzzy if-then rules. By computer simulations, high fitting ability of approaches in the first category and high interpolating ability of those in the second category are demonstrated.