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窗体顶端 Self-organizing polynomial neural networks based on polynomial and fuzzy polynomial neurons: analysis and design??Original Research ArticleFuzzy Sets and Systems, Volume 142, Issue 2, 1 March 2004, Pages 163-198Sung-Kwun Oh, Witold Pedrycz ?Close preview??|?? Related articles??|??Related reference work articles???? AbstractAbstract | ReferencesReferences Abstract In this study, we introduce and investigate a class of neural architectures of polynomial neural networks (PNNs), develop a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose structure (topology) is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated on the fly. In this sense, PNN is a self-organizing network. We distinguish between two kinds of SOPNN architectures, that is, (a) polynomial neuron (PN) based and (b) fuzzy polynomial neuron (FPN) based self-organizing networks. This taxonomy is based on the character of each neuron structure in the network. Each of them comes with two structures referred here to as basic and the modified topology. Moreover, for each topology of the SOPNN we identify two types that is a generic and advanced type. The essence of the design procedure of self-organizing polynomial neural networks (SOPNN) dwells on the group method of data handling (GMDH) (IEEE Trans. Systems Man and Cybernet. 12 (1971) 364). Each node of the PN based SOPNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. FPN based SOPNN dwells on the ideas of fuzzy rule-based computing and neural networks. Especially in FPN based SOPNN, the generic rules in the system assume the form “if A then y = P(x)” where A is a fuzzy relation in the condition space while P(x) is a polynomial forming a conclusion part of the rule. Each FPN (processing element) consists of a series of th