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NN-driven fuzzy reasoning. (English) Zbl 0733.68074
Summary: A new fuzzy reasoning that can solve two problems of conventional fuzzy reasoning by combining an artificial neural network (NN) and fuzzy reasoning is proposed. These problems are (1) the lack of design for a membership function except a heuristic approach and (2) the lack of adaptability for possible changes in the reasoning environment. The proposed fuzzy reasoning approach solves these problems by using the learning function and nonlinearity of an NN. First, the problems involved in conventional fuzzy reasoning and the NN used in this paper are identified. Then a proposed algorithm is formulated and a concrete explanation using realistic data is developed. An example structure of an NN-driven fuzzy reasoning system is given, and two applications of this method are presented. This new fuzzy reasoning is capable of automatic determination of inference rules and adjustment according to the time- invariant reasoning environment because of the use of NN in fuzzy reasoning. This proposed method can be applied to NN modeling and AI and is considered from the standpoint of the explicit incorporation of knowledge into the NN structure.

68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
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[1] McCulloch, W.S.; Pitts, W., A logical calculus of the ideas imminent in nervous activity, Bull. math. biophys., 5, 115-133, (1943) · Zbl 0063.03860
[2] Rosenblatt, F., The perception: a probabilistic model for information storage and organization in the brain, Psychol. rev., 65, 6, 386-408, (1958)
[3] Rumelhart, D.E.; Hinton, G.E.; Williams, R.J., Learning representations by back-propagating errors, Nature, 323, 9, 533-536, (1986) · Zbl 1369.68284
[4] Funahashi, K., On the approximate realization of continuous mappings by neural networks, Neural networks, 2, 3, 183-192, (1989)
[5] Hayashi, I.; Takagi, H., Formulation of fuzzy reasoning by neural network, (), 55-60, (in Japanese)
[6] Takagi, H.; Hayashi, I., Artificial_neural_network-driven fuzzy reasoning, (), 217-218
[7] Kang, G.T.; Sugeno, M., Fuzzy modelling, Trans. soc. instrum. control eng., 23, 6, 650-652, (1987), (in Japanese)
[8] Kondo, T., Revised GMDH algorithm estimating degree of the complete polynomial, Trans. soc. instrum. control eng., 22, 9, 928-934, (1986), (in Japanese)
[9] Fujita, S.; Koi, H., Application of GMDH to environmental system modelling and management, (), 257-275
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