模糊联想记忆网络理论及其在图象恢复技术中的应用

In this item a few of important fuzzy neural network (FNN) models, including FNN's based on triangular norm operators, fuzzy bi-directional associative memory, regular FNN's and neuro-fuzzy networks and so on, are studied from their topological architectures, performances and learning algorithms, comprehensively and systematically. The main results related are as following: (1) The discrimination conditions for global stability and Lypounov stability of fuzzy Hopfield networks and fuzzy bi-directional associative memory are established, and the transition laws of corresponding attractors are presented; (2) Fuzzy valued Berstein polynomials are used as the bridge to investigate the approximating capability of four-layer feed-forward regular FNN's, and the universal approximation problems related are solved, completely; (3) To simplify the equivalent conditions for universal approximations, a family of simple extended operations easy to realize are developed, and a novel FNN called as polygonal FNN is presented. Correspondingly, some simplified equivalent conditions for universal approximations are derived; (4) Within general framework the universal approximation problems related to neuro-fuzzy networks are investigated, thoroughly. With integral norm, both the general Mamdani fuzzy system and general Takagi-Sugeno fuzzy system are universal approximators. To study the universal approximation in random environments, the random Mamdani fuzzy system and random Takagi-Sugeno fuzzy system are defined, and with mean square sense this two random fuzzy systems are also universal approximators to a class of random processes. (5) Many learning algorithms are designed to realize the approximation procedures related. The above achievements are very important and essential to perfect the FNN theory. Also they provide us with the theoretic basis for another subject, i.e. image restoration techniques in the item. Fuzzy sets are employed to describe the gray levels of digital images. With the criterion of removing noises and preserving the fine structures of images, a family of fuzzy inference rules are established to develop FNN filters, by which the restoration images with high quality can be built from corrupted images degraded by high probability, even as 0.7 impulse noise. All kinds of simulation examples related are analyzed to demonstrate our conclusions.

对模糊联想记忆网络的结构及性能做系统的研究，寻求图象恢复技术中比前人更有效的处理方法。主要包括(1)内部运算基于模糊算子的前向模糊神经网络的性能及学习算法；(2)动态模糊神经网络的稳定性与容错性；(3)图象恢复的模糊模型及模糊神经网络求解技术。本课馐切畔⒖蒲ВШ腿斯ぶ悄芙徊娴谋咴笛Э疲扑慊蒲У闹匾。凶殴憷τ们熬啊