Integrated Methods Of Rough Sets And Neural Network And Their Applications In Pattern Recognition

The theory of rough sets is a powerful tool for processing uncertain, incomplete and imprecise information and it has become an important branch of uncertain computing. Analysis and modeling based on rough sets, which cover three kinds of human logical thinking, i.e. inductive reasoning, deductive reasoning and common sense reasoning, directly imitate human logical thinking ability. While as another important branch of uncertain computing, the neural network, which constructed by numerous of inter-connective neurons, shows powerful non-linear mapping, adaptive, self-learning, robust and fault-tolerant ability. And it is the mimic of human imaginal thinking. Due to complementary advantages in mode of information processing, knowledge acquisition, anti-noise capability and generalization ability, etc., rough neural network, which integrates rough sets and neural network technologies, reflects some characteristics of human intelligent, i.e. it is the compound of qualitative and quantitative, clear and implied, serial and parallel. Then the research of rough neural network certainly has leading, scientific and superior characteristics. As an important branch of present intelligent integration system, rough neural network promises to be the main technology to develop next generation expert system.A series of exploration and research are done in rough neural network by improving the information processing ability, building new decision system modeling methods, extending application fields and solving the problem of easily constructing and computing complexity. And the thesis proposes some new rough neural network integration methods and applies them to pattern recognition.The paper summarizes and generalizes the rough neural network integration methods that has been developed for last decade and categorizes them into three main integration modes, i.e. rough sets and neural network general integration system, rough boundary value neural network and rough-granular neural network. And present research status of each integration mode, also the principle and characteristic of them are analyzed and expounded in this paper.Be different from conventional literatures, where rough neural networks were studied based on rough sets data analysis and reduction. In this paper, based on rough logic theory, the design of rough neural network model with fuzzy neurons under the meaning of rough logic is studied. And the characteristics of rough logic neural network and fuzzy logic neural network are analyzed and compared. The validity of the rough logic neural network model can be verified in the land cover classification experiment of the Landsat TM remote sensing image of Chongqing area and Changbai moutain area. Moreover, the rough logic neural network indicates superiorities at the aspect of structure and convergence.A FRNN (Fuzzy Rough Neural Network) model, which is constructed by fuzzy neurons and rough neurons, is proposed by adding a fuzzy neuron layer between input layer and hidden layer. Due to indifferentiable feature of rough neurons, BP algorithm can't be adopted again. Thus a kind of GA (Genetic Algorithm) integrating with mountain climbing is applied to tune the weights of the FRNN. And the local search efficiency for optimum solution is improved in the later period of learning process. The results of simulation indicate that the FRNN, which integrates the ability to deal with fuzzy information and rough information, has better performance than BP network and rough neural network that constructed only by rough neurons in image fusion for filtering. Thus the FRNN is a kind of hybrid intelligent neural network that has good performance.Because fuzzy uncertainty and rough uncertainty are often both exist in information system, so fuzzy rough sets theory is needed to process them. A FRMFN (Fuzzy-Rough Membership Function Neural Network) model is established based on fuzzy-rough sets theory. The FRMFN reserves original fuzzy information, at the same time the rough uncertainty decreases at a large extent. The test results of classification for remote sensing image and vowel characters indicate that the FRMFN has better classification precision than RBF (Radial Basis Function) network. And it has the same merit of quick learning as RBF network.Application system designed by conventional Pawlak rough sets data analysis method has the defects of weak generalization and poor anti-noise ability. To better tackle these problems, the design of the rough neural network based on variable precision rough set model, in which the majority inclusion relation is used, is studied. Here the condition ofβ-approximation reduction is generalized. And the criteria for selecting an appropriateβ-approximation reduction, which based on the analysis of abnormal reduction and example is introduced. Moreover, the algorithm for extracting variable rough decision rules and computing related stableβ-threshold interval is introduced. In the experiment of the Brodatz texture image classification, the performances of conventional RNN (Rough Neural Network) and VPRNN (Variable Precision Rough Set Neural Network) are compared. The results indicate that VPRNN not only has more simplified structure and costs less training time, but also, because of its powerful approximate decision-making ability, has better generalization ability than RNN.Neural network ensemble based on rough sets reduction is proposed to decrease the computing complexity of conventional feature ensemble selection algorithms. Firstly, a dynamic reduction method, which integrates genetic algorithm and resample technology, is introduced. Then dynamic reduction method is used to get reduct sets that have stable and good generalization ability. Secondly, Multiple BP neural networks based on different reducts are built as base classifiers. And according to the idea of selection ensemble, the best generalization ability neural network ensemble can be found by some search strategies. Finally, classification based on neural network ensemble can be implemented by combination with vote rule. The method is verified in the experiment of classifying Landsat 7 bands remote sensing image of an area. Since a great number feature sets of poor performance were discarded by reduction based on rough sets. Thus compared with conventional feature selection algorithms, the method needs less time, has lower computing complexity, and the performance is satisfied.Generalization ability of ensemble networks can be improved if the diversity of the individual network be increased. Considering to this point, here, Rough_Boosting and Rough_Bagging are proposed as new individual network building algorithms. First, the training samples are disturbed by Boosting or Bagging methods, then, based on rough sets theory, proper attributes are selected by finding relative reducts. Thus, the mechanism of disturbing training data and the input attribute are combined to help generate accurate and diverse component networks. Experiment results show that the generalization ability of proposed method obviously better than that of Boosting and Bagging methods, and individual networks generated have more diversity than that of Boosting or Bagging. Compared with prevailing similar methods, the proposed method has close or corresponsive performance.While designing RBF network by conventional clustering methods, it is often contain blindness and subjectivity. And clustering result is sensitive to the value of initial status. Because only consider the similarity of the samples in input feature space, while their class label are not taken into account, so the clustering can't completely reflect the mapping relationship between input and output variables. Thus a method of designing RBF neural network, which based on a supervised rough clustering method by partition under indiscernibility relation, is proposed. Therein, continuous attributes are discretized by Boolean reasoning algorithm and original decision modes are generated. Then similarities among original decision modes can be measured by dissimilarity degree and original decision modes can be clustered. At last, final clustered decision modes are used to construct RBF neural network. Because the linear weights of output layer and nonlinear base function parameters of hidden layer are updated on different time scales , to quicken the training speed, a hybrid training algorithm is introduced in which the parameters of hidden layer and weights of output layer are tuned by back propagation algorithm and linear least squares filtering, respectively. Results of experiment indicate that the designed RBF neural network has refined structure and powerful generalization ability. And hybrid training algorithm has more rapid convergence speed than single back propagation algorithm.A rough logic neural network model with variable discretization precision is proposed to solve the contradiction between network precision and the size of network as well as generalization ability. Based on the approximation area partition, the universe can be partitioned into certain area and possible area. Because the important reason of misclassification is that the granularity of possible area is too coarse. Therefore, in this work, only possible area is refined and the precision of the rough logic neural network is improved while the size of network can be restrained. In the experiment of the remote sensing image classification about Changbai mountain area, the performance of conventional method achieves best when the discretization level is 7. While, the most approximate result is acquired, and less network cost and training time are expended, when this method is used.To avoid reduct calculation, under the view of bottom-up, a method based on FRM (fuzzy rough model) to construct rough neural network model, FRM_RNN_M, is addressed. By means of adaptive Gaustafason-Kessel (G-K) algorithm, fuzzy partition can be implemented in input-output product space. Then based on the search of cluster number and feature reduction sets, optimum FRM can be extracted and rough neural network model can be constructed by integrating neural network technique. The experiment results of classifying Brodatz texture image indicate that:①FRM_RNN_M is superior to conventional Bayesian and LVQ methods;②FRM_RNN_M has more powerful synthesis decision-making ability than single FRM model. And better optimum FRM will be searched if feature reduction is considered;③Compared with conventional RLNN (Rough Logic Neural Network), the neural network based on FRM_RNN_M has superiorities in structure, convergence speed and generalization ability. As a universal method for decision system modeling, the proposed method can be widely used in related fields.In the end, the main innovations of the thesis are summarized, and the fields for further investigation are expected.