In the last one hundred years, the mankind has invented a lot of convenient tools for pursuing beautiful and comfortable living environment. Computer is one of the most important inventions, and its operation ability is incomparable with the mankind. Because computer can deal with a large amount of data fast and accurately, people use this advantage to imitate human thinking. Artificial intelligence is developed extensively. Methods, such as all kinds of neural networks, data mining, fuzzy logic, etc., apply to each side fields (ex: fingerprint distinguishing, image compressing, antennal designing, etc.). We will probe into to prediction technology according to the decision tree and fuzzy clustering. The fuzzy decision tree proposed the classification method by using fuzzy clustering method, and then construct out the decision tree to predict for data. However, in the distance function, the impact of the target space was proportional inversely. This situation could make problems in some dataset. Besides, the output model of each leaf node represented by a constant restricts the representation capability about the data distribution in the node. We propose a more reasonable definition of the distance function by considering both input and target differences with weighting factor. We also extend the output model of each leaf node to a local linear model and estimate the model parameters with a recursive SVD-based least squares estimator. Experimental results have shown that our improved version produces higher recognition rates and smaller mean square errors for classification and regression problems, respectively.

We propose a novel approach for building a type-2 neuro-fuzzy system from a given set of input-output training data. For an input pattern, a corresponding crisp output of the system is obtained by combining the inferred results of all the rules into a type-2 fuzzy set which is then defuzzified by applying a type reduction algorithm. Karnik and Mendel proposed an algorithm, called KM algorithm, to compute the centroid of an interval type-2 fuzzy set efficiently. Based on this algorithm, Liu developed a centroid type-reduction strategy to do type reduction for type-2 fuzzy sets. A type-2 fuzzy set is decomposed into a collection of interval type-2 fuzzy sets by £\-cuts. Then the KM algorithm is called for each interval type-2 fuzzy set iteratively. However, the initialization of the switch point in each application of the KM algorithm is not a good one. In this thesis, we present an improvement to Liu's algorithm. We employ the result previously obtained to construct the starting values in the current application of the KM algorithm. Convergence in each iteration except the first one can then speed up and type reduction for type-2 fuzzy sets can be done faster. The efficiency of the improved algorithm is analyzed mathematically and demonstrated by experimental results. Constructing a type-2 neuro-fuzzy system involves two major phases, structure identification and parameter identification. We propose a method which incorporates self-constructing fuzzy clustering algorithm and a SVD-based least squares estimator for structure identification of type-2 neuro-fuzzy modeling. The self-constructing fuzzy clustering method is used to partition the training data set into clusters through input-similarity and output-similarity tests. The membership function associated with each cluster is defined with the mean and deviation of the data points included in the cluster. Then applying SVD-based least squares estimator, a type-2 fuzzy TSK IF-THEN rule is derived from each cluster to form a fuzzy rule base. After that a fuzzy neural network is constructed. In the parameter identification phase, the parameters associated with the rules are then refined through learning. We propose a hybrid learning algorithm which incorporates particle swarm optimization and a SVD-based least squares estimator to refine the antecedent parameters and the consequent parameters, respectively. We demonstrate the effectiveness of our proposed approach in constructing type-2 neuro-fuzzy systems by showing the results for two nonlinear functions and two real-world benchmark datasets. Besides, we use the proposed approach to construct a type-2 neuro-fuzzy system to forecast the daily Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX). Experimental results show that our forecasting system performs better than other methods.