A centroid type-reduction strategy for computing the centroids of type-2 fuzzy sets based on decomposed α-planes was proposed by Liu. However, it cannot be applied to type-2 fuzzy sets with concave secondary membership functions. In this paper, we extend the Liu's method so that the centroids of type-2 fuzzy sets with concave secondary membership functions can be derived. For each decomposed α-plane, we convert it into a group of interval type-2 fuzzy sets. The union of the centroids of its member interval type-2 fuzzy sets constitutes the centroid of the α-plane. Then, the weighted union of the centroids of the decomposed α-planes becomes the centroid type-reduced set of the original type-2 fuzzy set. When dealing with type-2 fuzzy sets with convex secondary membership functions, our proposed method is reduced to the Liu's method.

We propose a fuzzy based method for multilabel text classification in which a document can belong to one or more than one category. In text categorization, the number of the involved features is usually huge, causing the curse of the dimensionality problem. Besides, a category can be a nonconvex region, which is a union of several overlapping or disjoint subregions. An automatic classification system, thus, may suffer from large memory requirements or poor performance. By incorporating fuzzy techniques, our proposed method can overcome these issues. A fuzzy relevance measure is adopted to transform high-dimensional documents to low-dimensional fuzzy relevance vectors to avoid the curse of dimensionality problem. A clustering technique is used to divide the relevance space into a collection of subregions which are then combined to make up individual categories. This allows complex and nonconvex regions to be created. A number of experiments are presented to show the effectiveness of the proposed method in both performance and speed.

Measuring the similarity between documents is an important operation in the text processing field. In this paper, a new similarity measure is proposed. To compute the similarity between two documents with respect to a feature, the proposed measure takes the following three cases into account: a) The feature appears in both documents, b) the feature appears in only one document, and c) the feature appears in none of the documents. For the first case, the similarity increases as the difference between the two involved feature values decreases. Furthermore, the contribution of the difference is normally scaled. For the second case, a fixed value is contributed to the similarity. For the last case, the feature has no contribution to the similarity. The proposed measure is extended to gauge the similarity between two sets of documents. The effectiveness of our measure is evaluated on several real-world data sets for text classification and clustering problems. The results show that the performance obtained by the proposed measure is better than that achieved by other measures.

The multivalued neuron with periodic activation function (MVN-P) was proposed by Aizenberg for solving classification problems. The boundaries between two distinct categories are crisply specified in MVN-P, which may result in slow convergence or being unable to converge at all in the learning process. In this paper, we propose a revised model of MVN-P based on the idea of unsharp boundaries. In this revised model, a fuzzy buffer is provided around a boundary between two distinct categories, allowing incorrect assignments with membership degree less than a threshold to be tolerated in the training phase. Genetic algorithms are applied to derive optimal values for the parameters involved in this model, alleviating the burden of setting them manually by the user. Besides, MVN-P has difficulties solving the classification problems having a large number of categories. A tree structure is developed to overcome these difficulties. Simulation results demonstrate the effectiveness of our proposed ideas.

Discrete Multi-valued Neuron (MVN) was proposed for solving classification problems. The neuron has an activation function which is used to create an output value for an input instance. The learning algorithm associated with discrete MVN was designed for multi-class classification. However, the algorithm can never converge for the cases of two-class classification. In this paper, we propose a revised activation function to overcome this difficulty. A concept of tolerating areas is included. Another scheme adopting new targets is also proposed to work with discrete MVN. Simulation results show that the proposed ideas can improve the performance of discrete MVN.

Multi-valued neuron (MVN) is an efficient technique for classification and regression. It is a neuron with complex-valued weights and inputs/output, and the output of the activation function is moving along the unit circle on the complex plane. Therefore, MVN may have more functionalities than sigmoidal or radial basis function neurons. In some cases, a pair of weighted sums would oscillate between two sectors and the learning process can hardly converge. Besides, many weighted sums may be located around the borders of each sector, which may cause bad performance in classification accuracy. In this paper, we propose two modifications of multivalued neuron. One is involved with moving boundaries and the other one with targets at the center of sectors. Experimental results show that the proposed modifications can improve the performance of MVN and help it to converge more efficiently.

In this paper, we give a comparison of four methods for solving clustering problems, including similarity-based fuzzy clustering (SFC), elliptic basis function (EBF), versatile elliptic basis function (VEBF), and similarity-based fuzzy clustering with principal component analysis (PCSFC). PCSFC is a modified version of SFC with rotation, while VEBF is a refined version of EBF. SFC and PCSFC are based on Gaussian functions, and EBF and VEBF are based on elliptic basis functions. Each method is briefly described, together with the pros and cons of the solution it provides. Simulation results are presented to compare the induced errors between true values and predicted values obtained from using different methods to do clustering for benchmark data sets.

Neuro-fuzzy systems have been proposed for different applications for many years. In this paper, a k-NN based neuro-fuzzy predictor is developed for time series prediction. We use a neuro-fuzzy system to generate prediction results. A set of fuzzy rules can be generated by a self-constructing clustering method. These rules can be refined by a hybrid learning algorithm. In stead of using all training data to training a model, we utilize the k-NN method to dynamically select k instances for each prediction. Experimental results show that our approach can provide more accurate predictions than other methods.

Singular value decomposition (SVD) is a popular decomposition method for solving least squares estimation (LSE) problems. However, for large data sets, applying SVD directly on the coefficient matrix is very time consuming and memory demanding in obtaining least squares solutions. In this paper, we propose an iterative divide-and-merge-based estimator for solving large-scale LSE problems. Iteratively, the LSE problem to be solved is processed and transformed to equivalent but smaller LSE problems. In each iteration, the input matrices are subdivided into a set of small submatrices. The submatrices are decomposed by SVD, respectively, and the results are merged, and the resulting matrices become the input of the next iteration. The process is iterated until the resulting matrices are small enough which can then be solved directly and efficiently by SVD. The number of iterations required is determined dynamically according to the size of the input data set. As a result, the requirements in time and space for finding least squares solutions are greatly improved. Furthermore, the decomposition and merging of the submatrices in each iteration can be independently done in parallel. The idea can be easily implemented in MapReduce and experimental results show that the proposed approach can solve large-scale LSE problems effectively.

Type reduction does the work of computing the centroid of a type-2 fuzzy set. The result is a type-1 fuzzy set from which a corresponding crisp number can then be obtained through defuzzification. Type reduction is one of the major operations involved in type-2 fuzzy inference. Therefore, making type reduction efficient is a significant task in the application of type-2 fuzzy systems. Liu introduced a horizontal slice representation, called the α-plane representation, and proposed a type-reduction method for a type-2 fuzzy set. By exploring some useful properties of the α-plane representation and of the type reduction for interval type-2 fuzzy sets, a fast method is developed for computing the centroid of a type-2 fuzzy set. The number of computations and comparisons involved is greatly reduced. Convergence in each iteration can then speed up, and type reduction can be done much more efficiently. The effectiveness of the proposed method is analyzed mathematically and demonstrated by experimental results.

Karnik and Mendel proposed an 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 carry out 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 Karnik-Mendel algorithm is called for each interval type-2 fuzzy set iteratively. However, the initialization of the switch point in each application of the Karnik-Mendel algorithm is not a good one. In this paper, we present an improvement to Liu's algorithm. We employ the previously obtained result to construct the starting values in the current application of the Karnik-Mendel algorithm. Convergence in each iteration, except the first one, can then speed up, and type reduction for type-2 fuzzy sets can be carried out faster. The efficiency of the improved algorithm is analyzed mathematically and demonstrated by experimental results.

Feature clustering is a powerful method to reduce the dimensionality of feature vectors for text classification. In this paper, we propose a fuzzy similarity-based self-constructing algorithm for feature clustering. The words in the feature vector of a document set are grouped into clusters, based on similarity test. Words that are similar to each other are grouped into the same cluster. Each cluster is characterized by a membership function with statistical mean and deviation. When all the words have been fed in, a desired number of clusters are formed automatically. We then have one extracted feature for each cluster. The extracted feature, corresponding to a cluster, is a weighted combination of the words contained in the cluster. By this algorithm, the derived membership functions match closely with and describe properly the real distribution of the training data. Besides, the user need not specify the number of extracted features in advance, and trial-and-error for determining the appropriate number of extracted features can then be avoided. Experimental results show that our method can run faster and obtain better extracted features than other methods.

We propose a novel approach for building a type-2 neural-fuzzy system from a given set of input-output training data. A self-constructing fuzzy clustering method is used to partition the training dataset 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 a type-2 fuzzy Takagi-Sugeno-Kang IF-THEN rule is derived from each cluster to form a fuzzy rule base. A fuzzy neural network is constructed accordingly and the associated parameters are refined by a hybrid learning algorithm which incorporates particle swarm optimization and a least squares estimation. For a new input, 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 refined type reduction algorithm. Experimental results are presented to demonstrate the effectiveness of our proposed approach.

A novel Takagi-Sugeno-Kang (TSK) type fuzzy neural network which uses general type-2 fuzzy sets in a type-2 fuzzy logic system, called general type-2 fuzzy neural network (GT2FNN), is proposed for function approximation. The problems of constructing a GT2FNN include type reduction, structure identification, and parameter identification. An efficient strategy is proposed by using alpha-cuts to decompose a general type-2 fuzzy set into several interval type-2 fuzzy sets to solve the type reduction problem. Incremental similarity-based fuzzy clustering and linear least squares regression are combined to solve the structure identification problem. Regarding the parameter identification, a hybrid learning algorithm (HLA) which combines particle swarm optimization (PSO) and recursive least squares (RLS) estimator is proposed for refining the antecedent and consequent parameters, respectively, of fuzzy rules. Simulation results show that the resulting networks obtained are robust against outliers.

A novel approach with an incremental fuzzy clustering algorithm for vector quantization of images is proposed. For compression, a given image is divided into blocks of training vectors, and fuzzy clusters are generated progressively from those vectors. The obtained fuzzy clusters become the code-book from which the entire image is transformed into a sequence of indices. For decompression, the indices are decoded and the image is reconstructed. The advantages of our approach are that clusters generated are compact and dense, the real distribution of training vectors can be captured, and training vectors can be represented by prototyping clusters more appropriately. Experimental results have shown that our method can achieve a higher compression ratio and produce a smaller error than other methods.

Pedrycz and Sosnowski proposed C-fuzzy decision trees based on information granulation. The tree grows gradually by using fuzzy C-means clustering algorithm to split the patterns in a selected node with the maximum heterogeneity into C corresponding children nodes. However, the distance function was only defined on the input difference between a pattern and a cluster center, causing difficulties in some cases. 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 the input and output differences with weighting factors. 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.

The selection and learning of kernel functions is a very important but rarely studied problem in the field of support vector learning. However, the kernel function of a support vector machine has great influence on its performance. The kernel function projects the dataset from the original data space into the feature space, and therefore the problems which can not be done in low dimensions could be done in a higher dimension through the transform of the kernel function. In this paper, we introduce the gradient descent method into the learning of kernel functions. Using the gradient descent method, we can conduct learning rules of the parameters which indicate the shape and distribution of the kernel functions. Therefore, we can obtain better kernel functions by training of their parameters with respect to the risk minimization principle. The experimental results have shown that our approach can derive better kernel functions and thus has better generalization ability than other methods.

The selection and modification of kernel functions is a very important but rarely studied problem in the field of support vector learning. However, the kernel function of a support vector machine has great influence on its performance. The kernel function projects the dataset from the original data space into the feature space, and therefore the problems which can't be done in low dimensions could be done in a higher dimension through the transform of the kernel function. In this paper, we adopt the FCM clustering algorithm to group data patterns into clusters, and then use a statistical approach to calculate the standard deviation of each pattern with respect to the other patterns in the same cluster. Therefore we can make a proper estimation on the distribution of kernel functions. Experimental results have shown that our approach can derive better kernel functions than other methods, and also can have better learning and generalization abilities.

We propose a new representation of calendars such that users can specify fuzzy calendar constraints to discover asynchronous periodical association rules embedded in temporal databases. We borrow the fuzzy set theory and use the conjunction operation to construct fuzzy calendar patterns and each fuzzy calendar pattern represents an asynchronous periodical behavior. Moreover, different time intervals have different weights corresponding to their matching degrees to the specified fuzzy calendar pattern. An efficient algorithm is also proposed to find association rules with the specified fuzzy calendar pattern. Unlike level wise a priori-based approaches, our method scans the underlying database at most twice. In the first scan, frequent 2-itemsets with their weighted counts in the specified fuzzy calendar pattern are obtained and then all candidate item sets are generated from the discovered frequent 2-itemsets. Finally, all frequent item sets with their weighted counts in the specified fuzzy calendar pattern are discovered in one shot. Asynchronous periodical association rules in the specified fuzzy calendar pattern are then obtained

We develop a neurofuzzy network technique to extract TSK-type fuzzy rules from a given set of input-output data for system modeling problems. Fuzzy clusters are generated incrementally from the training dataset, and similar clusters are merged dynamically together through input-similarity, output-similarity, and output-variance tests. The associated membership functions are defined with statistical means and deviations. Each cluster corresponds to a fuzzy IF-THEN rule, and the obtained rules can be further refined by a fuzzy neural network with a hybrid learning algorithm which combines a recursive singular value decomposition-based least squares estimator and the gradient descent method. The proposed technique has several advantages. The information about input and output data subspaces is considered simultaneously for cluster generation and merging. Membership functions match closely with and describe properly the real distribution of the training data points. Redundant clusters are combined, and the sensitivity to the input order of training data is reduced. Besides, generation of the whole set of clusters from the scratch can be avoided when new training data are considered.

Temporal expressions are widely used in our daily life. Calendar algebra has been studied for years to provide a formal specification for constructing temporal expressions. However, temporal requirements specified by human beings tend to be ill-defined or uncertain. To deal with such kind of uncertain information, we propose the fuzzy calendar algebra which allows users to describe desired temporal expressions easily and naturally. The operations provided reflect the way in which people reason about temporal requirements in daily life. By using the fuzzy calendar algebra, users can define complicated calendars with multiple time granularities in which different time intervals can have different weights according to their matching degrees to the specified calendar. This can help users to discover the knowledge in the time intervals that are of interest to them. We show the usefulness of the algebra by incorporating it with an incremental data miner to mine fuzzy temporal association rules from temporal databases.

Sperduti and Starita proposed a new type of neural network which consists of generalized recursive neurons for classification of structures. In this paper, we propose an entropy-based approach for constructing such neural networks for classification of acyclic structured patterns. Given a classification problem, the architecture, i.e., the number of hidden layers and the number of neurons in each hidden layer, and all the values of the link weights associated with the corresponding neural network are automatically determined. Experimental results have shown that the networks constructed by our method can have a better performance, with respect to network size, learning speed, or recognition accuracy, than the networks obtained by other methods.

We propose a data mining system for discovering interesting temporal patterns from large databases. The mined patterns are expressed in fuzzy temporal association rules which satisfy the temporal requirements specified by the user. Temporal requirements specified by human beings tend to be ill-defined or uncertain. To deal with this kind of uncertainty, a fuzzy calendar algebra is developed to allow users to describe desired temporal requirements in fuzzy calendars easily and naturally. Fuzzy operations are provided and users can define complicated fuzzy calendars to discover the knowledge in the time intervals that are of interest to them. A border-based mining algorithm is proposed to find association rules incrementally. By keeping useful information of the database in a border, candidate itemsets can be computed in an efficient way. Updating of the discovered knowledge due to addition and deletion of transactions can also be done efficiently. The kept information can be used to help save the work of counting and unnecessary scans over the updated database can be avoided. Simulation results show the effectiveness of the proposed system. A performance comparison with other systems is also given.

The Distributed Coordination Function (DCF) which uses Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) and binary slotted exponential backoff scheme is the basis of the IEEE 802.11 Medium Access Control (MAC) protocol. However the DCF is not suitable for real-time traffic control since the backoff scheme may cause huge packet delay and jitter. We propose a modified DCF which uses a forward backoff scheme to remedy this disadvantage. In addition, a call admission control (CAC) is also proposed. Our protocols can guarantee service qualities such as the network throughput, packet delay, and jitter for real-time traffic. Besides, the modified DCF is still compliant with the IEEE 802.11 standard. Simulation results have shown that our method performs better than other DCF disciplines.

We propose a neuro-fuzzy approach for segmentation of human objects. A fuzzy self-clustering technique is used to divide the video frame into a set of segments. The existence of a face within a candidate face region is ensured by searching for possible constellations of eye-mouth triangles and verifying each eye-mouth combination with the predefined template. Then rough foreground and background are formed based on a combination of multiple criteria. Finally, human objects in the base frame and the remaining frames of the video stream are precisely located by a fuzzy neural network which is trained by a SVD-based hybrid learning algorithm. Through experiments, we compare our system with two other approaches, and the results have shown that our system can detect face locations and extract human objects more accurately.

The database used for knowledge discovery is dynamic in nature. Data may be updated and new transactions may be added over time. As a result, the knowledge discovered from such databases is also dynamic. Incremental mining techniques have been developed to speed up the knowledge discovery process by avoiding re-learning of rules from the old data. To maintain the large itemsets against the updated database, we develop an approach named Negative Border using Sliding-Window Filtering (NB-SWF) which adopts the idea of the negative border and the sliding-window filtering algorithm. Negative border can help reduce the number of scans over the original database and the sliding-window filtering algorithm is to discover new itemsets in the updated database. By integrating the sliding-window filtering algorithm with the negative border, a lot of effort in the re-computation of negative border can be saved, and the minimal candidate set of large itemsets and negative border in the updated database can be obtained efficiently. Simulation results have shown that the NB-SWF runs faster than other incremental mining techniques, especially when there are few new large itemsets in the updated database.

In this paper, we propose an improved TSK-type recurrent fuzzy network (ITRFN) for dynamic system identification. Due to the improper clustering method and the restriction of first-order internal dynamics, the original TRFN has a poor representation capability and becomes inefficient for high-order temporal problems. To improve the previous deficiencies, we propose a new incremental self-clustering method to initialize the network structure and weights in the structure learning phase. Our clustering method can generate clusters that fit the real data distribution better than the original TRFN. Besides, we extend the internal dynamics to be high-order, and add adaptive parameters for tuning the membership functions of internal variables. These extensions make the ITRFN more general and flexible. Experimental results have shown that our method can achieve a higher precision with less training time than the original TRFN.

We propose an approach for neuro-fuzzy system modeling. A neuro-fuzzy system for a given set of input-output data is obtained in two steps. First, the data set is partitioned automatically into a set of clusters based on input-similarity and output-similarity tests. Membership functions associated with each cluster are defined according to statistical means and variances of the data points included in the cluster. Then, a fuzzy IF-THEN rule is extracted from each cluster to form a fuzzy rule-base. Second, a fuzzy neural network is constructed accordingly and parameters are refined to increase the precision of the fuzzy rule-base. To decrease the size of the search space and to speed up the convergence, we develop a hybrid learning algorithm which combines a recursive singular value decomposition-based least squares estimator and the gradient descent method. The proposed approach has advantages of determining the number of rules automatically and matching membership functions closely with the real distribution of the training data points. Besides, it learns faster, consumes less memory, and produces lower approximation errors than other methods.

We propose a novel approach for segmentation of human objects, including face and body, in image sequences. Object segmentation is important for achieving a high compression ratio in modern video coding techniques, e.g., MPEG-4 and MPEG-7, and human objects are usually the main parts in the video streams of multimedia applications. Existing segmentation methods apply simple criteria to detect human objects, leading to the restriction of the usage or a high segmentation error. We combine temporal and spatial information and employ a neuro-fuzzy mechanism to overcome these difficulties. A fuzzy self-clustering technique is used to divide the base frame of a video stream into a set of segments which are then categorized as foreground or background based on a combination of multiple criteria. Then, human objects in the base frame and the remaining frames of the video stream are precisely located by a fuzzy neural network constructed with the fuzzy rules previously obtained and is trained by a singular value decomposition (SVD)-based hybrid learning algorithm. The proposed approach has been tested on several different video streams, and the results have shown that the approach can produce a much better segmentation than other methods.

In this paper, an architecture of fuzzy neural networks with Takagi-Sugeno-Kang (TSK) fuzzy rules is proposed. A novel learning algorithm [1]-[2] with self-organizing ability and fast learning rules is also presented. In the structure identification phase of our method, fuzzy IF-THEN rules are extracted with a self-constructing rule generation algorithm. In the parameter identification phase, a hybrid learning algorithm is used, in which the consequent parameters are derived optimally by a recursive SVD-based least squares estimator (RSVD) and the precondition parameters are tuned by the backpropagation algorithm. Simulation results have demonstrated that a more compact structure with a faster convergence rate and smaller mean square errors can be achieved by the proposed approach.

Radial basis function (RBF) networks are widely used for modeling a function from given input-output patterns. However, two difficulties are involved with traditional RBF (TRBF) networks: The initial configuration of an RBF network needs to be determined by a trial-and-error method, and the performance suffers when the desired output has abrupt changes or constant values in certain intervals. We propose a novel approach to over. come these difficulties. New kernel functions are used for hidden nodes, and the number of nodes is determined automatically by an adaptive resonance theory (ART)-like algorithm. Parameters and weights are initialized appropriately, and then tuned and adjusted by the gradient-descent method to improve the performance of the network. Experimental results have shown that the RBF networks constructed by our method have a smaller number of nodes, a faster learning speed, and a smaller approximation error than the networks produced by other methods.

A method of generating various shapes of kernel functions, such as rectangular shapes and Gaussian-like shapes, for constructing neural networks is proposed. Our method can dynamically adjust the kernel shapes to match the desired output. For example, a kernel function of rectangular shape can be generated for a desired output which has a constant value for some interval. Determination of the initial prototypes may greatly affect the performance of neural networks. Most papers use trial-and-error methods to determine the initial prototypes. We incorporate the ART algorithm to construct the initial prototypes of neural networks. We also define a measure based on entropy theory to detect the local shape of the desired output. The goal of the measurement is to generate suitable kernel shapes. Therefore, there is a critical difference between traditional methods and ours. In other words, our scheme can construct proper shapes, nodes and initial weights automatically. Experimental results show that our method has a better performance than traditional methods.

The problems with which we are often confronted in neuro-fuzzy modeling are how to adequately decide the number of fuzzy rules extracted from a set of input-output data and how to precisely define the membership functions of each fuzzy rule. In this paper, we propose a hybrid algorithm that can automatically extract fuzzy rules from a set of numerical data points. Our algorithm is mainly composed of two phases, viz. data partitioning and rule extraction. In the first phase, the data set is partitioned into several clusters according to the similarities between the data points. In other words, the nearby data points are grouped into the same cluster. This is completed by a sequence of combinations of movable fuzzy prototypes. In the second phase, a fuzzy IF-THEN rule is extracted from each cluster and the membership functions of the corresponding rule are determined by statistical techniques. Experimental results show that the proposed algorithm converges quickly and can generate fewer rules with a lower mean-square error.

We propose the use of a neural-fuzzy scheme for rate-based feedback congestion control in asynchronous transfer mode (ATM) networks. Available bit rate (ABR) traffic is not guaranteed quality of service (QoS) in the setup connection, and it can dynamically share the available bandwidth. Therefore, congestion can be controlled by regulating the source rate, to a certain degree, according to the current traffic flow. Traditional methods perform congestion control by monitoring the queue length. The source rate is decreased by a fixed rate when the queue length is greater than a prespecified threshold. However, it is difficult to get a suitable rate according to the degree of traffic congestion. We employ a neural-fuzzy mechanism to control the source rate. Through learning, membership values can be generated and cell loss can be predicted from the status of the queue length. Then, an explicit rate is calculated and the source rate is controlled appropriately. Simulation results have shown that our method is effective compared with traditional methods.

This paper presents a novel approach to the verification of rule-based systems (RBSs). A graph structure, called the rule-dependency graph (RDG), is introduced to describe the dependency relationship among the rules of an RBS, in which each type of improper knowledge forms a specific topological structure. Knowledge verification is then performed by searching for such topological structures through a token-flow paradigm. An algorithm is provided, which automatically generates a minimally sufficient set of literals as test tokens in the detection procedure. The proposed scheme can be applied to rules of non-Horn clause form in both propositional and first-order logic, and restrictions imposed by other graph-based approaches can be avoided. Furthermore, explicit and potential anomalies of RBSs can be correctly found, and efficient run-time validation is made possible.

We propose an improved learning algorithm for rule refinement in neuro-fuzzy modeling. This algorithm is mainly based on a well-known technique, i.e., singular value decomposition (SVD). By using the method of SVD, the learning algorithm can converge quickly. Besides, the reasoning operator adopted in our algorithm is a compensatory fuzzy operator which has the advantage of being more adaptive and effective. Experimental results show that the proposed algorithm converges quickly and the obtained fuzzy rules are more precise.

To discriminate among all possible diagnoses using Hou's theory of measurement in diagnosis from first principles, one has to derive all minimal conflict sets from a known conflict set. However, the result derived from Hou's method depends on the order of node generation in CS-trees. We develop a derivation method with mark set to overcome this drawback of Hou's method. We also show that our method is more efficient in the sense that no redundant tests have to be done. An enhancement to our method with the aid of extra information is presented. Finally, a discussion on top-down and bottom-up derivations is given.

Cios and Liu (1992) proposed an entropy-based method to generate the architecture of neural networks for supervised two-class discretization. For multiclass discretization, the inter-relationship among classes is reduced to a set of binary relationships, and an independent two-class subnetwork is created for each binary relationship. This two-class-based method ends up with the disability of sharing hidden nodes among different classes and a low recognition rate. We keep the interrelationship among classes when training a neural network. Entropy measure is considered in a global sense, not locally in each independent subnetwork. Consequently, our method allows hidden nodes and layers to be shared among classes, and presents higher recognition rates than the two-class-based method.

Many medium access control protocols have been proposed for wireless networks. However, most of the existing network protocols, such as CSMA/CA, RAP, etc., only support data transmission, and do not support real-time services such as voice transmission. We propose a reservation scheme for the randomly addressed polling (RAP) protocol for wireless local area networks to make it possible to support real-time integrated voice/data communication services. Throughput and average access delay for this new scheme are computed and compared.

KJ3 is the first system which incorporates theorem proving techniques with the Petri Net description scheme for knowledge validation of rule based systems (RBSs). By converting the validation tasks of RBSs to reachability problems of Enhanced High-level Petri Net (EHLPN), KJ3 performs validation by proving if the hypothetical reachability problem is true. The establishment of the hypothesis corresponds to the achievement of the validation tasks. Since the properties of RBSs, such as refraction, conservation of facts, variables, closed world assumption, and negative information, can be properly represented and handled by EHLPN, different types of RBSs can be processed in KJ3. Since checking user specifications becomes investigating the reachability problems of EHLPN, all types of validation tasks can be handled by KJ3. The validation results can be directly extracted from the inference process to allow the users to explain the validation results. The inference process is mathematically traceable, sound, and complete, KJ3 guarantees that the validation outcome is reliable.

We attempt to model the operation of a nonlinear system with a set of input-output data. First, we use the method of fuzzy partitions to cluster the data into several groups and give each group a fuzzy rule to describe the distribution of associated data. A rough fuzzy rule based model can be constructed by combining these generated rules. Next, for the purpose of higher precision, we use a fuzzy-neural network to improve the rules obtained previously by tuning the shapes of membership functions. We adopt the trapezoidal membership functions instead of Gaussian ones as proposed by Lin et al. (1997), and show that the trapezoidal model is better than the Gaussian one. Finally, we can easily extract the improved rules from the network to give more precise inference of the fuzzy rule based model. There are two advantages of this method: 1) the fuzzy-neural network can be trained rapidly; and 2) one can extract symbolic rules from the numerical weights of the fuzzy-neural network. Such a method is very simple and the simulated results are satisfactory.

B. Hussain and M.R. Kabuka (1994) proposed a feature recognition neural network to reduce the network size of neocognitron. However, a distinct subnet is created for every training pattern. Therefore, a big network is obtained when the number of training patterns is large. Furthermore, recognition rate can be hurt due to the failure of combining features from similar training patterns. We propose an improvement by incorporating the idea of fuzzy ARTMAP in the feature recognition neural network. Training patterns are allowed to be merged, based on the measure of similarity among features, resulting in a subnet being shared by similar patterns. Because of the fusion of training patterns, network size is reduced and recognition rate is increased.

Zero-defect is extremely important for VLSI designs. Formal techniques for verifying the correctness of logic designs overcome the limits of test case simulation. Many formal systems have been proposed for verification purpose. However, verification of VLSI designs is not enough. It would be equally or more important to correct wrong designs. Little attention has been paid on diagnosis of logic designs. We propose a formal system, based on a propositional logic theorem prover, to verify a combinational logic design and to fix the design if it is incorrect. By referring to the models obtained for an incorrect design and applying some heuristics, the system can locate errors and correct the design in an intelligent way.

Exploring the properties of rule-based expert systems through Petri net models has received a lot of attention. Traditional Petri nets provide a straightforward but inadequate method for knowledge verification/validation of rule-based expert systems. We propose an enhanced high-level Petri net model in which variables and negative information can be represented and processed properly. Rule inference is modeled exactly and some important aspects in rule-based systems (RBSs), such as conservation of facts, refraction, and closed-world assumption, are considered in this model. With the coloring scheme proposed in this paper, the tasks involved in checking the logic structure and output correctness of an RES are formally investigated. We focus on the detection of redundancy, conflicts, cycles, unnecessary conditions, dead ends, and unreachable goals in an RES. These knowledge verification/validation (KVV) tasks are formulated as the reachability problem and improper knowledge can be detected by solving a set of equations with respect to multiple colors. The complexity of our method is discussed and a comparison of our model with other Petri net models is presented.

We propose a method of optimal morphological decomposition. We first formulate this kind of problem into a set of linear constraints, and then find out the solution to the set of linear constraints by using an integer linear programming technique. Our method has the following three advantages: (1) the size of the factors can be any n/spl times/n (n/spl ges/3), (2) it can be applied to both convex and concave simply-connected images; (3) optimality is selective and flexible.

This paper exploits the parallelism of a hyper-linking based theorem prover. We analyze the unique properties of the the hyper-linking proof procedure and present the preliminary results. With respect to these properties four parallel strategies, phase-level, clause-level, literal-level, search level parallelism are designed for different implementation schemes of the prover. Results and analysis of the experiments on these parallel strategies are presented.

K.J. Clos and N. Liu (1992) proposed a neural network generation procedure for supervised two-class discretization based on a continuous ID3 algorithm. The method constructs neural networks consisting of neurons with linear activation functions. We extend the procedure to allow decision boundaries to be any arbitrary function. The advantage of the extension is revealed by the decrease in size of the generated neural networks.

A new rule-based expert system language is proposed. Based on the Rete rule network structure, the language represents knowledge in the form of predicates and supports non-Horn clauses. Variables are allowed to be contained in facts. Rules can be added/deleted dynamically, when consulting an expert system built in this language, without causing any inconsistency in the knowledge base.