智能系统中获取模糊规则的神经网络方法

智能系统中一类重要的定性知识要用模糊集理论中的模糊语言进行描述。本文在研究模糊定性知识形式描述和自组织竞争神经网络特性的基础上，提出了一种从一组具有数值特性的训练样本集中获取隶属函数和模糊规则的神经网络模型和方法。通过对Ｉｒｉｓ数据集的应用实验表明了该方法能对这一类数据进行有效的描述。     

Symbolical Reasoning about Numerical Data: A Hybrid Approach

By combining methods from artificial intelligence and signal analysis, we have developed a hybrid system for medical diagnosis. The core of the system is a fuzzy expert system with a dual source knowledge base. Two sets of rules are acquired, automatically from given examples and indirectly formulated by the physician. A fuzzy neural network serves to learn from sample data and allows to extract fuzzy rules for the knowledge base. A complex signal transformation preprocesses the digital data a priori to the symbolic representation. Results demonstrate the high accuracy of the system in the field of diagnosing electroencephalograms where it outperforms the visual diagnosis by a human expert for some phenomena.     

Opening the black box of neural networks for remote sensing image classification

Neural networks, which make no assumption about data distribution, have achieved improved image classification results compared to traditional methods. Unfortunately, a neural network is generally perceived as being a ‘black box’. It is extremely difficult to document how specific classification decisions are reached. Fuzzy systems, on the other hand, have the capability to represent classification decisions explicitly in the form of fuzzy ‘if-then’ rules. However, the construction of a knowledge base, especially the fine-tuning of the fuzzy set parameters of the fuzzy rules in a fuzzy expert system, is a tedious and subjective process. This research has developed a new, improved neuro-fuzzy image classification system based on the synergism between neural networks and fuzzy expert systems. It incorporates the best of both technologies and compensates for the shortcomings of each. The learning algorithms of neural networks developed here are used to automate the derivation of fuzzy set parameters for the fuzzy ‘if-then’ rules in a fuzzy expert system. The rules obtained, in symbolic form, facilitate the understanding of the neural network based image classification system. In addition, the image classification accuracy obtained from the improved neuro-fuzzy system was significantly superior to those of the back-propagation based neural network and the maximum likelihood approaches.     

Neural and Neuro-Fuzzy Integration in a Knowledge-Based System for Air Quality Prediction

In this paper we propose a unified approach for integrating implicit and explicit knowledge in neurosymbolic systems as a combination of neural and neuro-fuzzy modules. In the developed hybrid system, training data set is used for building neuro-fuzzy modules, and represents implicit domain knowledge. The explicit domain knowledge on the other hand is represented by fuzzy rules, which are directly mapped into equivalent neural structures. The aim of this approach is to improve the abilities of modular neural structures, which are based on incomplete learning data sets, since the knowledge acquired from human experts is taken into account for adapting the general neural architecture. Three methods to combine the explicit and implicit knowledge modules are proposed. The techniques used to extract fuzzy rules from neural implicit knowledge modules are described. These techniques improve the structure and the behavior of the entire system. The proposed methodology has been applied in the field of air quality prediction with very encouraging results. These experiments show that the method is worth further investigation.     

A computational model of an intuitive reasoner for ecosystem control

Intuition is the human capacity to make decisions under novel, complex situations where knowledge is incomplete and of variable levels of certainty. We take the view that intuition can be modeled as a rational and deductive mode of information processing which is suited to novel, complex situations. In this research, a computational algorithm, or “intuitive reasoner”, is proposed which mimics some aspects of human intuition by combining established mathematical tools, such as fuzzy set theory, and some novel innovations. A rule-based scheme is followed and a rule-learning module that allows rules to be learned from incomplete datasets is developed. The input and the rules drawn by the reasoner are allowed to be fuzzy, multi-valued, and low in certainty. A measure of the certainty level, Strength of Belief, is attached to each input as well as each rule. Solutions are formulated through iterations of consolidating intermediate reasoning results, during which the Strength of Belief of corroborating intermediate results is combined. An experimental implementation of the proposed intuitive reasoner is reported, in which the reasoner was used to solve a classification problem. The results showed that, when given increasingly sparse input data, the rule-learning module generated more rules of lower associated certainty than when presented with more complete data. The intuitive reasoner was able to make use of these low-certainty rules to solve the classification problems with an accuracy that compared favorably to that of traditional methods based on complete datasets.     

Knowledge Incorporation into Neural Networks From Fuzzy Rules

The incorporation of prior knowledge into neural networks can improve neural network learning in several respects, for example, a faster learning speed and better generalization ability. However, neural network learning is data driven and there is no general way to exploit knowledge which is not in the form of data input-output pairs. In this paper, we propose two approaches for incorporating knowledge into neural networks from fuzzy rules. These fuzzy rules are generated based on expert knowledge or intuition. In the first approach, information from the derivative of the fuzzy system is used to regularize the neural network learning, whereas in the second approach the fuzzy rules are used as a catalyst. Simulation studies show that both approaches increase the learning speed significantly.     

Neural networks that learn from fuzzy if-then rules

An architecture for neural networks that can handle fuzzy input vectors is proposed, and learning algorithms that utilize fuzzy if-then rules as well as numerical data in neural network learning for classification problems and for fuzzy control problems are derived. The learning algorithms can be viewed as an extension of the backpropagation algorithm to the case of fuzzy input vectors and fuzzy target outputs. Using the proposed methods, linguistic knowledge from human experts represented by fuzzy if-then rules and numerical data from measuring instruments can be integrated into a single information processing system (classification system or fuzzy control system). It is shown that the scheme works well for simple examples     

COMPRESSION AND EXPANSION OF FUZZY RULE BASES BY USING CRISP-FUZZY NEURAL NETWORKS

A fuzzy neural network with knowledge discovery FNNKD is designed to perform adaptive compensatory fuzzy reasoning based on more useful and more heuristic primary fuzzy sets. In order to overcome the weakness of the conventional crisp neural network and the fuzzy operation oriented neural network, we have developed a general fuzzy reasoning oriented fuzzy neural network called a crisp-fuzzy neural network CFNN that is capable of extracting high-level knowledge such as fuzzy IF-THEN rules from either crisp data or fuzzy data. A CFNN can effectively compress a 5 5 fuzzy IF-THEN rule base of a cart-pole balancing system to a 3 3 one, then to a 2 2 one, and finally to a 1 1 one, and can expand on invalid sparse 3 3 fuzzy IF-THEN rule base of a cart-pole balancing system to a valid 5 5 one. In addition, a CFNN can control a more complex cart-pole balancing system with random fuzzy noise inputs and outputs i.e., nonconventional using crisp inputs and outputs without any noise . The simulations have indicated that a CFNN is an efficient neurofuzzy system with abilities to discover new fuzzy knowledge from either numerical data or fuzzy data, compress and expand fuzzy knowledge, and do fuzzy reasoning.     

A fuzzy neural network with fuzzy impact grades

Fuzzy rule derivation is often difficult and time-consuming, and requires expert knowledge. This creates a common bottleneck in fuzzy system design. In order to solve this problem, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a fuzzy neural network based on mutual subsethood (MSBFNN) and its fuzzy rule identification algorithms. In our approach, fuzzy rules are described by different fuzzy sets. For each fuzzy set representing a fuzzy rule, the universe of discourse is defined as the summation of weighted membership grades of input linguistic terms that associate with the given fuzzy rule. In this manner, MSBFNN fully considers the contribution of input variables to the joint firing strength of fuzzy rules. Afterwards, the proposed fuzzy neural network quantifies the impacts of fuzzy rules on the consequent parts by fuzzy connections based on mutual subsethood. Furthermore, to enhance the knowledge representation and interpretation of the rules, a linear transformation from consequent parts to output is incorporated into MSBFNN so that higher accuracy can be achieved. In the parameter identification phase, the backpropagation algorithm is employed, and proper linear transformation is also determined dynamically. To demonstrate the capability of the MSBFNN, simulations in different areas including classification, regression and time series prediction are conducted. The proposed MSBFNN shows encouraging performance when benchmarked against other models.     

Design of fuzzy systems using neurofuzzy networks

Introduces a systematic approach for fuzzy system design based on a class of neural fuzzy networks built upon a general neuron model. The network structure is such that it encodes the knowledge learned in the form of if-then fuzzy rules and processes data following fuzzy reasoning principles. The technique provides a mechanism to obtain rules covering the whole input/output space as well as the membership functions (including their shapes) for each input variable. Such characteristics are of utmost importance in fuzzy systems design and application. In addition, after learning, it is very simple to extract fuzzy rules in the linguistic form. The network has universal approximation capability, a property very useful in, e.g., modeling and control applications. Here we focus on function approximation problems as a vehicle to illustrate its usefulness and to evaluate its performance. Comparisons with alternative approaches are also included. Both, non-noisy and noisy data have been studied and considered in the computational experiments. The neural fuzzy network developed here and, consequently, the underlying approach, has shown to provide good results from the accuracy, complexity, and system design points of view.     

Using fuzzy partitions to create fuzzy systems from input-outputdata and set the initial weights in a fuzzy neural network

We create a set of fuzzy rules to model a system from input-output data by dividing the input space into a set of subspaces using fuzzy partitions. We create a fuzzy rule for each subspace as the input space is being divided. These rules are combined to produce a fuzzy rule based model from the input-output data. If more accuracy is required, we use the fuzzy rule-based model to determine the structure and set the initial weights in a fuzzy neural network. This network typically trains in a few hundred iterations. Our method is simple, easy, and reliable and it has worked well when modeling large “real world” systems     

Improving error compensation via a fuzzy-neural hybrid model

Factors that influence the accuracy of machining and in-cycle measuring processes are varied. It is very difficult or impossible to identify and fix each error by in-cycle measuring systems with touch trigger probes. Moreover, even where errors have been determined, the effects and relationships among them are very complicated, and there are no existing mathematical models to be applied to control or compensate the machining processes. This paper introduces a new in-cycle measuring and error compensation system based on a fuzzy controller combined with a supervised neural network. The fuzzy neural hybrid compensation model consists of a multilayer feed-forward neural network trained with the back propagation gradient descent algorithm. The fuzzy rules are implemented by the hidden layer of the network, and the fuzzy max-min operations are replaced by the feed-forward summation. The proposed system reveals that it is feasible to achieve an improved machining performance by adapting the fuzzy membership functions and generating linguistic control rules. A series of experiments is performed, and the characteristics of the system are evaluated and discussed.     

自适应B样条模糊神经网络控制器的设计

B样条具有最小局部支撑和易于实现的优点。文章利用多变量B样条网络在运算表达式上与模糊神经网络结构之间的对等关系,并通过对其权值的训练,设计出自适应B样条模糊神经网络控制器。应用于具有严重非线性摩擦力影响的速度跟踪系统的仿真实验表明,所设计的控制器完全等价于模糊神经网络控制器,同时在计算量和实现上具有明显的优势。     

GenSoFNN: a generic self-organizing fuzzy neural network

Existing neural fuzzy (neuro-fuzzy) networks proposed in the literature can be broadly classified into two groups. The first group is essentially fuzzy systems with self-tuning capabilities and requires an initial rule base to be specified prior to training. The second group of neural fuzzy networks, on the other hand, is able to automatically formulate the fuzzy rules from the numerical training data. No initial rule base needs to be specified prior to training. A cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters. However, most existing neural fuzzy systems (whether they belong to the first or second group) encountered one or more of the following major problems. They are (1) inconsistent rule-base; (2) heuristically defined node operations; (3) susceptibility to noisy training data and the stability-plasticity dilemma; and (4) needs for prior knowledge such as the number of clusters to be computed. Hence, a novel neural fuzzy system that is immune to the above-mentioned deficiencies is proposed in this paper. This new neural fuzzy system is named the generic self-organizing fuzzy neural network (GenSoFNN). The GenSoFNN network has strong noise tolerance capability by employing a new clustering technique known as discrete incremental clustering (DIC). The fuzzy rule base of the GenSoFNN network is consistent and compact as GenSoFNN has built-in mechanisms to identify and prune redundant and/or obsolete rules. Extensive simulations were conducted using the proposed GenSoFNN network and its performance is encouraging when benchmarked against other neural and neural fuzzy systems.     

Air quality prediction by neuro-fuzzy modeling approach

This paper proposes an air quality prediction system based on the neuro-fuzzy network approach. Historical time series data are employed to derive a set of fuzzy rules, or equivalently a neuro-fuzzy network, for forecasting air pollutant concentrations and environmental factors in the future. Due to the uncertainty of the involved impact factors, fuzzy elements are added to the forecasting system. First of all, training data are partitioned into fuzzy clusters whose membership functions are characterized by the estimated means and variances. From these fuzzy clusters, fuzzy rules are extracted and a four-layer fuzzy neural network is constructed. Then genetic, particle swarm optimization, and steepest descent backpropagation algorithms are applied to train the network. The network outputs, derived through the fuzzy inference process, produce the forecast air pollutant concentrations or air quality indices. Our proposed approach has the following advantages: (1) Adding fuzzy elements can more appropriately deal with the uncertainty of the impact factors involved; (2) The distribution of training data can be described properly by fuzzy clusters with statistical means and variances; (3) Fuzzy rules are extracted automatically from the training data, instead of being supplied manually by human experts; (4) The obtained fuzzy rules are of high quality, and their parameters can be optimized effectively.     

基于模糊B 样条基函数神经网络控制的交流伺服系统

采用Ｂ样条函数八为模糊隶属函数,利用神经网络实现模糊推理,提出一种模糊Ｂ样条基品数神网络,并将其用于交流伺服系统的控制。仿真结果表明,该控制方法响应速度快,鲁棒性强,是一种有效的控制方法。     

Providing understanding of the behavior of feedforward neuralnetworks

The advent of artificial neural networks has stirred the imagination of many in the field of knowledge acquisition. There is an expectation that neural networks will play an important role in automating knowledge acquisition and encoding, however, the problem solving knowledge of a neural network is represented at a subsymbolic level and hence is very difficult for a human user to comprehend. One way to provide an understanding of the behavior of neural networks is to extract their problem solving knowledge in terms of rules that can be provided to users. Several papers which propose extracting rules from feedforward neural networks can be found in the literature, however, these approaches can only deal with networks with binary inputs. Furthermore, certain approaches lack theoretical support and their usefulness and effectiveness are debatable. Upon carefully analyzing these approaches, we propose a method to extract fuzzy rules from networks with continuous-valued inputs. The method was tested using a real-life problem (decision-making by pilots involving combat situations) and found to be effective.     

Dimensionality reduction based on rough set theory: A review

A rough set theory is a new mathematical tool to deal with uncertainty and vagueness of decision system and it has been applied successfully in all the fields. It is used to identify the reduct set of the set of all attributes of the decision system. The reduct set is used as preprocessing technique for classification of the decision system in order to bring out the potential patterns or association rules or knowledge through data mining techniques. Several researchers have contributed variety of algorithms for computing the reduct sets by considering different cases like inconsistency, missing attribute values and multiple decision attributes of the decision system. This paper focuses on the review of the techniques for dimensionality reduction under rough set theory environment. Further, the rough sets hybridization with fuzzy sets, neural network and metaheuristic algorithms have also been reviewed. The performance analysis of the algorithms has been discussed in connection with the classification.     

A generic fuzzy aggregation operator: rules extraction from and insertion into artificial neural networks

Multilayered feedforward artificial neural networks (ANNs) are black boxes. Several methods have been published to extract a fuzzy system from a network, where the input–output mapping of the fuzzy system is equivalent to the mapping of the ANN. These methods are generalized by means of a new fuzzy aggregation operator. It is defined by using the activation function of a network. This fact lets to choose among several standard aggregation operators. A method to extract fuzzy rules from ANNs is presented by using this new operator. The insertion of fuzzy knowledge with linguistic hedges into an ANN is also defined thanks to this operator.     

模糊B样条基神经网络磁共振图像分割方法

针对磁共振图像分割的特点,提出了一种基于模糊B样条基神经网络的磁共振图像分割方法。该方法采用B样条基函数作为模糊隶属函数,利用神经网络实现模糊推理,并采用反向误差传播算法对网络进行训练。实验结果表明,这种基于模糊B样条基神经网络的磁共振图像分割方法与普通神经网络分割方法相比,具有更高的分割精度和更快的训练收敛速度。