模糊数系发展综述

模糊数概念的提出近 30年历史 ,概括其发展过程有五个代表性思路 。

Direct adaptive fuzzy control based on integral-type Lyapunov function

A new scheme of direct adaptive fuzzy controller for a class of nonlinear systems with unknown triangular control gain structure is proposed. The design is based on the principle of sliding mode control and the approximation capability of the first type fuzzy systems. By introducing integral-type Lyapunov function and adopting the adaptive compensation term of optimal approximation error, the closed-loop control system is proved to be globally stable, with tracking error converging to zero. Simulation results demonstrate the effectiveness of the approach.

Performance analysis of air suspension system of heavy truck with semi-active fuzzy control

In order to analyze and evaluate the performance of the air suspension system of heavy trucks with semi-active fuzzy control, a three-dimensional nonlinear dynamical model of a typical heavy truck with 16-DOF（degree of freedom） is established based on Matlab/Simulink software. The weighted root-mean-square（RMS） acceleration responses of the vertical driver ＇s seat, the pitch and roll angle of the cab, and the dynamic load coefficient（DLC） are chosen as objective functions, and the air suspension system is optimized and analyzed by the semi-active fuzzy control algorithm when vehicles operate under different operation conditions. The results show that the influence of the roll angle of the cab on the heavy truck ride comfort is clear when vehicles move on the road surface conditions of the ISO level D and ISO level E at a velocity over 27.5 m/s. The weighted RMS acceleration responses of vertical driver＇ s seat, the pitch and roll angle of the cab are decreased by 24%, 30% and 25%, respectively,when vehicles move on the road surface condition of the ISO level B at a velocity of 20 m/s. The value of the DLC also significantly decreases when vehicles operate under different operation conditions. Particularly, the DLC value of the tractor driver axle is greatly reduced by 27.4% when the vehicle operates under a vehicle fully-loaded condition on the road surface condition of ISO level B at a velocity of 27.5 m/s.

Similarity measure application to fault detection of flight system

Fault detection technique is introduced with similarity measure. The characteristics of conventional similarity measure based on fuzzy number are discussed. With the help of distance measure, similarity measure is constructed explicitly. The designed distance-based similarity measure is applicable to general fuzzy membership functions including non-convex fuzzy membership function, whereas fuzzy number-based similarity measure has limitation to calculate the similarity of general fuzzy membership functions. The applicability of the proposed similarity measure to general fuzzy membership structures is proven by identifying the definition. To decide fault detection of flight system, the experimental data （pitching moment coefficients and lift coefficients） are transformed into fuzzy membership functions. Distance-based similarity measure is applied to the obtained fuzzy membership functions, and similarity computation and analysis are obtained with the fault and normal operation coefficients.

Automobile active suspension system with fuzzy control

A quarter-automobile active suspension model was proposed. High speed on/off solenoid valves were used as control valves and fuzzy control was chosen as control method . Based on force analyses of system parts, a mathematical model of the active suspension system was established and simplified by linearization method. Simulation study was conducted with Matlab and three scale coefficients of fuzzy controller (ke, kec, ku) were acquired. And an experimental device was designed and produced. The results indicate that the active suspension system can achieve better vibration isolation performance than passive suspension system, the displacement amplitude of automobile body can be reduced to 55%. Fuzzy control is an effective control method for active suspension system.

Evolution of two properties for scale-free network

Fitness of node can denote its competing power and clustering denotes the transitivity of network. Because the fitness of node is uncertain or fuzzy in some social networks, an explicit form of the degree distribution on fuzzy fitness is derived within a mean field approach. It is a weighted sum of different fuzzy fitness. It can be found that the fuzzy fitness of nodes may lead to multiscaling. Moreover, the clustering coefficient of node decays as power law and clustering coefficient of network behavior not-decrease-but-increase’ phenomenon after some time. Some computer simulation results of these models illustrate these analytical results.

The study of coal mine equipment’s comprehensive evaluation index system and evaluation method

Equipment management is one of the important parts of business administra- tion of coal. Most of coal mines take no account of their equipment management, and have no comprehensive and effective evaluation index system. Based on the analysis of the equipment evaluation measures of reform and the applications, the paper built up a comprehensive and effective evaluation index system of coal mine equipment, and im- proved the evaluation method with the use of fuzzy theory, analytic hierarchy process and entropy method.

Construction of reasonable pillar group for undersea mining in metal mine

In order to achieve the safe mining in Sanshandao Gold Mine,five schemes of secure pillar group are designed.Using the method of the renormalization group,the failure mechanism of the pillar group is explored,and the safety factor of the pillar system is also obtained.The displacement characteristics,stress-strain laws,distribution of plastic zone and damage range of different pillar group are analyzed using numerical calculation software FLAC3D.To determine a reasonable pillar group scheme,the pillar stability and roof deformation are utilized to evaluate the safety of the pillar group.In addition,the theory of fuzzy comprehensive evaluation is adopted to verify the optimal scheme.The pillar group with the lowest roof deformation value is chosen as the optimal plan,which renders a factor of safety of 2.06 for the pillar group.According to this scheme,pillars with the width of 10 m are set along the strike of undersea deposit with the interval of 50 m.Rib pillars of 15 m in width are set at the location of the exploration line of 127,151 and 167.The analysis can be used to provide guidance for optimal design of pillar structures in undersea mining.

Research on the fully fuzzy time-cost trade-off based on genetic algorithms

It is very difficult to estimate exact values of time and cost of an activity in project scheduling process because many uncertain factors, such as weather, productivity level, human factors etc. , dynamically affect them during project implementation process. A GAs-based fully fuzzy optimal time-cost trade-off model is presented based on fuzzy sets and genetic algorithms (GAs). In tihs model all parameters and variables are characteristics by fuzzy numbers. And then GAs is adopted to search for the optimal solution to this model. The method solves the time-cost trade-off problems under an uncertain environment and is proved practicable through a giving example in ship building scheduling.

Improving Land Resource Evaluation Using Fuzzy Neural Network Ensembles

Land evaluation factors often contain continuous-, discrete- and nominal-valued attributes. In traditional land evaluation, these different attributes are usually graded into categorical indexes by land resource experts, and the evaluation results rely heavily on experts＇ experiences. In order to overcome the shortcoming, we presented a fuzzy neural network ensemble method that did not require grading the evaluation factors into categorical indexes and could evaluate land resources by using the three kinds of attribute values directly. A fuzzy back propagation neural network （BPNN）, a fuzzy radial basis function neural network （RBFNN）, a fuzzy BPNN ensemble, and a fuzzy RBFNN ensemble were used to evaluate the land resources in Guangdong Province. The evaluation results by using the fuzzy BPNN ensemble and the fuzzy RBFNN ensemble were much better than those by using the single fuzzy BPNN and the single fuzzy RBFNN, and the error rate of the single fuzzy RBFNN or fuzzy RBFNN ensemble was lower than that of the single fuzzy BPNN or fuzzy BPNN ensemble, respectively. By using the fuzzy neural network ensembles, the validity of land resource evaluation was improved and reliance on land evaluators＇ experiences was considerably reduced.

Multi-level fuzzy comprehensive appraisal on social effects of projects

The application of multi-level fuzzy comprehensive appraisal on social effects of projects has been studied. The principles for setting up an index system have been analyzed and the index system has been set up according to projects of construction. Models for multi-level fuzzy comprehensive appraisal have been offered and relative calculation steps have been given according to project instances.

Quality index of bedded and joint-bearing rock mass and its applications

Based on the theory of Fuzzy Mathematics and Expert System, this paper presents the quantitative expression method of bedded and joint bearing rock mass quality "Stratum Quality Index"(SQI for short), and also introduces the successful application of the method in estimating stratum movement parameters.

Designing similarity measurement with distance measure and application on laterally directional mode flight test

Similarity measure construction has been proposed as fault detection of flight test method in order to obtain the primary control surface stuck and the combination stuck of primary control.Similarity measures were obtained through analyzing the certainty and uncertainty of fuzzy membership functions,which were designed based on well-known Hamming distance.It was applied to the fault detection of primary control surface stuck of uninhabited aerial vehicle(UAV).At post-failure control surface,if the UAV is controllable and trimmable using other control surfaces,the UAV is able to fly or return to the safety region through reconfiguration of flight control system.To detect the fault,similarity measure computations were carried out.This result could be applicable with the real-time parameter estimation method.By monitoring the value of coefficients due to the control surface deviation,it becomes aware that the control surface fault occurs or not.The control surface stuck position and value were separated by comparing the trim value with the reference value.This is the advantage of increasing in reliability without adding sensors or with additional low cost.

Modelling spatial vagueness based on type-2 fuzzy set

The modelling and formal characterization of spatial vagueness plays an increasingly important role in the imple- mentation of Geographic Information System (GIS). The concepts involved in spatial objects of GIS have been investigated and acknowledged as being vague and ambiguous. Models and methods which describe and handle fuzzy or vague (rather than crisp or determinate) spatial objects, will be more necessary in GIS. This paper proposes a new method for modelling spatial vagueness based on type-2 fuzzy set, which is distinguished from the traditional type-1 fuzzy methods and more suitable for describing and implementing the vague concepts and objects in GIS.

Element yield rate prediction in ladle furnace based on improved GA-ANFIS

The traditional prediction methods of element yield rate can be divided into experience method and data-driven method.But in practice,the experience formulae are found to work only under some specific conditions,and the sample data that are used to establish data-driven models are always insufficient.Aiming at this problem,a combined method of genetic algorithm(GA) and adaptive neuro-fuzzy inference system(ANFIS) is proposed and applied to element yield rate prediction in ladle furnace(LF).In order to get rid of the over reliance upon data in data-driven method and act as a supplement of inadequate samples,smelting experience is integrated into prediction model as fuzzy empirical rules by using the improved ANFIS method.For facilitating the combination of fuzzy rules,feature construction method based on GA is used to reduce input dimension,and the selection operation in GA is improved to speed up the convergence rate and to avoid trapping into local optima.The experimental and practical testing results show that the proposed method is more accurate than other prediction methods.

Joint adaptive waveform and baseline range design for bistatic radar

The problems of joint adaptive waveform design and baseline range design for bistatic radar to maximize the practical radar resolution were considered.Distinguishing from the conventional ambiguity function(AF)-based resolution which is only related with the transmitted waveform and bistatic geometry and could be regarded as the potential resolution of a bistatic radar system,the practical resolution involves the effect of waveform,signal-to-noise ratio(SNR)as well as the measurement model.Thus,it is more practical and will have further significant application in target detection and tracking.The constraint optimization procedure of joint adaptive waveform design and baseline range design for maximizing the practical resolution of bistatic radar system under dynamic target scenario was devised.Simulation results show that the range and velocity resolution are enhanced according to the adaptive waveform and bistatic radar configuration.

Extension of information entropy-based measures in incomplete information systems

It is helpful for people to understand the essence of rough set theory to study the concepts and operations of rough set theory from its information view. In this paper we address knowledge expression and knowledge reduction in incomplete infolvnation systems from the information view of rough set theory. First, by extending information entropy-based measures in complete information systems, two new measures of incomplete entropy and incomplete conditional entropy are presented for incomplete information systems. And then, based on these measures the problem of knowledge reduction in incomplete information systems is analyzed and the reduct definitions in incomplete information system and incomplete decision table are proposed respectively. Finally, the reduct definitions based on incomplete entropy and the reduct definitions based on similarity relation are compared. Two equivalent relationships between them are proved by theorems and an in equivalent relationship between them is illustrated by an example. The work of this paper extends the research of rough set theory from information view to incomplete information systems and establishes the theoretical basis for seeking efficient algorithm of knowledge acquisition in incomplete information systems.

A Direct Feedback Control Based on Fuzzy Recurrent Neural Network

A direct feedback control system based on fuzzy recurrent neural network is proposed, and a method of training weights of fuzzy recurrent neural network was designed by applying modified contract mapping genetic algorithm. Computer simulation results indicate that fuzzy recurrent neural network controller has perfect dynamic and static performances .

Analytical Model and Algorithm of Fuzzy Fault Tree

In the past, the probabilities of basic events were described as triangular or trapezoidal fuzzy number that cannot characterize the common distribution of the primary events in engineering, and the fault tree analyzed by fuzzy set theory did not include repeated basic events. This paper presents a new method to analyze the fault tree by using normal fuzzy number to describe the fuzzy probability of each basic event which is more suitably used to analyze the reliability in safety systems, and then the formulae of computing the fuzzy probability of the top event of the fault tree which includes repeated events are derived. Finally, an example is given.

DiagData： A Tool for Generation of Fuzzy Inference System

In this paper, it described the architecture of a tool called DiagData. This tool aims to use a large amount of data and information in the field of plant disease diagnostic to generate a disease predictive system. In this approach, techniques of data mining are used to extract knowledge from existing data. The data is extracted in the form of rules that are used in the development of a predictive intelligent system. Currently, the specification of these rules is built by an expert or data mining. When data mining on a large database is used, the number of generated rules is very complex too. The main goal of this work is minimize the rule generation time. The proposed tool, called DiagData, extracts knowledge automatically or semi-automatically from a database and uses it to build an intelligent system for disease prediction. In this work, the decision tree learning algorithm was used to generate the rules. A toolbox called Fuzzygen was used to generate a prediction system from rules generated by decision tree algorithm. The language used to implement this software was Java. The DiagData has been used in diseases prediction and diagnosis systems and in the validation of economic and environmental indicators in agricultural production systems. The validation process involved measurements and comparisons of the time spent to enter the rules by an expert with the time used to insert the same rules with the proposed tool. Thus, the tool was successfully validated, providing a reduction of time.