不确定度问题研究情况综述

不确定度是一个度量不确定性测度函数所表示对象的不确定程度的模型，不同的不确定性理论用不同的不确定性测度描述。很多文献针对不同对象的不同不确定性测度提出了各种不确定度模型。本文从经典Shannon熵和Hartley熵出发，对这些不确定度模型作一个综述，涉及到的不确定性理论包括概率论、模糊集合论、证据理论、可能性理论等。     

随机集理论在数据融合中的应用研究

数据融合研究的重点是建立一个具有严格数学基础的框架体系，随机集理论是解决这一问题的有效方法。在介绍随机集理论基本原理的基础上，阐述了数据融合系统中使用较多的证据理论、模糊逻辑和条件事件代数理论的随机集表示，使随机集理论能有效地处理数据融合系统中的不确定性、模糊性、经验性数据。     

A signal detection system based on Dempster-Shafer theory andcomparison to fuzzy detection

This paper describes a signal detection algorithm based on Dempster-Shafer theory. The detector combines evidence provided by multiple waveform features and explicitly considers uncertainty in the detection decision. The detector classifies waveforms as including a signal, not including a signal, or being uncertain, in which case no conclusion regarding presence or absence of a signal is drawn. The probability numbers required in the Dempster-Shafer formulation are defined as piecewise linear functions that can be described by two parameters, and the effects of these parameters on detector performance, using simulated data, are compared to Bayesian detection and to a fuzzy signal detector that also considers uncertainty. The performance of the Dempster-Shafer and fuzzy detectors shows similar dependence on the parameters, although, if parameters are adjusted so that the number of correctly classified waveforms are equal, the Dempster-Shafer detector has more uncertain classifications and fewer errors than the fuzzy detector, providing superior performance. The Dempster-Shafer detector incorporates a different type of uncertainty than the fuzzy detector, which may contribute to this difference in performance. The difference may also reflect the different mathematical operations used     

Fuzzy-set approach to select maintenance strategies for multistateequipment

Maintenance of any equipment based on its condition is unavoidable. The condition of the equipment can be represented using fuzzy sets. This paper details a fuzzy-set model for maintenance policy of multistate equipment; the model is based on: (a) equipment condition and remaining life, and (b) maximizing a known detailed utility function. The model is extended to maintenance planning for the entire life of the equipment. The results are useful for replacement decisions as well as for inventory control     

A new method for constructing fuzzy evidence based on the non-consonant random set

Natural-language information is often mathematically expressed by fuzzy sets. With the random set theory as a bridge, this kind of information can be transformed into fuzzy evidence in Dempster-Shafer (DS) theory. Then Dempster’s combination rule or other combination rules of evi- dence can be used perfectly for fusing natural-language and other information. However, this traditional transformation involves the use of α -cutsets to construct the focal elements which have to be repre- sented as consonant set...     

A framework for fuzzy recognition technology

Presents a scheme for object recognition by classificatory problem solving in the framework of fuzzy sets and possibility theory. The scheme has a particular focus on handling the imperfection problems that are common in application domains where the objects to be recognized (detected and identified) represent undesirable situations, referred to as crises. Crises develop over time, and observations typically increase in number and precision as the crisis develops. Early detection and precise recognition of crises is desired, since it increases the possibility of an effective treatment. The crisis recognition problem is central in several areas of decision support, such as medical diagnosis, financial decision making and early warning systems. The problem is characterized by vague knowledge and observations suffering from several kinds of imperfections, such as missing information, imprecision, uncertainty, unreliability of the source, and mutual (possibly conflicting or reinforcing) observations of the same phenomena. The problem of handling possibly imperfect observations from multiple sources includes the problems of information fusion and multiple-sensor data fusion. The different kinds of imperfection are handled in the framework of fuzzy sets and possibility theory     

模糊逻辑及其在数据融合中的应用

自从１９６５年Ｚａｄｅｈ发表关于模糊集理论的文章以来,模糊集理论已在工业控制、医疗诊断、经济决策、模式识别等领域得到广泛应用,随着模糊逻辑和可能性理论的提出和深入研究,它们在不确定推理模型的设计和多传感器信息融合中显示出越来越强大的优势,文中探讨它们在多传感器数据融合中的应用。     

Rough implication operation and residuated based fuzzy logic system

Theories of fuzzy sets and rough sets are different and complementary generalizations of classical set theory, both of them are motivated by practical needs to manage and process uncertainty information. The aim of this paper is to study the relationship between fuzzy sets and rough sets from the view of logic. A new implication operation of rough sets is constructed, and the rough sets semantics of residuated based fuzzy logic system is presented.     

基于神经网络与模糊理论的模糊自编码器

自编码器是深度学习中广泛使用的一种网络,许多深度网络都以其为基础构建特定的网络结构。对于传统自编码器及其变体,不同层单元之间的参数被限定为普通实数,这在某种程度限制了自编码器的能力,为了克服这种问题,文中以模糊理论为基础,通过将自编码器的参数设置为模糊数,构建了模糊自编码器模型,并引入了相应的学习算法。基于MINIST手写数字数据集的实验表明,模糊自编码器在表示能力和鲁棒性方面都要优于普通自编码器。     

A fuzzy set approach for yield learning modeling in wafermanufacturing

The yield of semiconductor manufacturing can be improved through a learning process. A learning model is usually used to describe the learning process and to predict future yields. However, in traditional learning models such as Gruber's general yield model, the uncertainty and variation inherent in the learning process are not easy to consider. Also there are many strict assumptions about parameter distributions that need to be made. These result in the unreliability and imprecision of yield prediction. To improve the reliability and precision of yield prediction, expert opinions are consulted to evaluate and modify the learning model in this study. The fuzzy set theory is applied to facilitate this consulting process. At first, fuzzy forecasts are generated to predict future yields. The necessity of specifying strict parameter distributions is thus relaxed. Fuzzy yield forecasts can be defuzzified, or their α-cuts can be considered in capacity planning. The interpretation of such a treatment is also intuitive. Then, experts are requested to evaluate the learning model and express their opinions about the parameters in suitable fuzzy numbers or linguistic terms defined in advance. Two correction functions are designed to incorporate expert opinions in the learning model. Some examples are used for demonstration. The advantages of the proposed method are then discussed     

A neural network based fuzzy set model for organizational decisionmaking

A neural network based fuzzy set model is proposed to support organizational decision making under uncertainty. This model incorporates three theories and methodologies: classical decision-making theory under conflict, as suggested by Luce and Raiffa (1957), the fuzzy set theory of Zadeh (1965, 1984), and a modified version of the backpropagation (BP) neural network algorithm originated by Rumelhart et al. (1986). An algorithm that implements the model is described, and an application of the model to a real data example is used to demonstrate its use     

基于FHT似然比检验的CRN协作频谱感知方案

针对认知无线电网络中由于噪声功率不确定性而影响频谱检测性能的问题,提出了一种基于模糊似然比检验的协作频谱检测方法。首先,将每个次用户(SU)中的噪声不确定性均建模为模糊假设检验(FHT);然后,在FHT上利用似然比检验构建带有阈值的模糊能量检测器,该阈值依赖于噪声功率不确定性边界;最后,在融合中心结合SU的局部硬决策并做出最终决策,从而检测主用户是否存在。通过Monte Carlo模拟受试者ROC曲线及检测概率/SNR曲线验证了本文方法的有效性,仿真结果表明,相比其他几种较新的能量检测器,本文方法获得了更好的检测性能。     

区间值Vague决策系统及其规则提取方法

区间值(i-v)模糊集合和Vague集是不精确知识表达的两种新理论.它们已被广泛地应用于决策系统中对于不确定决策数据的描述.本文将两者有机地结合,给出了i-v Vague集的有关概念,并详细地讨论了其性质.最后,结合一个决策系统实例,利用文中所提出的包含与相交因子,分析了规则生成策略.经过与传统Rough集方法的对比,发现两者所得结论是一致的,但该方法对于不确定性问题的处理却表现得更为灵活.     

Fuzzy logic systems for engineering: a tutorial

A fuzzy logic system (FLS) is unique in that it is able to simultaneously handle numerical data and linguistic knowledge. It is a nonlinear mapping of an input data (feature) vector into a scalar output, i.e., it maps numbers into numbers. Fuzzy set theory and fuzzy logic establish the specifics of the nonlinear mapping. This tutorial paper provides a guided tour through those aspects of fuzzy sets and fuzzy logic that are necessary to synthesize an FLS. It does this by starting with crisp set theory and dual logic and demonstrating how both can be extended to their fuzzy counterparts. Because engineering systems are, for the most part, causal, we impose causality as a constraint on the development of the FLS. After synthesizing a FLS, we demonstrate that it can be expressed mathematically as a linear combination of fuzzy basis functions, and is a nonlinear universal function approximator, a property that it shares with feedforward neural networks. The fuzzy basis function expansion is very powerful because its basis functions can be derived from either numerical data or linguistic knowledge, both of which can be cast into the forms of IF-THEN rules     

军用飞机研制风险的模糊综合评价方法

针对风险评价中信息的模糊性和不确定性,提出了军用飞机研制风险的模糊综合评价方法.首先,对风险评价的一般方法进行分析;然后,确定了军用飞机研制的风险源因素和风险后果因素.采用模糊集表示风险源因素对研制失败的影响和风险后果因素的大小,并对各个因素进行模糊评价;最后,根据各个因素的模糊评价矩阵及其权重,采用模糊综合评价方法获得研制风险的失败概率和失败后果,由失败概率和失败后果可得到研制风险的大小.算例表明,模糊综合评价方法可将风险评价中的模糊和不确定信息定量化处理,能够有效地对军用飞机的研制风险进行评价.     

Deregulated electricity market data representation by fuzzyregression models

In this paper, the authors present a fuzzy set-based model that represents the relation of electricity demand and price in a recently deregulated electricity market. A simple regression analysis shows the price data's nonlinear trend as the demand volume increases. We have divided the data cluster into two overlapping regions: low demand and high demand. Regression curves, obtained for the two clusters, are smoothly connected by a Takagi-Sugeno-Kang (TSK)-fuzzy model. The fuzzy model is further expanded to encompass the volatile data region by introducing fuzzy numbers in regression parameters. The developed model can indicate the possibility distribution of electricity prices for a given demand value. The model also has the flexibility of narrowing its focus by modifying the fuzzy numbers. California Power Exchange market data are analyzed as a numerical example     

基于可能性理论的测量数据处理

测量数据的可能性分布充分地反映测量值的不完备程度，不仅表达了测量值与真值的相容程度，还表示了不同置信水平下的置信区间。利用概率分布到可能性分布的最优转换以及简单三角形转换，可以建立3种常见的测量数据的可能性分布模型，并据此提出了3种测量不确定度的评估方法。     

Fuzzy classification of patient state with application toelectrodiagnosis of peripheral polyneuropathy

A methodology which accounts for uncertainty or imprecision in experimental observations and both norm and pathology definitions is developed on the basis of a distance measure between fuzzy numbers. These fuzzy numbers may represent, respectively, the measurements, norm, and pathology. The distance measure, called normalized fuzzy pathology index (NFPI), evaluates the difference of distance between observed experimental values for a given patient and norm on the one hand, and pathology on the other hand. The NFPI characterizes patient state as a continuous index; however, to conform to medical usage, categories of values are defined. Each of these categories corresponds to a linguistic variable. The case study used to illustrate the methodology is the electrodiagnosis of peripheral polyneuropathy in diabetic patients. Here, four initial linguistic categories are defined by a physician, namely: normal state, borderline state, clear-cut, and severe pathology. The NFPI is calculated in three cases that provide a sensitivity analysis on measurement fuzziness and distance function weighting. The model is calibrated using 203 cases and validated using 291 different cases. The results correspond very closely to the physician's diagnosis. The loss of information in discretizing the continuous state of patients is discussed. Transferring this fuzzy approach to other cases where the concept of distance is relevant offers no difficulty     

An optimization model of communications satellite planning

A mathematical planning model is developed to help make cost effective decisions on key physical and operational parameters, for a satellite intended to provide customer premises services. The major characteristics of the model are: (1) interactions and tradeoffs among technical variables are formally captured; (2) values for capacity and operational parameters are obtained through optimization; (3) effects of physical and regulatory constraints are included; and (4) the effects of market prices for transmission capacity on planning variables are explicitly captured. The model is solved optimally using geometric programming methods. Sensitivity analysis yields coefficients, analogous to shadow prices, that quantitatively indicate the change in objective function value resulting from variations in input parameter values. This helps in determining the robustness of planning decisions and in coping with some of the uncertainty that exists at the planning stage. The model can therefore be useful in making economically viable planning decisions for communications satellites