一类模糊模型的结构优化问题研究

提出了将模糊模型统计信息准则（FSIC）、基于奇异值分解（SVD）的模糊模型结构分析、模糊规则删除与合并、参数估计等方法集成的模糊模型结构迭代优化。研究表明,将SVD引入到模糊模型结构分析、结合FSIC指导模糊规则删除和合并,可从模型结构精简化、模型拟合和泛化性能等方面综合地确定最优模型结构;文中提出了实用可行的基于聚类加权组合和多重模糊聚类的规则合并算法。该迭代优化方法已成功地应用于非线性函数逼近和航空煤油干点估计器的模糊模型构造。仿真结果表明文中提出的方法简单实用,优化的模型结构比文献中给出的模型结构更加精简。     

基于模糊综合评价的课堂教学质量数据挖掘

本文从应用模糊综合评价法得到教师的课堂教学质量的评估等级和量化成绩,应用模糊聚类算法确定主关键条件属性集,使用模糊数据挖掘出评估数据库中教师课堂教学质量评估等级同评估指标之间的规则知识,以一个应用实例为对象建立的课堂教学质量模糊数据挖掘验证了该方法的可行性.     

基于模糊网络和粒子群优化的油田指标预测

针对油田开发指标预测问题,提出一种模糊神经网络模型,该模型包括输入层、模糊化层、规则层和输出层。模糊化层采用高斯隶属函数,规则层每个节点对应一条模糊逻辑规则。网络可调参数为模糊集参数和输出层权值。提出了基于改进量子粒子群优化的网络训练方法。以油田开发指标中含水率预测为例,结果表明该方法是有效的可行的。     

模糊聚类最大树算法在教学质量评估中的应用

应用模糊聚类最大树算法对教学质量评估指标进行聚类以确定关键评估指标集,使用模糊相似关系挖掘出大量数据中教学质量评估指标与评估等级之间的规则,并以本校数据实例为对象建立教学质量评估模糊数据挖掘验证了该方法的有效性。     

基于模糊粗糙集的粒度计算

粒度计算是一种新的智能计算的理论和方法，目前受到很多学者的关注。但是，具体可行的粒表示模型和不同粒的推理方法研究相对较少。本文将模糊粗糙集纳入粒度计算这种新的理论框架，对于处理复杂信息系统，求解复杂问题无疑具有重要的意义。首先利用笛卡尔积，构建了模糊关系下的信息粒；然后给出不同粒度下模糊粗糙算子的表示方法，进而形成一个分层递阶结构；最后考虑了对于模糊信息系统粒度粗细的选择问题，并给出一个实例，从而为粒度计算提供一个具体而实用的框架。     

基于贝叶斯风险最小化的航空发动机状态评估

为有效评估航空发动机所处运行状态，提出一种基于贝叶斯风险最小化原则的状态评估方法。利用模糊贝叶斯风险模型从发动机全寿命数据中挖掘得到最优特征子集及对应的权重，利用多属性决策集结运算结果和统计函数生成模糊规则，输出模糊语义形式的评估结果，从而实现逼近决策风险最小化的模糊状态评估。在数值试验中，以CMAPSS（Commercial Modular Aero-Propulsion System Simulation）发动机为研究对象，演示评估过程并验证所提方法的有效性，结果表明所提方法可有效评估发动机健康状态，为航空发动机状态评估提供了一种切实可行的模型。     

Takagi-Sugeno模糊系统双正则联合稀疏建模新方法

传统Takagi-Sugeno(T-S)模糊系统模型因模糊规则使用样本全部特征,导致模型的可解释性较差,冗余特征的存在还会导致模型的过拟合,降低模型的泛化性能。针对该问题,提出了一种模糊系统联合稀疏建模新方法L2-CFS-FIS(L2-common feature selection fuzzy inference systems),从而提高模型的泛化性能和可解释性。该方法充分考虑存在于模糊规则间的公共特征信息,同时引入模型过拟合处理机制,将模糊系统建模问题转化为一个基于双正则的联合优化问题,并使用交替方向乘子(alternating direction method of multipliers,ADMM)算法来进行求解。实验结果表明,该方法所构造的模糊系统不仅能够获得较为满意的泛化性能,而且通过有效地挖掘规则间重要的公共特征,可以确保模型具有较高的可解释性。     

基于模糊邻域粗糙集的启发式属性约简算法

属性约简是机器学习等领域中常用的数据预处理方法。在基于粗糙集理论的属性约简算法中,大多是根据单一的方法来度量属性重要度。为了从多角度对属性达到更为优越的评估效果,首先在已有的模糊邻域粗糙集模型中定义属性依赖度度量,然后根据粒计算理论中知识粒度的概念,在模糊邻域粗糙集模型下提出了模糊邻域粒度度量。由于属性依赖度和知识粒度代表了不同视角的属性评估方法,因此将这两种方法结合起来用于信息系统的属性重要度评估,最后给出一种启发式属性约简算法。实验结果表明,所提出的算法具有较好的属性约简性能。     

基于混沌DNA遗传算法的模糊递归神经网络建模

本文受生物DNA分子遗传机制和混沌优化算法的启发,提出了一种混沌DNA遗传算法,用于优化T-S模糊递归神经网络（FRNN）.该方法使用碱基序列表示T-S模糊递归神经网络的前件部分参数,包括模糊规则数,隶属度函数中心点和宽度;设计更为复杂的遗传操作算子来改进遗传算法的寻优性能;利用混沌优化算法优化种群中的较差个体.同时使用递推最小二乘法（RLS）来辨识T-S模糊递归神经网络的后件部分参数.最后,采用基于混沌DNA遗传算法的T-S模糊递归神经网络对一种典型的pH中和过程进行建模。通过与其他建模方法的比较,仿真实验结果表明了所建模型的有效性.     

基于聚类和遗传算法的解释性模糊模型设计

提出了一种基于模糊聚类和遗传算法构建解释性模糊模型的设计方法。定义了模糊模型的精确性指标，给出了模糊模型解释性的必要条件。然后利用模糊聚类算法和最小二乘法辨识初始的模糊模型；采用多目标遗传算法优化模糊模型；为提高模型的解释性，在遗传算法中利用基于相似性的模糊集合和模糊规则的简化方法对模型进行约简。采用该方法对Mackey-Glass系统进行建模，仿真结果验证了该方法的有效性。     

The granular extension of Sugeno-type fuzzy models based on optimal allocation of information granularity and its application to forecasting of time series

The Sugeno-type fuzzy models are used frequently in system modeling. The idea of information granulation inherently arises in the design process of Sugeno-type fuzzy model, whereas information granulation is closely related with the developed information granules. In this paper, the design method of Sugeno-type granular model is proposed on a basis of an optimal allocation of information granularity. The overall design process initiates with a well-established Sugeno-type numeric fuzzy model (the original Sugeno-type model). Through assigning soundly information granularity to the related parameters of the antecedents and the conclusions of fuzzy rules of the original Sugeno-type model (i.e. granulate these parameters in the way of optimal allocation of information granularity becomes realized), the original Sugeno-type model is extended to its granular counterpart (granular model). Several protocols of optimal allocation of information granularity are also discussed. The obtained granular model is applied to forecast three real-world time series. The experimental results show that the method of designing Sugeno-type granular model offers some advantages yielding models of good prediction capabilities. Furthermore, those also show merits of the Sugeno-type granular model: (1) the output of the model is an information granule (interval granule) rather than the specific numeric entity, which facilitates further interpretation; (2) the model can provide much more flexibility than the original Sugeno-type model; (3) the constructing approach of the model is of general nature as it could be applied to various fuzzy models and realized by invoking different formalisms of information granules.     

The modeling of time series based on fuzzy information granules

A lot of research has resulted in many time series models with high precision forecasting realized at the numerical level. However, in the real world, higher numerical precision may not be necessary for the perception, reasoning and decision-making of human. Model of time series with an ability of humans to perceive and process abstract entities (rather than numeric entities) is more adaptable for some problems of decision-making. With this regard, information granules and granular computing play a primordial role. Fox example, if change range (intervals) of stock prices for a certain period in the future is regarded as information granule, constructing model that can forecast change ranges (intervals) of stock prices for a period in the future is better able to help stock investors make reasonable decisions in comparison with those based upon specific forecasting numerical value of stock price. In this paper, we propose a new modeling approach to realize interval prediction, in which the idea of information granules and granular computing is integrated with the classical Chen’s method. The proposed method is to segment an original numeric time series into a collection of time windows first, and then build fuzzy granules expressed as a certain fuzzy set over each time windows by exploiting the principle of justifiable granularity. Finally, fuzzy granular model can be constructed by mining fuzzy logical relationships of adjacent granules. The constructed model can carry out interval prediction by degranulation operation. Two benchmark time series are used to validate the feasibility and effectiveness of the proposed approach. The obtained results demonstrate the effectiveness of the approach. Besides, for modeling and prediction of large-scale time series, the proposed approach exhibit a clear advantage of reducing computation overhead of modeling and simplifying forecasting.     

Optimal allocation of information granularity in system modeling through the maximization of information specificity: A development of granular input space

In this study, we introduce a concept of a granular input space in system modeling, in particular in fuzzy rule-based modeling. The underlying problem can be succinctly formulated in the following way: given is a numeric model, develop an efficient way of forming granular input variables so that the corresponding granular outputs of the model achieve the highest level of specificity. The rationale behind the formulation of the problem is offered along with several illustrative examples. In conjunction with the underlying idea, developed is an algorithmic framework supporting an optimization of the specificity of the model exposed to granular inputs (data). It is dwelled upon one of the principles of Granular Computing, namely an optimal allocation of information granularity. For illustrative purposes, the study is focused on information granules formalized in terms of intervals (however the proposed approach becomes equally relevant for other formalism of information granules). Some comparative analysis with the existing idea of global sensitivity analysis is also carried out by contrasting the essential differences among the two approaches and analyzing the results of computational experiments.     

Granular mappings

We are concerned with the granular representation of mappings (or experimental data) coming in the form R:R/spl rarr/[0,1] (for one-dimensional cases) and R:R/sup n//spl rarr/[0,1] (for multivariable cases) with R being a set of real numbers. As the name implies, a granular mapping is defined over information granules and maps them into a collection of granules expressed in some output space. The design of the granular mapping is discussed in the case of set and fuzzy set-based granulation. The proposed development is regarded as a two-phase process that comprises: 1) a definition of an interaction between information granules and experimental evidence or existing numeric mapping and 2) the use of these measures of interaction in building an explicit expression for the granular mapping. We show how to develop information granules in case of multidimensional numeric data by resorting to fuzzy clustering (fuzzy C-means). Experimental results serve as an illustration of the proposed approach.     

用模糊包含度构造超盒粒分类器

如何将训练集分割成大小不一的超盒粒是粒计算领域的关键问题之一。引入非线性正评价函数并用于构造超盒粒之间的模糊包含度函数,通过粒度阈值,对两个超盒粒有条件合并,构造含有大小不同超盒粒的分类器。实验结果表明超盒粒分类器与模糊格推理分类器相比提高了测试精度,与支持向量机相比加快了训练速度且提高了测试精度。     

Linguistic models and linguistic modeling

The study is concerned with a linguistic approach to the design of a new category of fuzzy (granular) models. In contrast to numerically driven identification techniques, we concentrate on budding meaningful linguistic labels (granules) in the space of experimental data and forming the ensuing model as a web of associations between such granules. As such models are designed at the level of information granules and generate results in the same granular rather than pure numeric format, we refer to them as linguistic models. Furthermore, as there are no detailed numeric estimation procedures involved in the construction of the linguistic models carried out in this way, their design mode can be viewed as that of a rapid prototyping. The underlying algorithm used in the development of the models utilizes an augmented version of the clustering technique (context-based clustering) that is centered around a notion of linguistic contexts-a collection of fuzzy sets or fuzzy relations defined in the data space (more precisely a space of input variables). The detailed design algorithm is provided and contrasted with the standard modeling approaches commonly encountered in the literature. The usefulness of the linguistic mode of system modeling is discussed and illustrated with the aid of numeric studies including both synthetic data as well as some time series dealing with modeling traffic intensity over a broadband telecommunication network.     

Granular neural networks: A study of optimizing allocation of information granularity in input space

In this paper, we develop a granular input space for neural networks, especially for multilayer perceptrons (MLPs). Unlike conventional neural networks, a neural network with granular input is an augmented study on a basis of a well learned numeric neural network. We explore an efficient way of forming granular input variables so that the corresponding granular outputs of the neural network achieve the highest values of the criteria of specificity (and support). When we augment neural networks through distributing information granularities across input variables, the output of a network has different levels of sensitivity on different input variables. Capturing the relationship between input variables and output result becomes of a great help for mining knowledge from the data. And in this way, important features of the data can be easily found. As an essential design asset, information granules are considered in this construct. The quantification of information granules is viewed as levels of granularity which is given by the expert. The detailed optimization procedure of allocation of information granularity is realized by an improved partheno genetic algorithm (IPGA). The proposed algorithm is testified effective by some numeric studies completed for synthetic data and data coming from the machine learning and StatLib repositories. Moreover, the experimental studies offer a deep insight into the specificity of input features.     

基于模糊格的超盒粒计算分类器

粒的表示、粒之间的关系和运算是粒计算的主要研究内容。利用向量表示超盒粒, 分析向量之间的偏序关 系和超盒粒之间的偏序关系的不一致性, 并引入保序函数消除该不一致性。利用格和其对偶格之间的非线性正评价函数和保序函数构造超盒粒之间模糊包含关系。为得到不同粒度的粒, 设计超盒粒之间的合并算子和分解算子, 证明由超盒粒集、超盒粒之间的模糊包含关系、合并算子、分解算子构成的代数系统是模糊格, 构造基于模糊格的超盒粒计算分类器。用机器学习数据集中的分类问题, 验证该分类器具有和模糊格推理分类器相同的推广能力并减少超盒粒的数量。     

Water quality prediction in a reservoir: Linguistic model approach for interval prediction

It is difficult to predict water quality in a reservoir because of the complex physical, chemical, and biological processes involved. In contrast to the well-known numeric models and artificial neural network models, Linguistic Models (LM) with context-based fuzzy clustering can offer reliable predictions of water quality. The main characteristics of LM are that it is user-centric and that it inherently dwells upon collections of highly interpretable and user-oriented entities, such as information granules. In this paper, we propose a model for evaluating water quality and then evaluate the effectiveness of the proposed method by performing comparisons on water quality data sets from a reservoir. Finally, we found that the proposed method not only has the better prediction performance than other models, but also can offer reliable intervals for uncertainty evaluation about the water quality.     

An optimization of allocation of information granularity in the interpretation of data structures: toward granular fuzzy clustering

Clustering forms one of the most visible conceptual and algorithmic framework of developing information granules. In spite of the algorithm being used, the representation of information granules-clusters is predominantly numeric (coming in the form of prototypes, partition matrices, dendrograms, etc.). In this paper, we consider a concept of granular prototypes that generalizes the numeric representation of the clusters and, in this way, helps capture more details about the data structure. By invoking the granulation-degranulation scheme, we design granular prototypes being reflective of the structure of data to a higher extent than the representation that is provided by their numeric counterparts (prototypes). The design is formulated as an optimization problem, which is guided by the coverage criterion, meaning that we maximize the number of data for which their granular realization includes the original data. The granularity of the prototypes themselves is treated as an important design asset; hence, its allocation to the individual prototypes is optimized so that the coverage criterion becomes maximized. With this regard, several schemes of optimal allocation of information granularity are investigated, where interval-valued prototypes are formed around the already produced numeric representatives. Experimental studies are provided in which the design of granular prototypes of interval format is discussed and characterized.