Similarities and distances in fuzzy regression modeling

We study the set of the solutions of a fuzzy regression model as a metric space. For each metric, we define a similarity ratio in order to compare the spaces of solutions of a fuzzy regression model. We prove that the similarity ratios, that can be extracted from these different metrics, are all the same as in [4]. As an application, we use the similarity ratio to produce fuzzy classification of models. A numerical example, involving economic data, is given.The research reported in this paper was carried out in the framework of MathInd Project     

A new approach to fuzzy modeling

This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm     

Gaussian kernel-based fuzzy inference systems for high dimensional regression

We propose a novel architecture for a higher order fuzzy inference system (FIS) and develop a learning algorithm to build the FIS. The consequent part of the proposed FIS is expressed as a nonlinear combination of the input variables, which can be obtained by introducing an implicit mapping from the input space to a high dimensional feature space. The proposed learning algorithm consists of two phases. In the first phase, the antecedent fuzzy sets are estimated by the kernel-based fuzzy c-means clustering. In the second phase, the consequent parameters are identified by support vector machine whose kernel function is constructed by fuzzy membership functions and the Gaussian kernel. The performance of the proposed model is verified through several numerical examples generally used in fuzzy modeling. Comparative analysis shows that, compared with the zero-order fuzzy model, first-order fuzzy model, and polynomial fuzzy model, the proposed model exhibits higher accuracy, better generalization performance, and satisfactory robustness.     

A new method for fuzzy information retrieval based on fuzzy hierarchical clustering and fuzzy inference techniques

In this paper, we extend the work of Kraft et al. to present a new method for fuzzy information retrieval based on fuzzy hierarchical clustering and fuzzy inference techniques. First, we present a fuzzy agglomerative hierarchical clustering algorithm for clustering documents and to get the document cluster centers of document clusters. Then, we present a method to construct fuzzy logic rules based on the document clusters and their document cluster centers. Finally, we apply the constructed fuzzy logic rules to modify the user's query for query expansion and to guide the information retrieval system to retrieve documents relevant to the user's request. The fuzzy logic rules can represent three kinds of fuzzy relationships (i.e., fuzzy positive association relationship, fuzzy specialization relationship and fuzzy generalization relationship) between index terms. The proposed fuzzy information retrieval method is more flexible and more intelligent than the existing methods due to the fact that it can expand users' queries for fuzzy information retrieval in a more effective manner.     

A new approach to formulate fuzzy regression models

A fuzzy regression model is developed to construct the relationship between the response and explanatory variables in fuzzy environments. To enhance explanatory power and take into account the uncertainty of the formulated model and parameters, a new operator, called the fuzzy product core (FPC), is proposed for the formulation processes to establish fuzzy regression models with fuzzy parameters using fuzzy observations that include fuzzy response and explanatory variables. In addition, the sign of parameters can be determined in the model-building processes. Compared to existing approaches, the proposed approach reduces the amount of unnecessary or unimportant information arising from fuzzy observations and determines the sign of parameters in the models to increase model performance. This improves the weakness of the relevant approaches in which the parameters in the models are fuzzy and must be predetermined in the formulation processes. The proposed approach outperforms existing models in terms of distance, mean similarity, and credibility measures, even when crisp explanatory variables are used.     

直觉F推理与普通F推理的比较研究

直觉F推理克服了普通F推理在不确定性信息的描述、推理结果可信性等方面存在的局限性。在介绍普通F推理直觉化扩展的基础上,首先分析了两类推理算法的相互转化问题,指出普通F推理是直觉F推理的一种特例,当直觉指数为0时二者可相互转化。其次,比较了两类算法的还原性,分析表明Zadeh型、Mamdani型、Larsen型直觉F推理算法与其对应的普通F推理算法具有相同的还原性。最后,通过实例研究了直觉F推理算法在推理结果精度、可信性上的优势,从而较普通F推理更适用于智能控制与决策。     

A general-purpose fuzzy inference processor

The SAE 81C99 processor exhibits 4 different operation modes, 8 programmable fuzzy algorithms, and up to 256 inputs, 64 outputs, and 16,384 rules. The 1.0-μm CMOS chip serves as a stand-alone device or as an on-chip module for 8- or 16-bit microcontrollers. At 20-MHz crystal frequency and a maximum inference speed of 10 million rules/s, it supports very complex systems and millisecond (and faster) processes such as automotive electronics and pattern recognition     

A new GRASS GIS fuzzy inference system for massive data analysis

GIS systems are frequently coupled with fuzzy logic systems implemented in statistical packages. For large GIS data sets including millions or tens of millions of cells, such an approach is relatively time-consuming. For very large data sets there is also an input/output bottleneck between the GIS and external software. The aim of this paper is to present low-level implementation of Mamdani’s fuzzy inference system designed to work with massive GIS data sets, using the GRASS GIS raster data processing engine.     

Fuzzy inference and fuzzy inference processor

Fuzzy inference, a data processing method based on the fuzzy theory that has found wide use in the control field, is reviewed. Consumer electronics, which accounts for most current applications of this concept, does not require very high speeds. Although software running on a conventional microprocessor can perform these inferences, high-speed control applications require much greater speeds. A fuzzy inference date processor that operates at 200000 fuzzy logic inferences per second and features 12-b input and 16-b output resolution is described     

一种基于模糊规则融合的模糊建模方法及其应用

为了有效地利用经验知识,弥补训练数据覆盖范围不足的问题,提出一种将经验知识以TSK (Takagi-Sugeno-Kang)型模糊规则引入模糊模型的建模方法.在结构辨识中,提出了模糊规则融合方法,用以确定初始模糊规则.在参数辨识中,改进了原梯度下降方法中的目标函数,并引入了经验知识准确性评价参数,用以平衡样本数据和经验知识对模型的影响.数值仿真和工程实例应用结果表明,所提出的方法可以有效地利用经验知识和样本数据,使预报结果更可靠、更精确.     

A new adaptive fuzzy inference system for electricity consumption forecasting with hike in prices

Large increase or hike in energy prices has proven to impact electricity consumption in a way which cannot be drawn from historical data, especially when price elasticity of demand is not significant. This paper proposes an integrated adaptive fuzzy inference system (FIS) to estimate and forecast long-term electricity consumption when prices experience large increase. To this end, first a novel procedure for construction and adaptation of Takagi–Sugeno fuzzy inference system (TS-FIS) is suggested. Logarithmic linear regressions are estimated with historical data and used to construct an initial first-order TS-FIS. Then, in the adaptation phase, expert knowledge is used to define new fuzzy rules which form a new secondary FIS for electricity forecasting. To show the applicability and usefulness of the proposed model, it is applied for forecasting of annual electricity consumption in Iran where removing energy subsidies has resulted in a hike in electricity prices. Gross domestic product (GDP), population and electricity price are three inputs for the initial TS-FIS. A questionnaire survey was conducted to collect the expert estimation on possible change in electricity per capita, change in electricity intensity and the ratio of GDP elasticity to population elasticity when price hikes. Based on the information collected, a fuzzy rule base is formed and used to construct the secondary FIS which is used for electricity forecasting until 2016. Furthermore, the performance of the proposed model of this paper is compared with three other models namely ANFIS, ANN and one-stage regression in terms of their mean absolute percentage error. The comparison shows a superior performance for the proposed FIS model.     

复合二维模糊控制器及其模糊推理方法的研究

实现三维模糊控制效果, 而控制规则数与二维模糊控制器相当. 模糊控制规则解析生成. 模糊推理方法基于相平面, 计算量小, 直接用输入连续量进行推理. 该控制器结构及算法简单, 易于在线实现, 具有通用性. 将其用于交流调速系统, 实验结果表明控制性能较PI算法更佳.     

基于核模糊聚类的多模型LSSVM回归建模

针对大规模数据采用单模型回归存在精度差和计算量较大的问题,提出一种基于核模糊聚类的多模型最小二乘支持向量回归建模方法.该方法首先使用基于条件正定核的模糊C均值聚类算法对数据集做出聚类划分;然后针对每个聚类做最小二乘支持向量回归估计;同时根据每个聚类内数据分布的特征,给出了一种简单的核参数选择方法.利用数值仿真实验进行非线性函数估计,实验结果表明了所提出的方法具有良好的精度和泛化能力.     

A hybrid fuzzy regression model and its application in hydrology engineering

The goal of this paper is to handle the large variation issues in fuzzy data by constructing a variable spread multivariate adaptive regression splines (MARS) fuzzy regression model with crisp parameters estimation and fuzzy error terms. It deals with imprecise measurement of response variable and crisp measurement of explanatory variables. The proposed method is a two-phase procedure which applies the MARS technique at phase one and an optimization problem at phase two to estimate the center and fuzziness of the response variable. The proposed method, therefore, handles two problems simultaneously: the problem of large variation issue and the problem of variation spreads in fuzzy observations. A realistic application of the proposed method is also presented, by which the suspended load is modeled using discharge in a hydrology engineering problem. Empirical results demonstrate that the proposed approach is more efficient and more realistic than some well-known least-squares fuzzy regression models.     

A new approach to fuzzy modeling and control of discrete-time systems

We present a new approach to fuzzy modeling and control of discrete-time systems which is based on the formulation of a novel state-space representation using the hyperbolic tangent function. The new representation, designated the hyperbolic model, combines the advantages of fuzzy system theory and classical control theory. On the one hand, the hyperbolic model is easily derived from a set of Mamdani-type fuzzy rules. On the other hand, classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of Mamdani-type fuzzy rules. Thus, this new approach combines the best of two worlds. It enables linguistic interpretability of both the model and the controller, and guarantees closed-loop stability and robustness.     

A context switchable fuzzy inference chip

This paper describes a novel design of a fuzzy inference chip that allows for real-time online context switching. A context refers to a situation or scenario of an application requiring specific domain knowledge. In particular, our focus is on the class of applications involving embedded fuzzy control. The domain knowledge therefore refers to fuzzy rules and memberships. The kind of applications being considered is real-time in nature, which necessitates the implementation of hardware for fuzzy inferencing. The chip architecture is described and details on the design of the chip is presented.     

基于Sugeno型模糊推理算法的模糊控制器及其应用

介绍了Sugeno型模糊推理算法的基本原理,给出了一种实现方法,并对其控制性能进行了仿真.     

Least-squares approach to regression modeling in full interval-valued fuzzy environment

A regression procedure is introduced when the observations of the response and the independent variables, as well as the coefficients that are to be estimated, are triangular interval-valued fuzzy numbers (IVFNs). The coefficients of the model are obtained by least square method, using a distance that we define on the space of IVFNs. Three real data sets, on soil sciences and hydrology engineering are used to test the applicability of the proposed method. The predictive performance of the models thus obtained are examined by cross-validation. To check the overall performance of the proposed method, two measures of goodness of fit are introduced and employed.     

一种新的动态关联规则及其挖掘算法

在分析原有定义不足的基础上,提出一种新的动态关联规则,其支持度向量和置信度向量与经典定义相吻合,能更好地反映规则随时间变化的动态信息．进一步提出两种新的动态关联规则挖掘算法：ＩＴＳ和ＥＦＰｇｒｏｗｔｈ．其中：两阶段ＩＴＳ算法具有较好的可理解性;基于扩展ＦＰ树的ＥＦＰｇｒｏｗｔｈ算法适宜于高密度海量数据的挖掘．实验结果表明,该算法具有较好的挖掘性能和可扩展性,适用于动态关联规则的有效挖掘．