Interval type-2 neuro-fuzzy system with implication-based inference mechanism

Neuro-fuzzy systems have been proved to be an efficient tool for modelling real life systems. They are precise and have ability to generalise knowledge from presented data. Neuro-fuzzy systems use fuzzy sets – most commonly type-1 fuzzy sets. Type-2 fuzzy sets model uncertainties better than type-1 fuzzy sets because of their fuzzy membership function. Unfortunately computational complexity of type reduction in general type-2 systems is high enough to hinder their practical application. This burden can be alleviated by application of interval type-2 fuzzy sets. The paper presents an interval type-2 neuro-fuzzy system with interval type-2 fuzzy sets both in premises (Gaussian interval type-2 fuzzy sets with uncertain fuzziness) and consequences (trapezoid interval type-2 fuzzy set). The inference mechanism is based on the interval type-2 fuzzy Łukasiewicz, Reichenbach, Kleene-Dienes, or Brouwer–Gödel implications. The paper is accompanied by numerical examples. The system can elaborate models with lower error rate than type-1 neuro-fuzzy system with implication-based inference mechanism. The system outperforms some known type-2 neuro-fuzzy systems.     

Data mining with a simulated annealing based fuzzy classification system

In this paper, the use of simulated annealing (SA) metaheuristic for constructing a fuzzy classification system is presented. In several previous investigations, the capability of fuzzy systems to solve different kinds of problems has been demonstrated. Simulated annealing based fuzzy classification system (SAFCS), hybridizes the learning capability of SA metaheuristic with the approximate reasoning method of fuzzy systems. The objective of this paper is to illustrate the ability of SA to develop an accurate fuzzy classifier. The use of SA in classification is an attempt to effectively explore and exploit the large search space usually associated with classification problems, and find the optimum set of fuzzy if–then rules. The SAFCS would be capable to extract accurate fuzzy classification rules from input data sets, and applies them to classify new data instances in different predefined groups or classes. Experiments are performed with eight UCI data sets. The results indicate that the proposed SAFCS achieves competitive results in comparison with several well-known classification algorithms.     

一种栅格图层的模糊叠置分析模型

为了更好地进行GIS空间分析，根据GIS应用领域中属性数据的区间值特征，首先利用区间值模糊集来描述模糊属性数据的模糊图层，然后基于区间值模糊集给出了一种栅格图层的模糊叠置分析模型，并改进了基于经典模糊集的模糊叠置分析方法。该模型利用区间值模糊集的基本运算，可以实现普通模糊叠置和加权模糊叠置，而采用区间值，则可以减少属性值模糊性的丢失，且叠置结果符合人们的认知和推理规律，实例结果表明，该模型能够较好地解决区间值属性图层间的模糊叠置分析问题。     

Fuzzy semi-parametric partially linear model with fuzzy inputs and fuzzy outputs

A large number of accounting studies have focused on parametric or non-parametric forms of fuzzy regression relationships between dependent and independent variables. Notably, semi-parametric partially linear model as a powerful tool to incorporate statistical parametric and non-parametric regression analyses has gained attentions in many real-life applications recently. However, fuzzy data find application in many real studies. This study is an investigation of semi-parametric partially linear model for such cases to improve the conventional fuzzy linear regression models with fuzzy inputs, fuzzy outputs, fuzzy smooth function and non-fuzzy coefficients. For this purpose, a hybrid procedure is suggested based on curve fitting methods and least absolutes deviations to estimate the fuzzy smooth function and fuzzy coefficients. The proposed method is also examined to be compared with a common fuzzy linear regression model via a simulation data set and some real fuzzy data sets. It is shown that the proposed fuzzy regression model performs more convenient and efficient results in regard to six goodness-of-fit criteria which concludes that the proposed model could be a rational substituted model of some common fuzzy regression models in many practical studies of fuzzy regression model in expert and intelligent systems.     

Reducing the number of parameters of a fuzzy system using scaling functions

Learning techniques are tailored for fuzzy systems in order to tune them or even for deriving fuzzy rules from data. However, a compromise between accuracy and interpretability has to be found. Flexible fuzzy systems with a large number of parameters and high degrees of freedom tend to function as black boxes. In this paper, we introduce an interpretation of fuzzy systems that enables us to work with a small number of parameters without loosing flexibility or interpretability. In this way, we can provide a learning algorithm that is efficient and yields accuracy as well as interpretability. Our fuzzy system is based on extremely simple fuzzy sets and transformations using interpretable scaling functions of the input variables.     

一种模糊区域的拓扑关系模型

空间区域拓扑关系建模是空间推理、地理信息系统(GIS)和计算机视觉等领域一个非常重要的主题，模糊区域的拓扑关系建模正日益受到相关领域研究者的重视，在分析现有模型的基础上，提出了一种模糊区域的拓扑关系模型，该模型利用模糊集来表示模糊区域，通过三个谓词的真值来判断区域间的拓扑关系，将分明区域作为特例统一处理，根据谓词的多种真值能够实现多层次上的拓扑关系分析．     

A coherent grid traversal approach to visualizing particle-based simulation data

We present an approach to visualizing particle-based simulation data using interactive ray tracing and describe an algorithmic enhancement that exploits the properties of these data sets to provide highly interactive performance and reduced storage requirements. This algorithm for fast packet-based ray tracing of multilevel grids enables the interactive visualization of large time-varying data sets with millions of particles and incorporates advanced features like soft shadows. We compare the performance of our approach with two recent particle visualization systems: one based on an optimized single ray grid traversal algorithm and the other on programmable graphics hardware. This comparison demonstrates that the new algorithm offers an attractive alternative for interactive particle visualization.     

Semi-parametric partially logistic regression model with exact inputs and intuitionistic fuzzy outputs

Some accounting studies have focused on logistic regression relationships between exact/fuzzy inputs/outputs. However, intuitionistic fuzzy sets find application in many real studies instead of fuzzy sets. On the other hand, semi-parametric partially linear model also has attracted attentions in recent years. This study is an investigation of intuitionistic fuzzy semi-parametric partially logistic model for such cases with exact inputs, intuitionistic fuzzy outputs, intuitionistic fuzzy smooth function and intuitionistic fuzzy coefficients. For this purpose, a hybrid procedure is suggested based on curve fitting methods and least absolutes deviations to estimate the intuitionistic fuzzy smooth function and intuitionistic fuzzy coefficients. The proposed method is also compared with a common fuzzy logistic regression model as a real fuzzy data set. It is shown that the proposed intuitionistic fuzzy logistic regression model performs better and efficient results in regard to some goodness-of-fit criteria suggest that the proposed model could be successfully applied in many practical studies of intuitionistic fuzzy logistic regression model in expert systems.     

Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic

Uncertainty is an inherent part in control systems used in real world applications. The use of new methods for handling incomplete information is of fundamental importance. Type-1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present in control systems. Type-2 fuzzy sets that are used in type-2 fuzzy systems can handle such uncertainties in a better way because they provide us with more parameters and more design degrees of freedom. This paper deals with the design of control systems using type-2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements, environmental noise, etc. The experimental results are divided in two classes, in the first class, simulations of a feedback control system for a non-linear plant using type-1 and type-2 fuzzy logic controllers are presented; a comparative analysis of the systems’ response in both cases was performed, with and without the presence of uncertainty. For the second class, a non-linear identification problem for time-series prediction is presented. Based on the experimental results the conclusion is that the best results are obtained using type-2 fuzzy systems.     

Integrating high resolution remote sensing,GIS and fuzzy set theory for identifying susceptibility areas of forest insect infestations

The use of fuzzy set theory has become common in remote sensing and geographical information system (GIS) applications to deal with issues surrounding the uncertainty of geospatial datasets. The objective of this study is to develop a model that integrates the concept of fuzzy set theory with remote sensing and GIS in order to produce susceptibility maps of insect infestations in forest landscapes. Fuzzy set theory was applied to information extracted from multiple‐year high resolution remote sensing data and integrated in a raster‐based GIS to create a map indicating the spatial variation of insect susceptibility in a landscape. Variable‐specific fuzzy membership functions were developed based on expert knowledge and existing data, and integrated through a semantic import model. The results from a case study on mountain pine beetle (Dendroctonus ponderosae Hopkins) illustrate that the model provides a method to successfully estimate areas of varying susceptibility to insect infestation from high resolution remote sensing images. It was concluded that fuzzy sets are an adequate method for dealing with uncertainty in defining susceptibility variables. The susceptibility maps can be utilized for guiding management decisions based on the spatial aspects of insect–host relationships.     

数据的模糊建模研究及其在加热炉中的应用

对于工业生产中的一些复杂、非线性系统,传统的建模方法很难描述其系统特性。但在实际生产中存在大量系统的输入输出数据、基于输入输出数据对复杂系统进行建模是一较好的途径。本文基于输入输出数据,提出一种决策树系统输入空间的划分方法,通过一定的数据训练,提取模糊规则,构成系统的模糊规则库,从而建立了非线性系统的模糊规则模型。仿真结果表明,该模型可以较好地描述系统的动态特性,同时也说明了该方法的快速性和有效性。     

Multi-objective genetic algorithms based automated clustering for fuzzy association rules mining

Researchers realized the importance of integrating fuzziness into association rules mining in databases with binary and quantitative attributes. However, most of the earlier algorithms proposed for fuzzy association rules mining either assume that fuzzy sets are given or employ a clustering algorithm, like CURE, to decide on fuzzy sets; for both cases the number of fuzzy sets is pre-specified. In this paper, we propose an automated method to decide on the number of fuzzy sets and for the autonomous mining of both fuzzy sets and fuzzy association rules. We achieve this by developing an automated clustering method based on multi-objective Genetic Algorithms (GA); the aim of the proposed approach is to automatically cluster values of a quantitative attribute in order to obtain large number of large itemsets in less time. We compare the proposed multi-objective GA based approach with two other approaches, namely: 1) CURE-based approach, which is known as one of the most efficient clustering algorithms; 2) Chien et al. clustering approach, which is an automatic interval partition method based on variation of density. Experimental results on 100 K transactions extracted from the adult data of USA census in year 2000 showed that the proposed automated clustering method exhibits good performance over both CURE-based approach and Chien et al.’s work in terms of runtime, number of large itemsets and number of association rules.     

双层模糊系统融合中心约束型最小包含球

与传统的TSK模糊系统相比,改进的双层TSK模糊系统CTSK(Central TSK Fuzzy System)有如下优点:良好的可解释性、更好的鲁棒性、较强的逼近能力。但对于大样本或超大样本数据集,其时间复杂度和空间复杂度的开销都极大地限制了它的实用性。针对此不足,通过模糊系统融合中心约束型最小包含球(CCMEB)理论提出了CCMEB-CTSK(CCMEB-based CTSK)算法。该算法在继承CTSK优点的同时,又较好地实现了处理大样本和超大样本数据集的有效性和快速性。仿真实验研究分析了采用不同模糊规则数的CCMEB-CTSK的性能指标和运行时间的比较,以及训练样本不加噪声和加入噪声情况下CCMEB-CTSK泛化能力和鲁棒性能的测试。     

Adaptive weighted fuzzy rule-based system for the risk level assessment of heart disease

Expert’s knowledge base systems are not effective as a decision-making aid for physicians in providing accurate diagnosis and treatment of heart diseases due to vagueness in information and impreciseness and uncertainty in decision making. For this reason, automatic diagnostic fuzzy systems are very time demanding to improve the diagnostic accuracy. In this paper, we have developed an automatic fuzzy diagnostic system based on genetic algorithm (GA) and a modified dynamic multi-swarm particle swarm optimization (MDMS-PSO) for prognosticating the risk level of heart disease. Our proposed fuzzy diagnostic system (FS) works as follows: i) Preprocess the data sets ii) Effective attributes are selected through statistical methods such as Correlation coefficient, R-Squared and Weighted Least Squared (WLS) method, iii) Weighted fuzzy rules are formed on the basis of selected attributes using GA, iv) MDMS-PSO is employed for the optimization of membership functions (MFs) of FS, v) Build the ensemble FS from the generated fuzzy knowledge base by fusing the different local FSs. Finally, to ascertain the efficiency of the adaptive FS, the applicability of the FS is appraised with quantitative, qualitative and comparative analysis on the publicly available different real-life data sets. From the empirical analysis, we see that this hybrid model can manage the knowledge vagueness and decision-making uncertainty precisely and it has yielded better accuracy on the different publicly available heart disease data sets than other existing methods so that it justifies its adaptability with different data sets.     

空间数据知识发现研究进展评述

首先对当前空间数据的复杂性特征进行了分析,提出海量的数据,空间属性之间的非线性关系,空间数据的尺度特征,空间信息的模糊性,空间维数的增高以及空间数据的缺值是当前空间数据复杂性的主要表现特征,并以其为线索将近年来在空间数据知识发现领域的研究进展及其热点进行了较为系统的归纳,在此基础上,对空间数据知识发现与GIS的关系进行了阐述,并对空间数据知识发现的未来发展趋势进行了展望。     

A general model for statistical analysis using fuzzy sets: Sufficient conditions for identifiability and statistical properties

Fuzzy sets and fuzzy state modeling require modifications of fundamental principles of statistical estimation and inference. These modifications trade increased computational effort for greater generality of data representation. For example, multivariate discrete response data of high (but finite) dimensionality present the problem of analyzing large numbers of cells with low event counts due to finite sample size. It would be useful to have a model based on an invariant metric to represent such data parsimoniously with a latent “smoothed” or low dimensional parametric structure. Determining the parameterization of such a model is difficult since multivariate normality (i.e., that all significant information is represented in the second order moments matrix), an assumption often used in fitting the most common types of latent variable models, is not appropriate. We present a fuzzy set model to analyze high dimensional categorical data where a metric for grades of membership in fuzzy sets is determined by latent convex sets, within which moments up to order J of a discrete distribution can be represented. The model, based on a fuzzy set parameterization, can be shown, using theorems on convex polytopes [1], to be dependent on only the enclosing linear space of the convex set. It is otherwise measure invariant. We discuss the geometry of the model's parameter space, the relation of the convex structure of model parameters to the dual nature of the case and variable spaces, how that duality relates to describing fuzzy set spaces, and modified principles of estimation.     

Designing fuzzy inference systems from data: Aninterpretability-oriented review

Fuzzy inference systems (FIS) are widely used for process simulation or control. They can be designed either from expert knowledge or from data. For complex systems, FIS based on expert knowledge only may suffer from a loss of accuracy. This is the main incentive for using fuzzy rules inferred from data. Designing a FIS from data can be decomposed into two main phases: automatic rule generation and system optimization. Rule generation leads to a basic system with a given space partitioning and the corresponding set of rules. System optimization can be done at various levels. Variable selection can be an overall selection or it can be managed rule by rule. Rule base optimization aims to select the most useful rules and to optimize rule conclusions. Space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters. Structure optimization is of a major importance: selecting variables, reducing the rule base and optimizing the number of fuzzy sets. Over the years, many methods have become available for designing FIS from data. Their efficiency is usually characterized by a numerical performance index. However, for human-computer cooperation another criterion is needed: the rule interpretability. An implicit assumption states that fuzzy rules are by nature easy to be interpreted. This could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts. The paper analyzes the main methods for automatic rule generation and structure optimization. They are grouped into several families and compared according to the rule interpretability criterion. For this purpose, three conditions for a set of rules to be interpretable are defined     

基于模糊集和粗糙集联系度的商务决策系统

粗糙集理论和模糊集理论都是研究信息系统中知识的不完整、不确定性问题,把集对分析中的联系度概念应用于粗糙集中,说明了粗糙集联系度与下近似集和上近似集的值化的关系,将粗糙集联系度理论与模糊集理论相结合,提出了一种基于模糊集和粗糙集联系度的综合评价方法,实例验证了该方法对一大类复杂信息系统的知识发现具有一定的应用价值。     

Knowledge acquisition in incomplete fuzzy information systems via the rough set approach

Abstract: Machine learning can extract desired knowledge from training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete and incomplete data sets. If attribute values are known as possibility distributions on the domain of the attributes, the system is called an incomplete fuzzy information system. Learning from incomplete fuzzy data sets is usually more difficult than learning from complete data sets and incomplete data sets. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete fuzzy data sets based on rough sets. The notions of lower and upper generalized fuzzy rough approximations are introduced. By using the fuzzy rough upper approximation operator, we transform each fuzzy subset of the domain of every attribute in an incomplete fuzzy information system into a fuzzy subset of the universe, from which fuzzy similarity neighbourhoods of objects in the system are derived. The fuzzy lower and upper approximations for any subset of the universe are then calculated and the knowledge hidden in the information system is unravelled and expressed in the form of decision rules.