基于二叉树型分层的广义混合模糊系统推理规则数的缩减

为避免广义混合模糊系统因输入变量个数的增加而引起规则爆炸现象,应用二叉树型分层方法给出混合推理规则,进而对广义混合模糊系统的输入实施二叉树型分层,从理论上获得了该系统分层后的输入输出表达式和推理规则总数的计算公式.此外,通过实例对该系统分层和不分层的规则总数进行了比较和分析,结果表明分层后广义混合模糊系统可大幅度缩减推理规则总数,并可有效地避免规则爆炸.     

A high performance edge detector based on fuzzy inference rules

Edge detection is an important topic in computer vision and image processing. In this paper, a novel edge detector based on fuzzy If-Then inference rules and edge continuity is proposed. The fuzzy If-Then rule system is designed to model edge continuity criteria. The maximum entropy principle is used in the parameter adjusting process. We also discuss the related issues in designing fuzzy edge detectors. We compare it with the popular edge detectors: Sobel and Canny edge detectors. The proposed fuzzy edge detector does not need parameter setting as Canny edge detector does, and it can preserve an appropriate detection in details. It is very robust to noise and can work well under high level noise situations, while other edge detectors cannot. The detector efficiently extracts edges in images corrupted by noise without requiring the filtering process. The experimental results demonstrate the superiority of the proposed method to existing ones.     

Adaptive-tree-structure-based fuzzy inference system

A new fuzzy inference system named adaptive-tree-structure-based fuzzy inference system (ATSFIS) is proposed, which is abbreviated as fuzzy tree (FT). The fuzzy partition of input data set and the membership function of every subset are obtained by means of the fuzzy binary tree structure based algorithm. Two structures of FT, FT-I, and FT-II, are presented. The characteristics of FT are: 1) The parameters of antecedent and consequent for a Takagi-Sugeno fuzzy model are learned simultaneously; and 2) The fuzzy partition of input data set is adaptive to the pattern of data distribution to optimize the number of the subsets automatically. The main advantage of FT is more suitable to solve the problems, for which the number of input dimension is large, since by using the fuzzy binary tree, every farther set will be partitioned into only two subsets no matter how large the input dimension is. Therefore, in some sense the "rule explosion" will be avoided possibly. In comparison with some existing fuzzy inference systems, it is shown that the FT is also of less computation and high accuracy. The advantages of FT are illustrated by simulation results.     

Interpreting and extracting fuzzy decision rules from fuzzy information systems and their inference

Information systems, which contain only crisp data, precise and unique attribute values for all objects, have been widely investigated. Due to the fact that in realworld applications imprecise data are abundant, uncertainty is inherent in real information systems. In this paper, information systems are called fuzzy information systems, and formalized by (objects; attributes; f), in which f is a fuzzy set and expresses some uncertainty between an object and its attribute values. To interpret and extract fuzzy decision rules from fuzzy information systems, the meta-theory based on modal logic proposed by Resconi et al. is modified. The modified meta-theory not only expresses uncertainty between objects and their attributes, but also uncertainty in the process of recognizing fuzzy information systems. In addition, according to perception computing (proposed by Zadeh), granules of fuzzy information systems can be represented by fuzzy decision rules, so that, fuzzy inference methods can be used to obtain the decision attribute of a new object. Finally, a novel way of combining evidences based on the modified meta-theory is introduced, which extends the concept of combining evidences based on Dempster-Shafer theory.     

改进的模糊推理规则图像边缘检测算法

图像边缘检测是数字图像处理领域的关键技术,边缘检测的结果决定了图像后续处理的质量。模糊推理规则边缘检测算法具有较强的边缘检测能力,并且具备一定的抗噪效果。但是,这种算法只在高斯噪声较小时有效,当高斯噪声较大时它的边缘检测效果甚至比Canny等算子的效果还差。针对模糊推理规则算法在强高斯噪声时效果较差的问题,提出一种改进的模糊边缘检测算法。该算法能够根据图像含噪情况调整边缘检测方案：当噪声较弱时,使用模糊推理规则边缘检测算法;当噪声较强时,为提高算法抑制噪声的能力,使用改进的模糊推理规则边缘检测算法。实验结果表明,该方法具有更好的抗噪性能和边缘检测能力。     

Increasing fuzzy rules cooperation based on evolutionary adaptive inference systems

This article presents a study on the use of parametrized operators in the Inference System of linguistic fuzzy systems adapted by evolutionary algorithms, for achieving better cooperation among fuzzy rules. This approach produces a kind of rule cooperation by means of the inference system, increasing the accuracy of the fuzzy system without losing its interpretability. We study the different alternatives for introducing parameters in the Inference System and analyze their interpretation and how they affect the rest of the components of the fuzzy system. We take into account three applications in order to analyze their accuracy in practice. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1035–1064, 2007.     

基于小波隶属函数的模糊推理规则优化

隶属函数决定着模糊集的特征,建立小波基函数与隶属函数之间的联系,从而利用小波分析探讨模糊推理的实质,以一种非对称Haar小波基与三角型、梯型隶属函数的对应关系为基础,将小波分析、遗传算法与模糊系统结合,利用遗传算法实现小波隶属函数的训练学习,进而实现模糊推理规则的优化。     

基于小波隶属函数的模糊推理规则优化

隶属函数决定着模糊集的特征，建立小波基函数与隶属函数之间的联系，从而利用小波分析探讨模糊推理的实质，以一种非对称Haar小波基与三角型、梯型隶属函数的对应关系为基础，将小波分析、遗传算法与模糊系统结合，利用遗传算法实现小波隶属函数的训练学习，进而实现模糊推理规则的优化。     

A fuzzy inference system for fault detection and isolation: Application to a fluid system

This work focuses on the design and implementation of a fuzzy inference system for fault detection and isolation (FDI) which can learn from example fault data, and the determination of a suitable optimisation strategy for the membership functions. A FDI system was developed which is based on adaptive fuzzy rules. A number of optimisation strategies were then applied; it was found that an evolutionary algorithm not only produced the best results but did so with relatively little processing effort and with excellent consistency.The adaptive fuzzy system, thus optimised, was tested against a neural network, which was trained to produce analogue outputs as an indication of fault magnitude. The fuzzy solution produced the best accuracy.We can conclude that an adaptive fuzzy inference system for FDI, using an evolutionary algorithm to learn from examples, can provide an accurate and readily comprehensible solution to diagnosing and evaluating fluid process plant faults.     

A fuzzy inference approach to template-based visual tracking

The tracking of visual features using appearance models is a well studied but still open area of computer vision. In the absence of knowledge about the structural constraints of the tracked object, the validity of the model can be compromised if only appearance information is used. We propose a fuzzy inference scheme that can be used to selectively update a given template-based model in tracking tasks. This allows us to track moving objects under translation, rotation, and scale changes with minimal feature drift. Moreover, no rigidity constraint needs to be enforced on the moving target. Some experiments have been performed using several targets, and the results are very close to the ground truth paths. The computational cost of our approach is low enough to allow its application in real-time tracking using modest hardware requirements.     

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 fuzzy inference and categorization approach for supplier selection using compensatory and non-compensatory decision rules

Fuzzy set theory has been used as an approach to deal with uncertainty in the supplier selection decision process. However, most studies limit applications of fuzzy set theory to outranking potential suppliers, not including a qualification stage in the decision process, in which non-compensatory types of decision rules can be used to reduce the set of potential suppliers. This paper presents a supplier selection decision method based on fuzzy inference that integrates both types of approaches: a non-compensatory rule for sorting in qualification stages and a compensatory rule for ranking in the final selection. Fuzzy inference rules model human reasoning and are embedded in the system, which is an advantage when compared to approaches that combine fuzzy set theory with multicriteria decision making methods. Fuzzy inference combined with a fuzzy rule-based classification method is used to categorize suppliers in qualification stages. Classes of supplier performance can be represented by linguistic terms, which allow decision makers to deal with subjectivity and to express qualification requirements in linguistic formats. Implementation of the proposed method and techniques were analyzed and discussed using an illustrative case. Three defuzzification operators were used in the final selection, yielding the same ranking. Factorial design was applied to test consistency and sensitivity of the inference rules. The findings reinforce the argument that including stages of qualification based on fuzzy inference and categorization makes this method especially useful for selecting from a large set of potential suppliers and also for first time purchase.     

Online probabilistic learning for fuzzy inference system

Online learning is a key methodology for expert systems to gracefully cope with dynamic environments. In the context of neuro-fuzzy systems, research efforts have been directed toward developing online learning methods that can update both system structure and parameters on the fly. However, the current online learning approaches often rely on heuristic methods that lack a formal statistical basis and exhibit limited scalability in the face of large data stream. In light of these issues, we develop a new Sequential Probabilistic Learning for Adaptive Fuzzy Inference System (SPLAFIS) that synergizes the Bayesian Adaptive Resonance Theory (BART) and Rule-Wise Decoupled Extended Kalman Filter (RDEKF) to generate the rule base structure and refine its parameters, respectively. The marriage of the BART and RDEKF methods, both of which are built upon the maximum a posteriori (MAP) principle rooted in the Bayes’ rule, offers a comprehensive probabilistic treatment and an efficient way for online structural and parameter learning suitable for large, dynamic data stream. To manage the model complexity without sacrificing its predictive accuracy, SPLAFIS also includes a simple procedure to prune inconsequential rules that have little contribution over time. The predictive accuracy, structural simplicity, and scalability of the proposed model have been exemplified in empirical studies using chaotic time series, stock index, and large nonlinear regression datasets.     

Boosting fuzzy rules in classification problems under single‐winner inference

In previous studies, we have shown that an Adaboost‐based fitness can be successfully combined with a Genetic Algorithm to iteratively learn fuzzy rules from examples in classification problems. Unfortunately, some restrictive constraints in the implementation of the logical connectives and the inference method were assumed. Alas, the knowledge bases Adaboost produces are only compatible with an inference based on the maximum sum of votes scheme, and they can only use the t‐norm product to model the “and” operator. This design is not optimal in terms of linguistic interpretability. Using the sum to aggregate votes allows many rules to be combined, when the class of an example is being decided. Because it can be difficult to isolate the contribution of individual rules to the knowledge base, fuzzy rules produced by Adaboost may be difficult to understand linguistically. In this point of view, single‐winner inference would be a better choice, but it implies dropping some nontrivial hypotheses. In this work we introduce our first results in the search for a boosting‐based genetic method able to learn weighted fuzzy rules that are compatible with this last inference method. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1021–1034, 2007.     

A hybrid model based on adaptive-network-based fuzzy inference system to forecast Taiwan stock market

In recent years, many academy researchers have proposed several forecasting models based on technical analysis to predict models such as Engle, 1982, Cheng et al., 2010. After reviewing the literature, two major drawbacks are found in past models: (1) the forecasting models based on artificial intelligence algorithms (AI), such as neural networks (NN) and genetic algorithms (GAs), produce complex and unintelligible rules; and (2) statistic forecasting models, such as time series, require some basic assumptions for variables and build forecasting models based on mathematic equations, which are not easily understandable by stock investors. In order to refine these drawbacks of past models, this paper has proposed a model, based on adaptive-network-based fuzzy inference system which uses multi-technical indicators, to predict stock price trends. Three refined processes have proposed in the hybrid model for forecasting: (1) select essential technical indicators from popular indicators by a correlation matrix; (2) use the subtractive clustering method to partition technical indicator value into linguistic values based on an data discretization method; (3) employ a fuzzy inference system (FIS) to extract rules of linguistic terms from the dataset of the technical indicators, and optimize the FIS parameters based on an adaptive network to produce forecasts. A six-year period of the TAIEX is employed as experimental database to evaluate the proposed model with a performance indicator, root mean squared error (RMSE). The experimental results have shown that the proposed model is superior to two listing models (Chen’s and Yu’s models).     

A systematic approach to the assessment of fuzzy association rules

In order to allow for the analysis of data sets including numerical attributes, several generalizations of association rule mining based on fuzzy sets have been proposed in the literature. While the formal specification of fuzzy associations is more or less straightforward, the assessment of such rules by means of appropriate quality measures is less obvious. Particularly, it assumes an understanding of the semantic meaning of a fuzzy rule. This aspect has been ignored by most existing proposals, which must therefore be considered as ad-hoc to some extent. In this paper, we develop a systematic approach to the assessment of fuzzy association rules. To this end, we proceed from the idea of partitioning the data stored in a database into examples of a given rule, counterexamples, and irrelevant data. Evaluation measures are then derived from the cardinalities of the corresponding subsets. The problem of finding a proper partition has a rather obvious solution for standard association rules but becomes less trivial in the fuzzy case. Our results not only provide a sound justification for commonly used measures but also suggest a means for constructing meaningful alternatives.

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.     

Using fuzzy inference system for architectural space analysis

Though architectural space is the main source and the only indispensable component of any architectural construction, in many cases its boundaries are uncertain, leading intuitive spatial design. Creating a mathematical model of architectural space with concrete results will offer many possibilities for design process in analysing spatial organization, independently from in architect's experience and intuitions. This paper presents a fuzzy inference system based spatial analysis model for spatial analysis for architectural design which brings many advantages to design process. The aim of this article is to investigate the potential of a fuzzy system with a Mamdami inference engine, considering different numbers of membership functions. Two venues have been selected and the fuzzy inference system based spatial analysis model is applied. For better judgement, outcomes of the model have been compared to depthmap analysis model. The results of the model indicate that fuzzy inference system based spatial analysis model performs very well, even with the limited and imprecise data. Such prototype can evolve into a tool for identifying spatial formations for improvements during the architectural design process.     

Concrete bridge deterioration diagnosis using fuzzy inference system

Bridge management systems (BMSs) are being developed in recent years to assist various authorities on the decision making in various stages of bridge maintenance, which requires, first of all, appropriate preliminary deterioration diagnosis and modeling. This paper presents a knowledge-based system for bridge damage diagnosis that aims to provide bridge designers with valuable information about the impacts of design factors on bridge deterioration. The validity of the influence parameters is verified by the principal component analysis (PCA). Fuzzy logic is utilized to handle uncertainties and imprecision involved, and a modified mountain clustering method (MMM) is employed for knowledge acquisition. The generated rule base is further optimized by the descent method (DM). Illustrative examples indicate that the techniques of the MMM, the PCA and the DM are reliable and efficient tools in generating diagnosis rules and in developing inference systems.     

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。