A hierarchical model of a linguistic variable

In this work a theoretical hierarchical model of dichotomous linguistic variables is presented. The model incorporates certain features of the approximate reasoning approach and others of the Fuzzy Control approach to Fuzzy Linguistic Variables. It allows sharing of the same hierarchical structure between the syntactic definition of a linguistic variable and its semantic definition given by fuzzy sets. This fact makes it easier to build symbolic operations between linguistic terms with a better grounded semantic interpretation. Moreover, the family of fuzzy sets which gives the semantics of each linguistic term constitutes a multiresolution system, and thanks to that any fuzzy set can be represented in terms of the set of linguistic terms. The model can also be considered a general framework for building more interpretable fuzzy linguistic variables with a high capacity of accuracy, which could be used to build more interpretable Fuzzy Rule Based Systems (FRBS).     

FRACTAL GEOMETRY: A TOOL FOR FUZZY REASONING

Abstract

A new procedure for construction of a fuzzy number is given, based on the covering of points by consequently contracting intervals. The approach leads to the membership function in the form of Devil's staircase, a borderline fractal finding many applications in the modern physics. The alternative definition of subsethood based on the self-similarity of the sets is also given.     

Learning fuzzy rules with tabu search-an application to control

We present an approach for the automatic definition of the fuzzy rules for a fuzzy controller based on the use of the tabu search (TS) scheme. We show also how the application of the TS process to the learning of a fuzzy rule base can be improved using heuristic symbolic meta rules. The paper is divided in two parts. The first part presents an introduction to TS and different learning schemes which can be used to apply it for the determination of the fuzzy control rules. The second part illustrates the application of the proposed techniques to a specific control problem-the parking of a truck and trailer. In particular, Section V illustrates the definition of a rule base for a static fuzzy controller, while Section VI presents the construction of an adaptive parking controller     

A PRACTICAL APPROACH TO PRIORITIZE PROJECT ACTIVITIES THROUGH FUZZY RANKING

Effective management of project activities is a critical issue for project managers, especially when the projects are complex. This is more essential for projects where the number of activity attributes is numerous. In such circumstances, prioritizing of project activities is an important issue and can enable better management of projects by focusing more on the most critical activities. However, in many cases prioritizing project activities can be a difficult task because some of the activity attributes might not be expressed easily in crisp terms. In this article, a practical fuzzy rating and ranking approach is proposed to prioritize project activities with fuzzy attributes. The proposed approach is also tested through an example problem from the literature.     

An algorithmic approach for fuzzy inference

To apply fuzzy logic, two major tasks need to be performed: the derivation of production rules and the determination of membership functions. These tasks are often difficult and time consuming. This paper presents an algorithmic method for generating membership functions and fuzzy production rules; the method includes an entropy minimization for screening analog values. Membership functions are derived by partitioning the variables into the desired number of fuzzy terms and production rules are obtained from minimum entropy clustering decisions. In the rule derivation process, rule weights are also calculated. This algorithmic approach alleviates many problems in the application of fuzzy logic to binary classification     

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。     

A VLSI fuzzy inference processor based on a discrete analogapproach

In this paper we present a design for a general-purpose fuzzy processor, the core of which is based on an analog-numerical approach combining the inherent advantages of analog and digital implementations, above all as regards noise margins. The architectural model proposed was chosen in such a way as to obtain a processor capable of working with a considerable degree of parallelism. The internal structure of the processor is organized as a cascade of pipeline stages which perform parallel execution of the processes into which each inference can be decomposed. A particular feature of the project is the definition of a `fuzzy-gate', which executes elementary fuzzy computations, on which construction of the whole core of the processor is based. Designed using CMOS technology, the core can be integrated into a single chip and can easily be extended. The performance obtainable, in the order of 50 Mega fuzzy rules per second, is of a considerable level     

Stability analysis and design of Takagi-Sugeno fuzzy systems

This work presents stable composite control criteria for multivariable Takagi-Sugeno (T-S) fuzzy systems. On the basis of the linear matrix inequality (LMI) control strategy and parametric optimization, the composite fuzzy control algorithms are derived. Unlike earlier studies of fuzzy control systems on an LMI framework, this investigation develops a supervisory control approach, such that a fuzzy controller can be synthesized more efficiently. Moreover, a robust control scheme is applied to the T-S fuzzy model with parametric uncertainties. The sufficient conditions are deduced in the form of reduced LMIs and adaptive tuning rules. Finally, numeric simulations are given to validate the proposed approach.     

Similarity measures,penalty functions,and fuzzy entropy from new fuzzy subsethood measures

In this study, we discuss a new class of fuzzy subsethood measures between fuzzy sets. We propose a new definition of fuzzy subsethood measure as an intersection of other axiomatizations and provide two construction methods to obtain them. The advantage of this new approach is that we can construct fuzzy subsethood measures by aggregating fuzzy implication operators which may satisfy some properties widely studied in literature. We also obtain some of the classical measures such as the one defined by Goguen. The relationships with fuzzy distances, penalty functions, and similarity measures are also investigated. Finally, we provide an illustrative example which makes use of a fuzzy entropy defined by means of our fuzzy subsethood measures for choosing the best fuzzy technique for a specific problem.     

Designing decision trees with the use of fuzzy granulation

In this study, we discuss the use of fuzzy sets regarded as a well-rounded algorithmic vehicle in the construction of decision trees. The concept of fuzzy granulation realized via context-based clustering is aimed at the quantization (discretization) of continuous attributes as well as handling continuous classes encountered in classification problems. Two detailed experimental studies are presented concerning well-known data sets available on the Web     

A solution to the end-effector position optimisation problem in robotics using neural networks

The paper presents an original application of the Hopfield-type neural network to a robotics optimisation problem. The robot considered features an arm composed of three revolute joints, the last of which is the end-effector. The robot is planar as the movement of the end-effector is limited to one plane. The mechanical characteristics of the actuators in the joints, the accuracy of the angle position sensors, and dimensional errors in the mechanical elements which make up the end-effector all contribute towards an end-effector positioning error along an assigned trajectory. The computational complexity of the algorithmic solution to the minimisation of this error is at times incompatible with certain particularly critical industrial applications. To reduce the calculation time, the author presents a neural approach based on a Hopfield-type model. A detailed definition of the neural approach is given, its capacity for solving the problem is demonstrated, and the computational complexity is analysed. This analysis shows the drastic computational reduction provided by the neural approach as compared with an algorithmic solution to the problem of end-effector position optimisation.     

一种基于模糊聚类的图象分割方法

模糊Ｃ－均值（ＦＣＭ）算法用于图象分割，是一种非监督模糊聚类后标定的过程，但是，ＦＣＭ算法存在着一些不足，进而限制了它在某些方面的应用，本文提出了一种基于模糊聚类的图象分割方法，较好解决了ＦＣＭ算法所遇到的问题，且本文从数学上和实验上证明了这种方法的有效性。     

一种进化模糊逻辑控制器的新方法

结合进化学习分类器的密歇根和匹兹堡方法的优点,首次将对单条控制规则的评价引入了模糊逻辑控制器（ＦＬＣ）的进化过程中,解决了匹兹堡类型的学习分类器系统“强化信息的带宽窄”的问题,实现了ＦＬＣ在控制器级和规则级的同时进化,控制器的控制规则数目也可以自由变化,实验结果表明新方法有较高的效率,优化的模糊控制器的结构简单,性能良好。     

基于模糊数学的数字图像模糊度

图像的品质评定是图像处理领域的一项重要课题，难以对其给出客观的评价，文中引进模糊数学中的三角模算子与非模糊基数学模拟，定主了数字图像模糊度，理论与实现表明，该定义比模糊指数更符合人眼的视觉特征，并可用于评价图像器质，图像模糊度能够明显提高图像处理系统的效率。     

基于PAR的算法形式化开发

形式化方法是构建可信软件的重要途径.基于对算法问题的分析,针对形式化方法PAR开发算法的特征,刻划了问题分划、递推关系构造方面的规律.从一类问题的形式化功能规约出发,可机械地完成问题的分划及规约的变换,自然地揭示出求解问题的算法思想,在相关工具的支持下自动生成算法程序.研究结果将算法设计中尽可能多的创造性劳动转化为非创造性劳动,降低了形式化求解算法问题的难度,提高了算法程序的可靠性和形式化开发效率.     

MODEL-BASED FUZZY LOGIC CONTROL OF A NONLINEAR PLANT

A full-envelope controller for nonlinear systems is developed based on a novel model-based fuzzy logic control (MBFLC) approach. This approach envisages a bank of linear compensators, with each compensator optimized for a different operating point throughout the operational envelope. The fuzzy logic module properly blends the compensator outputs into a composite control signal, and avoids instability when none of the individual compensators are valid. In general practice, in the strongly nonlinear system under consideration, the fuzzy element of the MBFLC dominates due to the extremely small regions of validity of perturbation models of the strongly nonlinear plant. The MBFLC, with the composite control input smoothed by a linear compensator, provides full-envelope control of the benchmark plant. © 1997 by John Wiley & Sons, Ltd. This paper was produced under the auspices of the US Government and it is therefore not subject to copyright in the US.     

A fuzzy analytic hierarchy process approach in modular product design

Product development stages. The analytic hierarchy process (AHP), which breaks down a complex problem into simple hierarchical decision-making processes, can be incorporated with fuzzy logic to suggest the relative strength of the factors in the corresponding criteria, thereby enabling the construction of a fuzzy judgement matrix to facilitate decision-making. This paper proposes a fuzzy AHP approach in modular product design complemented with a case example to validate its feasibility in a real company. Test findings indicate that the approach is helpful for providing key decision support information in terms of product module selection during product development stages. The significance of the contribution of this paper is the suggestion of a novel approach in modular product design, embracing a combination of computational intelligence and traditional techniques, thereby providing more alternatives and ideas for those researchers who are interested in this field of study.     

Investigating a relevance of fuzzy mappings

The study introduces a concept of relevance of fuzzy mappings regarded as fundamental constructs of granular computing and rule-based systems, in particular. The notion of relevance of the fuzzy mappings is instrumental in the quantification of the quality of such mappings prior to their detailed construction. For the purposes of such quantification, we introduce shadowed sets and discuss as an algorithmic framework to be instrumental in expressing and quantifying the property of relevance of the fuzzy mappings. It is revealed that shadowed sets provide an interesting three-valued quantification of this property (such as acceptable mapping, marginal mapping, and a lack of mapping). The paper includes a number of detailed calculations concerning two commonly exploited classes of triangular and Gaussian fuzzy sets. Numerical studies are discussed as well.