区间Type-2 T-S间接自适应模糊控制

本文在Type-1 T-S间接自适应模糊控制器的基础上,利用Type-2模糊系统理论,提出了区间Type-2 T-S间接自适应模糊控制器的设计方法.由于该系统的规则前件是区间Type-2模糊集合,后件为精确数,使构造的控制方法既具备Type-2模糊集处理诸多不确定性的特点,能够减少由于规则不确定对系统的影响,同时又具有T-S模糊模型后件为各输入变量的线性组合的特点,可以提高系统的建模精度,减少系统的规则数等优点.本文利用Lyapunov合成方法,研究了在所有变量一致有界的意义下,闭环系统的全局稳定性,分析了区间Type-2 T-S间接自适应模糊控制系统的收敛性,并给出了系统参数的自适应律.通过倒立摆跟踪模型进行仿真,验证其有效性和优越性.     

粗糙模糊集的近似表示

粗糙模糊集是利用粗糙集的 Pawlak 知识空间来近似刻画一个模糊集（不确定概念）的理论模型．粗糙模糊集用上、下近似模糊集作为目标概念的边界模糊集,它没有给出在当前知识基下如何得到目标模糊概念的近似模糊集或近似精确集的方法．文中首先给出模糊集的相似度（近似度）的概念,定义了 Pawlak 知识空间U／R 下的阶梯模糊集、均值模糊集、0．5-精确集等概念;然后分析得出U／R 知识空间下的均值模糊集是所有阶梯模糊集中与目标模糊集最接近的模糊集,U／R 知识空间下0．5-精确集是目标模糊集最接近的近似精确集;分析了均值模糊集、0．5-精确集分别与目标模糊集之间的相似度随知识粒度变化的变化规律．从新的视角提出了不确定性目标概念的近似表示和处理的方法,促进了不确定人工智能的发展．     

红外图像的一种Type-Ⅱ模糊增强算法

提出了一种基于Type-Ⅱ模糊集的红外图像增强算法,该算法首先根据像素的邻域相关性对图像进行预处理,然后以Ostu分割阈值为基础,构造了红外图像的Type-Ⅱ模糊特征平面;然后,采用不同的变换规则对图像进行模糊增强,并将结果进行融合;最后,通过Type reduction和去模糊化操作得到增强后的输出图像。对几幅典型的红外图像的增强实验表明,提出的方法能够有效地提高红外图像的对比度。     

模糊寻优问题的模糊遗传算法FGA

针对模糊寻优问题，本文基于模糊集的质心概念来确定模糊集的大小，并进而提出了模糊遗传算法ＦＧＡ。算法ＦＧＡ与遗传算法ＧＡ有本制区别，能用效地找到了模糊寻优问题的近似解，本文对算法ＦＧＡ的有效性作了较深入的分析。     

Matlab与C混合编程实现Type-2模糊系统

Type-2模糊系统的理论有着广泛的应用,但是Type-2模糊系统结构较Type-1模糊系统复杂,且编程实现难度和计算强度都较大.Matlab平台下,运用M语言调试算法,在实现Type-2模糊系统的基础上,利用C语言的高效性优化算法,改进程序,克服了Matlab计算瓶颈的问题.给出的Matlab C混合编程实现Type-2模糊系统的程序,编译后可以函数的形式调用,既保留了Matlab平台处理数据的便捷性,又具有很高的执行效率.仿真结果表明该方法的有效性.     

永磁同步电机自适应高阶滑模Type-2模糊控制

针对t永磁同步电机数学模型不确定问题,提出一种自适应高阶滑模Type-2模糊控制方法.采用积分滑模面二阶滑模控制律,保持传统滑模控制的鲁棒性并实现不含不确定高阶输入输出有限时间稳定;不需要预先确定干扰与不确定上边界,利用yapunov理论获得自适应调节Type-2模糊规则生成Super--Twisting信号削弱抖振.仿真结果表明永磁同步电机具有良好的跟踪性能,同时验证了该方法的可行和有效性.     

关于Vague集的模糊熵

由于Vague集是Zadeh's模糊集的一个扩展,为计算Vague集的模糊熵,有学者提出将Vague集转化为模糊集,然后借用模糊集有关熵的计算方法来讨论它们。该文首先给出反例说明Li's(2003)的方法在某些情况下和基于模糊集的Vague集模糊熵定义不一致。在指出Vague集的模糊性主要来自未知信息和不确定性信息的基础上,提出了一个基于非模糊集的Vague集模糊熵公理化定义,给出了该类模糊熵的计算公式,最后通过定理证明了它确实同时考虑到了影响Vague集模糊熵的两个因素。     

两类正规模糊集的相似度量

基于对不确定性信息处理的背景,讨论了常见的两类正规模糊集的相似度量,给出了正规三角模糊集和正规梯形模糊集相似度量的一般计算公式,研究了它们的有关性质,为基于相似度量的近似推理和模糊控制提供了理论准备.     

多重粗糙模糊集模型

为了充分揭示知识颗粒间的重叠性、对象的重要度差别及其多态性,基于多重集合,对Dubois粗糙模糊集意义下的粗糙模糊集模型的论域进行了扩展,提出了基于多重集的粗糙模糊集模型,给出了该模型的完整定义、相关定理和重要性质,其中包括多重粗糙模糊近似集、近似精度和可定义集的定义及其各种性质的证明、多重集意义下的粗糙模糊近似算子之间的关系及其与Dubois意义下的粗糙模糊近似算子之间的关系等。多重粗糙模糊集可用于从具有一对多依赖性关系的且具有模糊特性的数据中挖掘知识。     

基于模糊集截集的模糊粗糙集模型

基于L.A.Zadeh模糊集的截集的概念给出了论域U上任意模糊子集的上、下近似的刻画,得到了基于模糊集的截集的粗糙集模型,亦即模糊粗糙集,实现了用论域U中的模糊集近似论域上的任意模糊集,进一步推广了Z.Pawlak粗糙集模型,扩展了粗糙集的应用范围。最后,研究了其基本性质以及其与其他粗糙集模型的关系。     

A fast method for computing the centroid of a type-2 fuzzy set

Type reduction does the work of computing the centroid of a type-2 fuzzy set. The result is a type-1 fuzzy set from which a corresponding crisp number can then be obtained through defuzzification. Type reduction is one of the major operations involved in type-2 fuzzy inference. Therefore, making type reduction efficient is a significant task in the application of type-2 fuzzy systems. Liu introduced a horizontal slice representation, called the α-plane representation, and proposed a type-reduction method for a type-2 fuzzy set. By exploring some useful properties of the α-plane representation and of the type reduction for interval type-2 fuzzy sets, a fast method is developed for computing the centroid of a type-2 fuzzy set. The number of computations and comparisons involved is greatly reduced. Convergence in each iteration can then speed up, and type reduction can be done much more efficiently. The effectiveness of the proposed method is analyzed mathematically and demonstrated by experimental results.     

一种区间型二型模糊集重心的快速解法

针对区间型二型模糊集,分析其上下隶属度函数转换点与重心区间的关系,推导出计算该转换点的闭合公式及相应的相向搜索算法,最终得到了一种计算区间型二型模糊集重心的新方法.并且证明了所求隶属度函数转换点随着采样率的增加,最终将收敛到重心端点的特性.实验结果表明,与常用的Enhanced Karnik-Mendel迭代方法相比,所提方法在不损失计算精度的条件下具有更快的计算速度.     

A new extension of fuzzy sets using rough sets: R-fuzzy sets

This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some examples are provided.     

基于模糊结构元的模糊数直觉模糊多准则决策方法

针对准则权重信息不完全确定的模糊数直觉模糊多准则决策问题,采用模糊结构元方法进行处理.基于模糊数直觉模糊集的模糊结构元表示、模糊数比较和排序的模糊结构元方法以及直觉模糊数的记分函数和距离测度,定义了模糊数直觉模糊数的记分函数和距离测度,进而提出两种准则权重信息不完全确定而准则值为模糊数直觉模糊数的多准则决策方法:记分函数法和逼近理想解排序(TOPSIS)法.实例分析表明了这两种方法的可行性和有效性.     

General type-2 fuzzy rough sets based on \alpha -plane Representation theory

Rough sets theory and fuzzy sets theory are mathematical tools to deal with uncertainty, imprecision in data analysis. Traditional rough set theory is restricted to crisp environments. Since theories of fuzzy sets and rough sets are distinct and complementary on dealing with uncertainty, the concept of fuzzy rough sets has been proposed. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle highly uncertainties. Some researchers proposed interval type-2 fuzzy rough sets by combining interval type-2 fuzzy sets and rough sets. However, there are no reports about combining general type-2 fuzzy sets and rough sets. In addition, the $\alpha $ -plane representation method of general type-2 fuzzy sets has been extensively studied, and can reduce the computational workload. Motivated by the aforementioned accomplishments, in this paper, from the viewpoint of constructive approach, we first present definitions of upper and lower approximation operators of general type-2 fuzzy sets by using $\alpha $ -plane representation theory and study some basic properties of them. Furthermore, the connections between special general type-2 fuzzy relations and general type-2 fuzzy rough upper and lower approximation operators are also examined. Finally, in axiomatic approach, various classes of general type-2 fuzzy rough approximation operators are characterized by different sets of axioms.     

On the influence of using fuzzy extensions in linguistic fuzzy rule-based regression systems

Fuzzy Rule-Based Systems, FRBSs, are powerful tools to address regression problems. They can model the relationship between inputs and outputs by linguistic concepts. However, those FRBSs which are based on the conventional Type-1 fuzzy sets may not be able to handle some difficulties of real-world applications. In such situations, using novel representations of fuzzy sets seems like a good idea. Different extensions of fuzzy sets usually help to provide more precise models in the real-world problems. In this study, the influence of using fuzzy extensions in improving the efficiency of linguistic fuzzy rule-based regression models is investigated. For this purpose, a conventional Type-1 Mamdani FRBS is adapted to the three extensions of fuzzy sets, namely Interval Type-2, Intuitionistic, and Interval Type-2 Intuitionistic fuzzy sets. A two-pass method is proposed to define membership (non-membership) functions of these fuzzy sets; this method is based on the 3-tuples representation of the standard Type-1 membership functions. Wang and Mendel’s rule learning method is adapted to extract fuzzy rules from regression data. In order to tune the membership functions up to different extents, three evolutionary extensions are also presented for each type of the proposed FRBSs. Individual, internal, and external comparisons of the proposed FRBSs were done using 22 real-world regression datasets and statistical tests. Experimental results confirm that all the three proposed FRBSs outperform the classical Type-1 framework; furthermore, the Interval Type-2 Intuitionistic FRBS is the superior system so that an appropriate tuning of its parameters makes it the most accurate model.     

Using structured steiner trees for hierarchical global routing

The Steiner problem in a hierarchical graph model, the structured graph, is defined. The problem finds applications to hierarchical global routing. Properties of minimum-cost Steiner trees in structured graphs are investigated. A “top-down” approximate solution to the Steiner problem in structured graphs, called a top-down Steiner tree, is defined, and an algorithm is given to compute such solution. The top-down Steiner tree provides also an approximate solution to the Steiner problem in graphs admitting a structured representation. The properties of such solution are discussed and some experimental results on the quality of the approximation are presented. A reduction in time complexity is demonstrated with respect to both exact and heuristic algorithms applied to such graphs.     

广义二型模糊逻辑系统降型及其采样离散Nie-Tan算法

广义二型模糊逻辑系统在近年来成为学术研究的热点问题,而降型是该系统中的核心模块。最近的研究证明了连续Nie-Tan(CNT)算法是计算区间二型模糊集质心的准确方法。发现了离散Nie-Tan(NT)算法中的求和运算和CNT算法中的求积分运算的内在联系,用2类算法完成基于广义二型模糊集α-平面表达理论的广义二型模糊逻辑系统质心降型。3个计算机仿真实验表明,当适当增加主变量采样点个数时,所提出的基于主变量采样的离散NT算法计算出的广义二型模糊逻辑系统质心降型集和解模糊化值结果可以精确地逼近基准的CNT算法,且采样离散NT算法的计算效率远远高于CNT算法的效率。     

Comments on Singh and Zeng: “Approximation theory of fuzzysystems-SISO case” [and reply]

The author comments on the paper by Singh and Zeng (see ibid., vol.2, no.2, p.162-76, 1994). He states that every bounded function f: R→R has an exact representation as an additive fuzzy system. If f is not constant, one fuzzy set and two rules define the system. Otherwise, a single rule suffices. This result shows that the approximation properties of one-input fuzzy systems derive solely from interpolation between output extrema. The basis for the interpolation at any point is the value of the input fuzzy sets at that point. In reply Singh and Zeng state that in the comments by Watkins, it is proven that every SISO function can be exactly represented by a fuzzy system, which implies that fuzzy approximation (i.e., to approximate functions by fuzzy systems) is unnecessary or moot. However, they state that this conclusion is invalid because his presented representation scheme does not meet the basic requirements in the applications of fuzzy systems and is impractical     

Type-2 fuzzy sets made simple

Type-2 fuzzy sets let us model and minimize the effects of uncertainties in rule-base fuzzy logic systems. However, they are difficult to understand for a variety of reasons which we enunciate. In this paper, we strive to overcome the difficulties by: (1) establishing a small set of terms that let us easily communicate about type-2 fuzzy sets and also let us define such sets very precisely, (2) presenting a new representation for type-2 fuzzy sets, and (3) using this new representation to derive formulas for union, intersection and complement of type-2 fuzzy sets without having to use the Extension Principle