范畴与其内蕴幺半群范畴的乘积之间的关系

在具有任意乘积的范畴中引入内蕴幺半群范畴的概念,研究范畴与内蕴幺半群范畴的乘积之间的关系,证明了关于乘积封闭的范畴的内蕴幺半群范畴也是乘积封闭的.     

有界Rl-幺半群的犹豫模糊滤子北大核心

将犹豫模糊集应用到有界剩余格序幺半群(Rl-幺半群)中,引入有界Rl-幺半群的犹豫模糊滤子的概念,研究其相关性质。获得了犹豫模糊滤子的一些等价刻画,建立了犹豫模糊滤子与其水平滤子之间的关系。讨论了犹豫模糊集成为犹豫模糊滤子的条件,给出了由一个给定犹豫模糊集生成的犹豫模糊滤子的表达式。     

仿射Weyl群上的Demazur乘积

Demazure乘积是定义在一般Coxeter群上的一类幺半群乘积.它自然地出现在李理论中的不同领域中.本文将研究仿射Weyl群上Demazur乘积.我们的主要结果是发现了它与有限Weyl群上的量子Bruhat图之间的一个紧密联系.作为应用,我们给出了仿射Weyl群最低双边胞腔元素之间Demazure乘积的显示表达式,并得到了最低双边胞腔元素的一般牛顿点以及Lusztig-Vogan映射的具体刻画.     

基于模糊球的模糊逻辑系统及其逼近性质

基于模糊球概念构造了一个具有向量形式规则的模糊逻辑系统,然后利用其逼近性质给出了在紧致域上逼近多元连续函数的方法.首先,依据所给论域自身的几何特点,将其进行模糊划分,其次使用各个子论域上的采样点和母函数构造开模糊球,然后基于模糊球构造出描述每个子论域的模糊逻辑系统(FLS),最后在整个论域上生成逼近紧集上连续函数的模糊逻辑系统(FLS).这种模糊逻辑系统的规则为向量形式且具有较强的语言解释能力.与传统的FLS相比,本文提出的FLS用来描述高维情形时不必使用张量乘积构造规则,从而在一定程度上避免了维数灾难问题.最后的仿真例子说明了本文所采用方法的有效性.     

L－逆左系对幺半群的刻画

正则左Ｓ-系是ｖｏｎ Ｎｅｕｍａｎｎ正则半群的自然推广，逆左Ｓ-系是逆半群的自然推广．作为左逆半群的自然推广，本文引入了Ｌ-逆左系的概念，并用来刻画了几类幺半群，如左逆幺半群，逆幺半群，ａｄｅｑｕａｔｅ幺半群等．     

半群的区间值反模糊子半群的性质

作为模糊代数的一个研究领域,区间值模糊子半群对模糊子半群的研究至关重要.引入了半群的区间值反模糊子半群的概念,对区间值反模糊子半群的性质进行了研究.讨论了半群的区间值反模糊子半群关于并运算的封闭性质.最后给出了半群的区间值模糊子半群的同态像和原像的相关性质.相关的研究结果丰富了半群的模糊理论.     

L—逆左系对幺半群的刻画

正则左Ｓ－系是ｖｏｎ ｎｅｕｍａｎｎ正则半群的自然推广，逆左Ｓ－系是逆半群的自然扩广，作为左逆半群的自然推广，本文引入了Ｌ－逆左系的概念，并用来刻画了几类幺半群，如左逆幺半群，逆幺半群，ａｄｅｑｕａｔｅ幺半群等。     

可逆模糊自动机

首先提出了可逆模糊自动机的概念,研究了能被可逆模糊自动机接受的语言(简记为F(∑))的一些性质.其次给出了自由群上被可逆模糊自动机接受的模糊子集的概念,详细研究了可逆模糊语言与经典可逆语言的关系.最后,通过引入语法幺半群刻画了F(∑)的代数性质.通过这些性质可以有效的判断一个模糊语言是否能被一个可逆模糊自动机接受.     

幺半群的内射类及投射类刻画

类比于一般环上模的内射类,定义了幺半群上的S-系的内射类和投射类,并利用它们刻画了几类特殊的幺半群．证明了完全内射幺半群和完全拟内射幺半群是等价的．并且证明了对于标致幺半群S,它是完全投射的当且仅当它是完全拟投射的当且仅当它上面的投射S-系构成了一个投射类．     

灰色数学的新分支——灰群

给出灰子半群、强灰子半群、灰子幺半群、强灰子幺半群、灰子群和强灰子群的定义和有关定理，在此基础上，讨论灰子群一模糊子群、一般子群的关系。并且研究了灰正规子群。     

Wreath products of ordered semigroups

In this paper ordered wreath products of ordered monoids by ordered acts are investigated. In 4. we characterize idempotent isotone wreath products. In 3. the monoid of order preserving endomorphisms of a free ordered act is represented as Cartesian ordered isotone wreath product. Moreover, we give conditions for this wreath product to be I-regular.     

Intuitionistic Fuzzy Logic Control for Heater Fans

The concept of intuitionistic fuzzy systems, including intuitionistic fuzzy sets and intuitionistic fuzzy logic, was introduced by Atanassov as a generalization of fuzzy systems. Intuitionistic fuzzy systems provide a mechanism for communication between computing systems and humans. In this paper, we describe the development of an intuitionistic fuzzy logic controller for heater fans, developed on the basis of intuitionistic fuzzy systems. Intuitionistic fuzzy inference systems and defuzzification techniques are used to obtain crisp output (i.e., speed of the heater fan) from an intuitionistic fuzzy input (i.e., ambient temperature). The speed of the heater fan is calculated using intuitionistic fuzzy rules applied in an inference engine using defuzzification methods.     

模糊推理的灵敏度

借助于模糊逻辑连接词的灵敏度，定义了模糊推理系统的灵敏度，研究了几种常见的模糊推理系统的灵敏度，进一步估算了各种模糊推理机的灵敏度，并将模糊推理系统的灵敏度与模糊连接词灵敏度的关系用等式表示出来。     

BIK+-逻辑与非可换模糊逻辑

引入BIK -逻辑的概念,证明了BIK -逻辑的可靠性定理(基于BCC-代数)。同时,研究了BIK -逻辑与非可换模糊逻辑的关系,说明了各种源于模糊逻辑的代数结构之间的内在联系,并用一个图示表达了这些关系。     

L-拓扑空间中的W-仿紧性

利用α-局部有限族在L-拓扑空间中定义了一种新型强F仿紧性--W-仿紧性,证明了这种仿紧性具有一些好的性质,比如L-good extension,闭遗传,弱同胚不变性,强F紧集与W-仿紧集的乘积是W-仿紧集.并同时证明了W-仿紧性可以增强分离性,最后讨论了W-仿紧性与其他仿紧性之间的关系.     

Fuzzy qualitative trigonometry

This paper presents a fuzzy qualitative representation of conventional trigonometry with the goal of bridging the gap between symbolic cognitive functions and numerical sensing & control tasks in the domain of physical systems, especially in intelligent robotics. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; a Cartesian translation and orientation are defined by their normalized fuzzy partitions. Conventional trigonometric functions, rules and the extensions to triangles in Euclidean space are converted into their counterparts in fuzzy qualitative coordinates using fuzzy logic and qualitative reasoning techniques. This approach provides a promising representation transformation interface to analyze general trigonometry-related physical systems from an artificial intelligence perspective.Fuzzy qualitative trigonometry has been implemented as a MATLAB toolbox named XTRIG in terms of 4-tuple fuzzy numbers. Examples are given throughout the paper to demonstrate the characteristics of fuzzy qualitative trigonometry. One of the examples focuses on robot kinematics and also explains how contributions could be made by fuzzy qualitative trigonometry to the intelligent connection of low-level sensing & control tasks to high-level cognitive tasks.     

Fuzzy qualitative trigonometry

This paper presents a fuzzy qualitative representation of conventional trigonometry with the goal of bridging the gap between symbolic cognitive functions and numerical sensing & control tasks in the domain of physical systems, especially in intelligent robotics. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; a Cartesian translation and orientation are defined by their normalized fuzzy partitions. Conventional trigonometric functions, rules and the extensions to triangles in Euclidean space are converted into their counterparts in fuzzy qualitative coordinates using fuzzy logic and qualitative reasoning techniques. This approach provides a promising representation transformation interface to analyze general trigonometry-related physical systems from an artificial intelligence perspective.Fuzzy qualitative trigonometry has been implemented as a MATLAB toolbox named XTRIG in terms of 4-tuple fuzzy numbers. Examples are given throughout the paper to demonstrate the characteristics of fuzzy qualitative trigonometry. One of the examples focuses on robot kinematics and also explains how contributions could be made by fuzzy qualitative trigonometry to the intelligent connection of low-level sensing & control tasks to high-level cognitive tasks.     

Exact inversion of decomposable interval type-2 fuzzy logic systems

It has been demonstrated that type-2 fuzzy logic systems are much more powerful tools than ordinary (type-1) fuzzy logic systems to represent highly nonlinear and/or uncertain systems. As a consequence, type-2 fuzzy logic systems have been applied in various areas especially in control system design and modelling. In this study, an exact inversion methodology is developed for decomposable interval type-2 fuzzy logic system. In this context, the decomposition property is extended and generalized to interval type-2 fuzzy logic sets. Based on this property, the interval type-2 fuzzy logic system is decomposed into several interval type-2 fuzzy logic subsystems under a certain condition on the input space of the fuzzy logic system. Then, the analytical formulation of the inverse interval type-2 fuzzy logic subsystem output is explicitly driven for certain switching points of the Karnik–Mendel type reduction method. The proposed exact inversion methodology driven for the interval type-2 fuzzy logic subsystem is generalized to the overall interval type-2 fuzzy logic system via the decomposition property. In order to demonstrate the feasibility of the proposed methodology, a simulation study is given where the beneficial sides of the proposed exact inversion methodology are shown clearly.     

BCH-代数的模糊H-理想的某些构造性质

讨论了BCH-代数的Fuzzy H-理想的某些构造性质,如Fuzzy H-理想的Cartesian积等.     

Design of fuzzy logic controllers based on generalized T-operators

Since Zadeh first proposed the basic principle of fuzzy logic controllers in 1968, the and operators have been popular in the design of fuzzy logic controllers. In this paper, the general concept of T-operators is introduced into the conventional design methods for fuzzy logic controllers so that a general and flexible methodology for the design of these fuzzy logic controllers is available. Then, by computer simulations, studies are made so as to determine the relations between the various T-operators and the performance of a fuzzy logic controller. It is concluded that the performance of the fuzzy logic controller for a given class of plants very much depends upon the choice of the T-operators.