生成反模糊子群

引入生成反模糊子群的概念,给出生成反模糊子群的代数刻画式,讨论了生成反模糊子群的基本性质.     

关于模糊拟阵的独立模糊集生成问题的一些结果

本文首先定义"生成模糊集族",利用这个概念构建了闭模糊拟阵的独立模糊集生成定理,并利用这个定理找到了模糊拟阵是闭模糊拟阵的一个充要条件;然后,利用"基子集套"概念讨论了模糊拟阵闭包的一个等价描述,通过这个等价描述详细探讨了模糊拟阵与其闭包的关系;最后,利用这些关系,得到了普通模糊拟阵的独立模糊集次生成定理。     

一类模糊值凸函数的若干运算性质

在Goetschel-Voxman所引进的序关系下,首先给出了生成函数的概念,证明了由一类凸集生成的函数是模糊值凸函数;其次利用上图的性质,建立了模糊值凸函数的下卷积、右乘等概念,并给出了相应的定理;最后讨论了模糊值函数的凸化问题,并给出了其刻画定理.     

正则剩余格上的模糊理想基

首先,在正则剩余格中引入模糊理想基的概念,介绍了模糊理想基的一些重要性质,并且利用这些性质,给出了模糊理想基的三种等价形式;其次,结合具体实例讨论了模糊理想基与模糊理想的关系;最后,给出由模糊集生成模糊理想基及由模糊理想基生成模糊理想的方法.     

BCI-代数的余模糊理想

在BCI-代数中引入了余模糊理想的概念,讨论了它的某些性质,研究了BCI-代数的模糊理想和余模糊理想的关系.特别是,给出了一个如何由一个模糊子集生成一个余模糊理想和闭余模糊理想的过程.     

效应代数中的模糊滤子

在效应代数中引入模糊滤子和模糊理想的概念,讨论了它们的性质;引入并研究了强模糊滤子;在全序效应代数中提出了一个模糊同余关系并证明了这样生成的同余类是一个全序格效应代数.     

格蕴涵代数的生成(∈,∈∨q)-Ⅳ模糊LI理想

基于常规Ⅳ模糊集合包含序?,引入格蕴涵代数的由一个Ⅳ模糊集生成的(∈,∈∨q)-Ⅳ模糊LI理想概念并考察其结构性质.建立并证明了生成(∈,∈∨q)-Ⅳ模糊LI理想的表示定理.为研究(∈,∈∨q)-Ⅳ模糊LI理想全体之集在?下的格结构特征奠定了基础.     

基于结构元的模糊值函数的一般表示方法

文[1]提出了模糊结构元的概念，并给出了模糊数与模糊值函数的模糊结构元表示，以及一类由模糊结构元线性生成的模糊值函数的微分和积分(黎曼意义下的)的表达形式。本文在文[1]的基础上进一步给出了由模糊结构元生成的模糊值函数的一般表达形式，并得到了一般表达形式下的模糊值函数的连续性和微分、黎曼积分的定义，它们与传统模糊分析中相应定义是等价的。     

基于模糊集合论的Agent联盟生成

多Agent系统中联盟的生成是关键问题,主要研究如何在多Agent系统中构造面向任务的最优Agent联盟.对联盟生成问题作了新的描述,讨论了现有联盟生成方法的特点及不足,提出了一种基于模糊集合论的联盟生成方法.基于模糊集合论的隶属度概念,计算Agent对任务的隶属程度,并依据λ-截矩阵理论生成面向任务的Agent联盟,从而使任务由能力最适合的Agent组成的联盟来求解.实例分析说明了此方法的有效性.     

拟BCK-代数的扰动模糊理想

引入了拟BCK-代数的扰动模糊理想的概念,刻画了拟BCK-代数的扰动模糊理想的特征;给出拟BCK-代数上的一个扰动模糊集成为扰动模糊理想的条件;构造了由给定扰动模糊集生成的最小扰动模糊理想;研究了拟BCK-代数的扰动模糊理想的同态性质。     

On Inverse Limits and Direct Limits for Fuzzy Topological Spaces

Li has introduced the concepts of inverse system and direct system for fuzzy topological spaces and studied inverse limits and direct limits on such spaces by presenting the explicit constructions of these limits.In this paper some important concepts of fuzzy topology,such as,product fuzzy topology,quotient fuzzy topology,fuzzy continuity etc.,are used for further study of inverse limits and direct limits for fuzzy topological spaces.     

Stability analysis of fuzzy linear differential equations

Differential equation is a very important field of study not only in theory but in applications, and stochastic differential equation is also a significant branch of research in theory and applications. Based on the concepts of fuzzy process and fuzzy differential equation, we present some concepts of stability for fuzzy differential equations. Furthermore we propose the sufficient and necessary conditions of stability for fuzzy linear differential equations.     

属性模糊集的分解特征

在模糊集理论研究的基础上,结合粗糙集的属性集、元素迁移的相关知识,提出属性模糊集的概念,利用给出属性模糊集的有关知识,结合模糊集与粗糙集合的有关理论,得到了属性模糊集的一系列重要定理,为模糊集合理论的进一步研究奠定了理论基础.     

Concepts and fuzzy sets: Misunderstandings, misconceptions, and oversights

The psychology of concepts has been undergoing significant changes since the early 1970s, when the classical view of concepts was seriously challenged by convincing experimental evidence that conceptual categories never have sharp boundaries. Some researchers recognized already in the early 1970s that fuzzy set theory and fuzzy logic were potentially suitable for modeling of concepts and obtained encouraging results. This positive attitude abruptly changed in the early 1980s, and since that time fuzzy set theory and fuzzy logic have been portrayed as problematic and unsuitable for representing and dealing with concepts. Our aim in this paper is to identify some of the most notorious claims regarding fuzzy set theory and fuzzy logic that have propagated through the literature on psychology of concepts and to show that they are, by and large, false. We trace the origin and propagation of these claims within the literature in this area. It is shown in detail that these claims are consistently erroneous and that they are based on various misunderstandings, misconceptions, and oversights. The ultimate purpose of this paper is to document these various erroneous claims.     

Fuzzy值Fuzzy测度的完备化

引入Fuzzy值Fuzzy测度的完备化定义,证明Fuzzy值Fuzzy测度的完备化定理,讨论完备化Fuzzy值Fuzzy测度的某些重要性质。     

Concepts and fuzzy sets: Misunderstandings,misconceptions, and oversights

The psychology of concepts has been undergoing significant changes since the early 1970s, when the classical view of concepts was seriously challenged by convincing experimental evidence that conceptual categories never have sharp boundaries. Some researchers recognized already in the early 1970s that fuzzy set theory and fuzzy logic were potentially suitable for modeling of concepts and obtained encouraging results. This positive attitude abruptly changed in the early 1980s, and since that time fuzzy set theory and fuzzy logic have been portrayed as problematic and unsuitable for representing and dealing with concepts. Our aim in this paper is to identify some of the most notorious claims regarding fuzzy set theory and fuzzy logic that have propagated through the literature on psychology of concepts and to show that they are, by and large, false. We trace the origin and propagation of these claims within the literature in this area. It is shown in detail that these claims are consistently erroneous and that they are based on various misunderstandings, misconceptions, and oversights. The ultimate purpose of this paper is to document these various erroneous claims.     

Convex fuzzy mapping with differentiability and its application in fuzzy optimization

The concepts of differentiability, convexity, generalized convexity and minimization of a fuzzy mapping are known in the literature. The purpose of this present paper is to extend and generalize these concepts to fuzzy mappings of several variables using Buckley–Feuring approach for fuzzy differentiation and derive Karush–Kuhn–Tucker condition for the constrained fuzzy minimization problem.     

A concept of fuzzy transition probabilities

Starting from fuzzy real numbers with an arbitrary lattice of belief and following the extension principle, we develop concepts of fuzzy probabilities, transition probabilities and random variables and of their combinations, and show that these concepts are consistent. We derive some results on fuzzy real numbers, on the expectation of fuzzy random variables and on fuzzy stochastic processes. To sketch the range of applications of fuzzy stochastics, we give two examples that show how real-world problems may be modeled by means of fuzzy probabilities and that give small numerical examples. Moreover, we give a brief outlook for a possible expansion of our theory to fuzzy Markovian decision processes by means of a partial order on the set of all fuzzy real numbers.     

模糊概念的EI代数分解

应用 AFS结构 [6] 上的 EI代数[6] 分析模糊概念的数学结构 ,证明有限集上任意一个模糊概念都是一类极其简单的模糊概念的 EI代数分解。     

关于拟概率测度的收敛理论

本文研究了拟概率空间上收敛概念之间的关系这一问题.利用类比的方法,在拟概率空间上提出了一些新的关于拟-随机变量的收敛概念并讨论了这些收敛概念之间的关系,获得了模糊测度下的收敛理论,推广了关于经典测度的收敛概念.