模糊值测度与模糊鞅

本文在一般测度空间（T，J，μ）中证明模糊值测度关于μ的Radon-Nikodym导数（R－N导数）的存在性和唯一性。在完备的概率空间（Ω，H，P）中引进一个模糊随机变量关于H的一个子σ代数H0的模糊条件期望，并证明这样定义的模糊条件期望存在且唯一，还就其某些性质作了讨论。最后给出模糊鞅的定义并证明模糊鞅收敛定量。     

Fuzzy数的Fuzzy距离与Fuzzy极限

本文引入了两个重要概念,即Fuzzy数的Fuzzy距离和Fuzzy数序列的Fuzzy极限,并得到它们的一些完全类似实数绝对值与实数序列极限的性质。     

模糊分析计算中的结构元方法

提出模糊结构元的概念，研究模糊结构元的性质，给出模糊数和模糊值函数的结构元表现定理。利用模糊数和模糊值函数的结构元表现形式，使得过去必须依赖扩张原理和表现定理来刻画的模糊数运算、模糊值函数的微积分运算等变得更加简单与直观。     

模糊连通度与模糊核度

本文给出了衡量模糊连通性的三个工量：模糊连通度，模糊边连通度与模糊核度及其相关的性质。与普通图连通性的分析相比较，由于考虑了模糊性，这三个量能更好，更深入地刻划出不同的图在连通性方面的微妙差异。     

Fuzzy子格与Fuzzy同态

每个代数结构一般都可引入相应的Ｆｕｚｚｙ子结构，为了进一步研究Ｆｕｚｚｙ子和以及Ｆｕｚｚｙ同态的各种性质，本文引入了亚格的概念，并建立了Ｆｕｚｚｙ子格与亚格的对应关系（定理１．７）；给出了Ｆｕｚｚｙ同态（同构）的分解定理（定理２．５和推论２．７）；最后讨论了同余关系商格的Ｆｕｚｚｙ子格问题，证明了在自然映射下，任一保序映射可以引导出商格中应的Ｆｕｚｚｙ子格，并由此引出了φ－Ｆｕｚｚｙ商子格的概念。     

n维模糊度量空间及其完备性

定义了n维模糊向量的模糊距离、n维模糊度量空间及其完备性的概念,实现了用R上的模糊数度量模糊向量间距离的目的,不仅使得模糊距离的度量更加合理、更加贴切,也创立一套独立于实数的模糊数学分析理论打下了基础。     

模糊群的模糊同态

引进模糊群的模糊同态概念，给出模糊同态下子模糊群(正规子模糊群)间的对应关系’建立模糊群的模糊同态基本定理，同时讨论模糊群的若干性质，得到一系列等价条件。     

模糊群的若干性质

本文证明了下述结果：设μ是群Ｇ的模糊子群，那么１，若ν（ｘｙ＾－１）≥ｍａｘ（μ（ｘ），μ（ｙ），μ（ｘ）＝μ（ｙ）；２。若ｘμ＝ｙμ，则μ（ｘ）＝μ（ｙ）；３．μ是模糊正规子群当且仅当μｖ＝ｖμ。４本文指出［３］的命题２与定理６的证明都是错误的，但定理６的结论是正确的，本文给出一新的证明。     

模糊识别、决策与聚类理论模型

本文首先建立了一个新的模糊模式识别理论模型。然后提出新的模糊综合决策与模糊聚类模型,文中也指出了ISODATA聚类方法存在的不足。     

模糊过程与模糊微分方程的解法

本文在模糊变量和动态模糊集合的基础上定义了模糊过程、构造了它的F样本函数,然后用F样本函数定义了模糊过程的a.f.s微积分,并讨论了它们的性质;在此基础上,本文提出了非齐次项是模糊过程的微分方程的基本解法,从而为分析动态系统受模糊干扰的响应提供了基础。     

A type of fuzzy ring

In this study, by the use of Yuan and Lee’s definition of the fuzzy group based on fuzzy binary operation we give a new kind of fuzzy ring. The concept of fuzzy subring, fuzzy ideal and fuzzy ring homomorphism are introduced, and we make a theoretical study their basic properties analogous to those of ordinary rings.      

Editorial

Linear programming problems with fuzzy parameters are formulated by fuzzy functions. The ambiguity considered here is not randomness, but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership. Parameters on constraint and objective functions are given by fuzzy numbers. In this paper, our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters. This fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential.     

Fuzzy addition in the L-fuzzy real line

Under the hypothesis L is a chain, we construct a binary operation ⊕ on the L-fuzzy real line $\text{R}$(L) which reduces to the usual addition on $\text{R}$ if ⊕ is restricted to the embedded image of $\text{R}$ in $\text{R}$(L), which yields a partially ordered, abelian cancellation semigroup with identity, and which is jointly fuzzy continuous on $\text{R}$(L). We show ⊕ is unique, i.e. it is the only extension of addition to $\text{R}$(L) which is consistent. We study the relationship between ⊕ and other fuzzy continuous extensions of the usual addition. We also show that fuzzy translation is a weak fuzzy homeomorphism and, under certain conditions, a fuzzy homeomorphism.     

群,环上的Fuzzy关系

一些学者已对群和环上的Ｆｕｚｚｙ关系进行了研究，本文进一步研究了群、环上的Ｆｕｚｚｙ关系，得出了若干重要的结论。     

Toward extended fuzzy logic—A first step

Fuzzy logic adds to bivalent logic an important capability—a capability to reason precisely with imperfect information. Imperfect information is information which in one or more respects is imprecise, uncertain, incomplete, unreliable, vague or partially true. In fuzzy logic, results of reasoning are expected to be provably valid, or p-valid for short. Extended fuzzy logic adds an equally important capability—a capability to reason imprecisely with imperfect information. This capability comes into play when precise reasoning is infeasible, excessively costly or unneeded. In extended fuzzy logic, p-validity of results is desirable but not required. What is admissible is a mode of reasoning which is fuzzily valid, or f-valid for short. Actually, much of everyday human reasoning is f-valid reasoning.f-Valid reasoning falls within the province of what may be called unprecisiated fuzzy logic, FLu. FLu is the logic which underlies what is referred to as f-geometry. In f-geometry, geometric figures are drawn by hand with a spray pen—a miniaturized spray can. In Euclidean geometry, a crisp concept, C, corresponds to a fuzzy concept, f-C, in f-geometry. f-C is referred to as an f-transform of C, with C serving as the prototype of f-C. f-C may be interpreted as the result of execution of the instructions: Draw C by hand with a spray pen. Thus, in f-geometry we have f-points, f-lines, f-triangles, f-circles, etc. In addition, we have f-transforms of higher-level concepts: f-parallel, f-similar, f-axiom, f-definition, f-theorem, etc. In f-geometry, p-valid reasoning does not apply. Basically, f-geometry may be viewed as an f-transform of Euclidean geometry.What is important to note is that f-valid reasoning based on a realistic model may be more useful than p-valid reasoning based on an unrealistic model.     

A New Form of Fuzzy Compact Spaces and Related Topics via Fuzzy Idealization

Fuzzy ideals and the notion of fuzzy local function were introduced and studied by Sarkar[12] and by Mahmoud in [9]. The purpose of this paper deals with a fuzzy compactness modulo a fuzzy ideal. Many new sorts of weak and strong fuzzy compactness have been introduced to fuzzy topological spaces in the last twenty years but not have been studied using fuzzy ideals so,the main aim of our work in this paper is to define and study some new various types of fuzzy compactness with respect to fuzzy ideals namely fuzzy L-compact and L*-compact spaces. Also fuzzy compactness with respect to ideal is useful as unification and generalization of several others widely studied concepts. Possible application to superstrings and E∞ space-time are touched upon.     

A new approach to fuzzy programming

A fuzzy program is defined in the usual way as a sequence of statements (instruction) which are considered as functions (possibly fuzzy functions) and fuzzy predicates defined on the given input domain. The essential difference in the approach presented in this paper is the new interpretation of the execution of fuzzy programs, and a new method of evaluating fuzzy predicates. The result of the fuzzy program execution is an appropriate fuzzy subset in the output domain.     

半群的模糊理论研究进展

介绍半群的模糊理论研究的基本内容、方法,重点介绍半群的模糊理想、模糊同余以及目前半群的模糊理论研究进展。