定义在区间值上的Fuzzy关系方程

Ｆｕｚｚｙ关系方程Ａ。Ｘ＝Ｂ中的矩阵Ａ、Ｂ的元素均为区间值，称为定义在区间值上的Ｆｕｚｚｙ关系方程。它是目前关于Ｆｕｚｚｙ关系方程理论研究中的主要问题之一￣［１］。本文讨论了区间值上Ｆｕｚｚｙ关系方程解的定义，并用符号定值法求出其全体解集。     

有限Fuzzy关系方程与Fuzzy矩阵秩进一步研究

在［１］的基础上,讨论了一般有限Ｆｕｚｚｙ 关系方程极小解的结构;将［１］中特殊有限Ｆｕｚｚｙ 关系方程与矩阵秩的关系推广到一般有限Ｆｕｚｚｙ 关系方程,运用矩阵秩给出了有限Ｆｕｚｚｙ关系方程极小解个数的上界估计,同时给出了求一般有限Ｆｕｚｚｙ 关系方程全部极小解一种全新算法．     

格的Fuzzy同余理想

文「１」提出了格的Ｆｕｚｚｙ理想，Ｆｕｚｚｙ同余关系等概念并对其性质进行了探讨。本文在此基础上提出了格的Ｆｕｚｚｙ同余理想的概念并分别讨论了格，Ｆｕｚｚｙ商格及格直积的Ｆｕｚｚｙ同余理想，得到了一些初步结果。     

求Fuzzy关系方程所有极小解的递归算法

本文给出了一种求Ｆｕｚｚｙ关系方程所有极小解的计算机递归算法，该算法具有算法简明，计算速度快等显著特点，尤其适合于求解大型Ｆｕｚｚｙ关系方程。     

Fuzzy矩阵方程A~x~=b~的解及性质

本文首先给出了矩阵方程Ａ＾￣ｘ＾￣＝ｂ＾￣的解的定义，然后对此解进行了深入的研究，给出了锥形Ｆｕｚｚｙ集的概念，讨论了方程Ａｘ＾￣＝ｂ＾￣与锥形Ｆｕｚｚｙ集之间的关系，最后，证明了一类锥形Ｆｕｚｚｙ集全体构成完备的Ｆｕｚｚｙ度量空间。     

-可分解Fuzy关系及其*-传递性

对［０，１］上一般的算子‘＊’引入＊－紧Ｆｕｚｚｙ关系及其○＊－可分解Ｆｕｚｙ关系的概念，证明了有单位元１的保序算子‘＊’及有单位元０的保序算子‘＊－’所定义的○＊－可分解和○＊－－可分解Ｆｕｚｚｙ关系在某种意义上构成了新的可传递Ｆｕｚｚｙ关系类，并且还给出了这些类在不同类型的传递性之间的一种位置关系，特别地，对二元○∨－可分解Ｆｕｚｚｙ关系，该文还得到了一个关于其传递性的完全刻画．     

Fuzzy集的势与可数Fuzzy基数

本文首先定义了Ｆｕｚｚｙ集的等势关系和Ｆｕｚｚｙ集的势，并讨论了有关Ｆｕｚｚｙ集的势的若干命题，然后在自然数集上定义了可数Ｆｕｚｚｙ基数。最后给出了确定可数论域上Ｆｕｚｚｙ集的Ｆｕｚｚｙ基数的方法，并对其若干性质进行了讨论。上述定义均以经典集论中相应定义为特款。     

Fuzzy映射和乘积Fuzzy测度

从研究Ｆｕｚｚｙ集合的直积和Ｆｕｚｚｙ关系出发,讨论了Ｆｕｚｚｙ关系和Ｆｕｚｚｙ映射的一些性质,最后利用Ｆｕｚｚｙ关系的截影性质给出了乘积Ｈ型Ｆｕｚｚｙ测度的存在性定理。     

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。     

L^2[0,1]上的正交小波基

从尺度因子Ｍ＝４的正交小波基出发,利用折叠方法得到了Ｌ＾２「０,１」空间的正交小波基,这种小波不同于折叠前的小波基,它是完全限制在有限区间「０,１」上,且保持小波基的正交性,并在使用过程中拥有更大的灵活性。也可用类似方法对一般尺度小波进行折叠。     

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.      

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.     

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 class of strong forms of fuzzy complete continuity

The aim of this paper is devoted to make use of operations on I^X of a fuzzy topological space X to unify and generalize classes of strong forms of fuzzy complete continuity. Furthermore, we add more types of strong forms of fuzzy completely continuous functions by choosing special operations. A comparison between these types of functions is of interest. Preservations of some fuzzy aspects under these functions are studied.     

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。     

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.     

一类特殊的Fuzzy局部凸空间

文中给出了Ｆｕｚｙ有界型空间的定义，在此基础上，讨论了Ｆｕｚｙ有界型空间的等价定理，最后证明了Ｑ－Ｃ_ＩＦｕｚｙ局部凸空间是有界型的．     

A fuzzy goal programming method with imprecise goal hierarchy

Two most widely used approaches to treating goals of different importance in goal programming (GP) are: (1) weighted GP, where importance of goals is modelled using weights, and (2) preemptive priority GP, where a goal hierarchy is specified implying infinite trade-offs among goals placed in different levels of importance. These approaches may be too restrictive in modelling of real life decision making problems. In this paper, a novel fuzzy goal programming method is proposed, where the hierarchical levels of the goals are imprecisely defined. The imprecise importance relations among the goals are modelled using fuzzy relations. An additive achievement function is defined, which takes into consideration both achievement degrees of the goals and degrees of satisfaction of the fuzzy importance relations. Examples are given to illustrate the proposed method.     

A new solution method for fuzzy chance constrained programming problem

This paper deals with an optimization model, where both fuzziness and randomness occur under one roof. The concept of fuzzy random variable (FRV), mean and variance of FRV is used in the model. In particular, the methodology is developed in the presence of FRV in the constraint. The methodology is verified through numerical examples.     

序半群素模糊理想的刻画

研究序半群S的素模糊理想，通过S的模糊左（右）理想和序模糊点给出了S的素模糊理想的等价刻画。