模糊信号码的一点注记

利用模糊信号码的代数性质给出了模糊信号码的一个充要条件:设A是字母表X上的一个模糊前缀码,那么A是模糊信号码当且仅当X*=T∪A0.∪P0.,这里P=AX-,T={u∈X*|X*uX*∩A0.=φ},满足条件T∩P0.=φ=T∩A0.,T■A0.X .同时讨论了一个模糊码满足X*A0.■A0.X*的一些等价条件,对最大模糊前缀码的性质也作了一些研究。     

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。     

正则强码的分解与伯努利分布

本文得到正则强码的伯努利分布定理。还研究强码的分解,给出正则强码可分解为两个正则强码复合的充要条件。     

基于结构元理论的模糊最大流算法研究

运用结构元理论来求解模糊弧容量网络的最大流问题.先简要介绍模糊结构元及相关定理.之后证明了模糊网络最大流的判定定理,该定理表明:求模糊网络最大流等价求一经典网络最大流.最后,通过一个例子来说明求解过程。     

模糊树自动机的同余与同态

从代数角度出发研究模糊树自动机的同余与同态,得出模糊树自动机的同态基本定理和同构基本定理,且对模糊树自动机的语言及模糊树自动机的极小化问题进行研究.     

LF拓扑线性空间上Fuzzy线性泛函的连续性

文（４）中给出了Ｘ（Ｌ）上的模糊线性算子的定义。作为其特例，本文证明了ＬＦ拓扑线性空间上模糊线性泛函连续性的几个等价命题和模糊线性泛函的Ｈａｈｎ－Ｂａｎａｃｈ延拓定理，进而给出了ＬＦ拓扑线性空间上存在非零连续模糊线性泛函的一个充要条件。     

群的模糊同态与模糊商群的同构定理

利用模糊映射，给出群的模糊同态的概念，并得到模糊同态基本定理，同时建立模糊商群的同构定理。     

关于有限论域上模糊度定理的一个注记

设F（U）为有限论域U={u1,u2,…,un}上的模糊幂集.令D：F（U）→[0,1],AaD（A）=g（∑i=1^n ci fi（A（ui）））,其中ci〉0,fi：[0,1]→[0,＋∞）满足（1）fi（x）=fi（1-x）,（2）fi（0）=0,（3）fi在[0,0.5]上严格递增.又设a=∑i=1^n ci fi（0,5）,且g：[0,a]→[0,1]严格递增,g（0）=0,g（a）=1.某教材中的定理断定具有上述性质的映射D为F（U）上的模糊度函数.本文构造出具有上述性质的D,但D不满足模糊度函数定义中的可加性条件,故不为F（U）上的模糊度函数.本文进一步指出,若将g的定义域扩展为[0,2a],并再假定g是可加的,则可使D为F（U）上的模糊度函数.     

模糊数的一种新运算方法及其若干应用

首先给出了模糊数的一种新的函数表示定理;基于该表示定理 ,提出了模糊数的一种新运算方法并将其直接应用到模糊数理论中若干问题的讨论,包括:模糊数的差问题,绝对值问题以及模糊数的确界问题 .     

推广的模糊横贯理论

定义p-模糊横贯的概念,得到p-模糊横贯的一些性质艺及p-模糊横贯与缺失的关系,研究模糊集上的Hall定理与Hall-Ore定理。最后给出p-模糊横贯的一个应用。     

Generalized fuzzy matrices

We give a systematic development of fuzzy matrix theory. Many of our results generalize to matrices over the two element Boolean algebra, over the nonnegative real numbers, over the nonnegative integers, and over the semirings, and we present these generalizations. Our first main result is that while spaces of fuzzy vectors do not have a unique basis in general they have a unique standard basis, and the cardinality of any two bases are equal. Thus concepts of row and column basis, row and column rank can be defined for fuzzy matrices. Then we study Green's equivalence classes of fuzzy matrices. New we give criteria for a fuzzy matrix to be regular and prove that the row and column rank of any regular fuzzy matrix are equal. Various inverses are also studied. In the next section, we obtain bounds for the index and period of a fuzzy matrix.     

模糊集的相对扰动

在模糊推理的理论研究中,模糊推理方法的扰动性分析是一个重要的研究方向,即讨论模糊推理前件的变化对后件的影响。本文给出模糊集的相对扰动的概念,讨论由模糊集运算产生的相对扰动,以及模糊推理的相对扰动性,给出一些有趣的性质。     

测试模糊码的一种算法

Abstract. How to verify that a given fuzzy set A∈F(X ) is a fuzzy code? In this paper, an al-gorithm of test has been introduced and studied with the example of test. The measure notionfor a fuzzy code and a precise formulation of fuzzy codes and words have been discussed.     

模糊化内缀码和模糊化外缀码

在自由幺半群上引进模糊化内缀码和模糊化外缀码的概念，并进一步讨论它们的基本代数性质。     

模糊共生结构的加细及其性质

介绍模糊拓扑,模糊邻近,模糊拟一致框架下的模糊(半)拓扑序、模糊共生结构的概念,研究模糊(半)拓扑序,模糊共生结构的加细,得到一些重要性质。     

正规模糊格的素中理想

研究正规模糊格的素中理想与极大中理想的联系；并在一定的条件下证明了：正规模糊格的素中理想与模糊格同态之间存在一一对应关系。     

Fuzzy analytic hierarchy process: Fallacy of the popular methods

The fuzzy Analytic Hierarchy Process (fuzzy AHP) is a very popular decision making method and literally thousands of papers have been published about it. However, we find the basic logic of this approach has problems. From its methodology, the definition and operational rules of fuzzy numbers not only oppose the main logic of fuzzy set theory, but also oppose the basic principles of the AHP. In dealing with the outcomes, fuzzy AHP does not give a generally accepted method to rank fuzzy numbers and a way to check the validity of the results. Besides, we discuss the validity of the Analytic Hierarchy/Network Process (AHP/ANP) in complex and uncertain environments and find that fuzzy ANP is a false proposition because there is no fuzzy priority in the super matrix which provides the basis for the ANP. Although fuzzy AHP has been applied in many cases and cited hundreds of times, we hoped that those who use fuzzy AHP would understand the problems associated with this method.     

关于模糊群的上确界性质的几个结果及其应用

研究了模糊子群的上确界性质并给出了模糊具有上确界性质的充要条件,利用它研究了循环群模糊子群的结构。最后,本文研究了一种比上确界性质弱一些的条件,在该条件下模糊可以具有好的性质。     

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。     

Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T_ω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show T_ω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply T_ω-based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L-R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.