关于QL-、D-蕴涵的分配性方程的解

研究了[r→（t∧s）]≡[（r→t）∧（r→s）],[r→（t∨s）]≡[（r→t）∨（r→s）],[（p∧q）→r]≡[（p→r）∨（q→r）],[（p∨q）→r]≡[（p→r）∧（q→r）]4个分配性方程,它们在模糊集理论中的形式分别是I（r,T₁（t,s））=T₂（I（r,t）,I（r,s））,I（r,S₁（t,s））=S₂（I（r,t）,I（r,s））,I（T₁（p,q）,r）=S₁（I（p,r）,I（q,r））,I（S₁（p,q）,r）=T₁（I（p,r）,I（q,r））,其中p,q,r,s,t∈[0,1],T₁、T₂为任意三角模,S₁、S₂为任意三角余模,给出了I为QL-、D-蕴涵时满足分配性方程的充要条件。     

(I,A)-蕴涵及其基本性质

模糊蕴涵在模糊逻辑和近似推理领域中发挥着十分重要的作用，模糊蕴涵的构造是相关领域中的重要研究课题。基于模糊蕴涵[I]和聚合算子[A]构造出[(I,A)]-算子，研究[(I,A)]-算子成为模糊蕴涵的条件，其次研究[(I,A)]-蕴涵包括分配性和输入性在内的一些基本性质。     

直觉模糊三角模的剩余蕴涵及其性质

研究了直觉模糊三角模的剩余蕴涵及其性质。首先,定义了直觉模糊三角模的剩余蕴涵;其次,推导了直觉模糊三角模的剩余蕴涵与三角模的剩余蕴涵的关系;最后,证明了直觉模糊三角模的剩余蕴涵的16条性质。直觉模糊三角模的剩余蕴涵及其性质在直觉模糊推理、群决策等领域具有广阔的应用前景。     

基于Kleene-Dienes蕴涵算子的Vague集相似度量方法

通过分析现有Vague集相似度量方法,指出这些相似度量方法的不足之处。根据Kleene-Dienes蕴涵算子及其否定算子的包含和相交关系,提出一种基于Kleene-Dienes蕴涵算子的Vague集相似度量方法,并证明该方法满足相似度量的条件。通过与现有相似度量方法的比较,说明该相似度量方法能克服现有相似度量方法的缺陷,能够有效区分数据,具有一定的优越性,为研究Vague集相似度量方法提供了一种新的思路。     

不同蕴涵算子下三I方法的解

以R_M、R_Z、R₀三个蕴涵算子为基础,研究了11种形式的三I算法的解,并在此基础上给出了这11种解的同一形式：B*（y）=SUP{A*（x）∧φ（x,y）},其中φ：X×Y→[0,1]表示某一函数,而且φ（x,y）与E_Y的选取依赖蕴涵算子R_i的选取。     

广义三角模和广义剩余蕴涵之间的对应关系

进一步讨论了广义三角模和广义剩余蕴涵的对应性质,完善和修正了过去已有的一些定理结论,证明广义三角模和广义剩余蕴涵两者之间存在着两大类的对应关系,一类是可以构成伴随对的,而另一类则不能构成伴随对。     

区间值(α,β)一模糊格蕴涵子代数

摘要把拟重合的思想应用到区间值模糊集上,引进了一种广义模糊格蕴涵子代数,即区间值(α,β)一模糊格蕴涵子代数。研究了区间值(α,β)-模糊格蕴涵子代数的性质,并研究了区间值(α,β)-模糊格蕴涵子代数与格蕴涵子代数的关系,最后得到了该类模糊子代数的等价刻画。     

蕴涵算子族R(q,p)-LGN及其三I支持算法

给出了一族新的左连续三角模族T(q,p)-LGN族及其伴随蕴涵算子族R(q,p)-LGN,它包括Lukasiewicz蕴涵算子、Godel蕴涵算子及R0 蕴涵算子;提出了基于蕴涵算子族的模糊推理的思想,并给出了基于蕴涵算子族R(q,p)-LGN的FMP模型的三I支持算法.     

基于蕴涵算子族H(p,λ)的三I算法模糊系统

针对蕴涵算子族H(p,λ),给出了FMP问题三I支持算法和α-三I支持算法的计算公式;讨论了基于三I算法的模糊系统及其响应性能,结果表明,蕴涵算子族H(p,λ)的模糊系统只具有阶跃输出能力,不具有函数逼近泛性;揭示了蕴涵算子族H(p,λ)的模糊系统的概率意义,给出了其概率分布,它充当模糊系统的“系统内核”作用.     

直觉区间值模糊推理的三I算法

本文讨论了直觉区间值模糊三I算法的两种最简单形式：MP（Modus Ponens）和MT（Modus Tollens）问题,分别给出直觉区间值模糊环境下的MP问题和MT问题的三I解的一般形式。讨论全蕴涵解的存在条件,基于满足剩余原理的直觉区间值模糊剩余蕴涵,为直觉区间值模糊推理建立全蕴涵算法,即为MP和MT问题建立α-三I算法。     

Scaled runge-kutta-nyström methods for the second order differential equation ÿ = f(x,y)

New Runge-Kutta-Nyström algorithms are presented which determine an approximation of the solution and its derivative of the second order differential equation ÿ = f(x,y) at intermediate points of a given integration step, as well as at the end of each step. These new algorithms, called scaled Runge-Kutta-Nyström (SRKN) methods, are designed to be used with existing Runge-Kutta-Nyström (RKN) formulas, using the function evaluations of these methods as the core of the new system. Thus, for a slight increase of the cost, the solution may be generated within a successful step, improving so the efficiency of the existing RKN methods.     

Solutions to the functional equation I(x, y) = I(x, I(x, y)) for three types of fuzzy implications derived from uninorms

This paper investigates an iterative Boolean-like law with fuzzy implications derived from uninorms. More precisely, we characterize the solutions to the functional equation I(x, y) = I(x, I(x, y)) that involve RU-, (U, N)- and QLU-implications generated by the most usual classes of uninorms.     

2004=f（x,y,z）

2004=f(x，y，z)，这个公式表明，信息化在2004年依旧是一个复杂的方程，或许变量还会更多。即使是3个变量，也是一个三维空间的几何形状，谁能预测2004年这个三维形状会是什么样子的?这不仅在2003年底无法做到，并且到2004年底，也未必有人能将它总结出来。但是我们还是有一些好奇心，急切想知道有一些事物，到2004年会是怎样的，比如：     

On the system of word equations x i 1 x i 2…x i m=y i 1 y i 2…y i n (i=1, 2, …) in a free monoid

 It is proved that the system of word equations x ⁱ ₁=y ⁱ ₁ y ⁱ ₂…y ⁱ _n , i=1, 2,…, ⌈n/2⌉ +1, has only cyclic solutions. Some sharpenings concerning the cases n=5, 7 and n≥9 are derived as well as results concerning the general system of equations x ⁱ ₁ x ⁱ ₂…x ⁱ _m =y ⁱ ₁ y ⁱ ₂…y ⁱ _n , i=1, 2,… . Applications to test sets of certain bounded languages are considered. Received: 18 May 1995/2 January 1996     

An optimum generalized trapezoidal formula for the numerical integration of y′=f(x,y)

We report the determination of the parameter α in the generalized trapezoidal formula (GTF(α)) which minimizes the local truncation error.     

Hermitesche Differenzenverfahren zur Approximation der Lösung von Differentialgleichungen der Formu xy =f(x,y, u,u x,u y )

Hermitean, stable convergent one- and multistep methods of high acuray are developed for the numerical treatment of initial-value problems for the differential equationu _xy =f(x, y, u, u _x ,u _y ). Some methods are tested by well known examples.     

On the Law of Importation $(x wedge y) longrightarrow z equiv (x longrightarrow (y longrightarrow z))$ in Fuzzy Logic

The law of importation, given by the equivalence (x Lambda y) rarr z equiv (xrarr (y rarr z)), is a tautology in classical logic. In A-implications defined by Turksen et aL, the above equivalence is taken as an axiom. In this paper, we investigate the general form of the law of importation J(T(x, y), z) = J(x, J(y, z)), where T is a t-norm and J is a fuzzy implication, for the three main classes of fuzzy implications, i.e., R-, S- and QL-implications and also for the recently proposed Yager's classes of fuzzy implications, i.e., f- and g-implications. We give necessary and sufficient conditions under which the law of importation holds for R-, S-, f- and g-implications. In the case of QL-implications, we investigate some specific families of QL-implications. Also, we investigate the general form of the law of importation in the more general setting of uninorms and t-operators for the above classes of fuzzy implications. Following this, we propose a novel modified scheme of compositional rule of inference (CRI) inferencing called the hierarchical CRI, which has some advantages over the classical CRI. Following this, we give some sufficient conditions on the operators employed under which the inference obtained from the classical CRI and the hierarchical CRI become identical, highlighting the significant role played by the law of importation.