模糊数学理论产物——模糊计算机

人类思维的重要特点是逻辑推理和经验推理并用，但现阶段的计算机系统仍局限于用逻辑推理进行“思维”，尚未涉及到更接近人类思维的形象思维和直接思维形式。为了更好地表现人类所具有的主观模糊性，并对其进行处理，美国控制论专家扎德教授于１９６５年率先提出了模糊数学理论的新概念。它拓宽了经典数学中的“非此即彼”的界限，找到一种解决概念划分不确定性现象的描述方法，即用“隶属度”来刻画某事物“亦此亦彼”的中间过渡状态，亦即“１”和“０”之间非“１”、“０”的状态，受到广泛关注。模糊理论采用形容词汇来表现多样化的文…     

ZnO压敏陶瓷最佳掺杂含量的理论计算

从对电子薄膜材料研究中得到的最佳掺杂含量定量理论推广到ZnO陶瓷材料。该理论建立了电子薄膜材料的某一物理性能与晶体结构、制备方法和掺杂剂含量之间的联系，给出了一个能够拟合实验曲线的具有确定物理意义的抛物线方程。该方程的极值点确定了最佳掺杂含量与晶体结构和制备方法之间的定量关系，进而得到了一个掺杂最佳含量的表达式。系统地分析了ZnO压敏陶瓷的掺杂改性的实验结果，应用此表达式定量计算了ZnO压敏陶瓷的最佳掺杂含量，定量计算的结果与实验数据相符合。该理论也适用于其他薄膜材料最佳掺杂含量的理论计算。     

水平中段模糊算子

本文提出“水平中段模糊算子”的概念,并且应用清晰域的观点研究了它们的性质,从而在实质上较文[1]更深刻地揭示了一般模糊算子的性质,为实际应用各种模糊算子提供了进一步的依据。     

QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS

This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.     

ON THE SINGULAR DIRECTIONS OF VALUE DISTRIBUTION OF HOLOMORPHIC CURVES IN P^n（C）

This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space Pn(C). An example is given to complement these results.     

~ Transform Demonstration of Dark Soliton Solutions Found by Inverse Scattering

One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.     

我国中小企业选择可靠信用担保机构的模式识别方法

首先运用模糊评价方法结合中小企业选择信用担保机构现状，构建了当前我国信用担保机构5种标准信用等级的模糊向量，然后在此基础上采用“择近原则”得到m个等待选择的信用机构所处于的最为“贴近”的标准信用等级，从而为我国中小企业选择可靠信用担保机构提供了一种新的量化方法。     

基于VAGUE集多准则决策的模糊TOPSIS方法

给出了V AGUE集之间距离的新定义,在此基础上,提出一个基于V AGUE集多准则决策的模糊TOP-S IS方法,它为决策系统提供了一个有用的工具,并通过例子阐明本文方法的有效性.