综合函数与扩展原理

本文首先对合情扩展映射的公理化条件的完备性与独立性进行讨论,之后给出了扩展原理的一般形式及合情扩展映射的等价定义。最后,利用综合函数,特别是变维综合函数列,给出了扩展原理的一些具体形式     

复Fuzzy函数的Buckley导数与Buckley积分

本文对Ｊ．Ｊ．Ｂｕｃｋｌｅｙ在［１］、［２］中给出的实变量复Ｆｕｚｚｙ数值函数的导数与积分加以推广,引出复变量复Ｆｕｚｚｙ数值的导数与积分概念,为研究Ｆｕｚｚｙ复分析打下一定的基础。     

On fuzzy subgroups and fuzzy ideals under triangular norms

In this communication, we explicitly point out that the principal results of Liu 1982 basically deduced from the definition of binary operation ° on the set F(X) of all fuzzy subsets of X, also hold if one uses the weaker definition of product under triangular norm °_t. Fuzzy ideals with respect to the triangular norms are also defined.     

On the loss of information due to fuzziness in experimental observations

The absence of exactness in the observation of the outcomes of a random experiment always entails a loss of information about the experimental distribution. This intuitive assertion will be formally proved in this paper by using a mathematical model involving the notions of fuzzy information and fuzzy information system (as intended by Tanaka, Okuda and Asai) and Zadeh's probabilistic definition. On the basis of this model we are first going to consider a family of measures of information enclosing some well-known measures, such as those defined by Kagan, Kullback-Leibler and Matusita, and then to establish methods for removing the loss of information due to fuzziness by increasing suitably the number of experimental observations.     

Fuzzy Ordered Filters in Negatively Partially Ordered Semigroups

本文将引入负偏序半群的Ｆｕｚｚｙ序滤子的概念，并研究Ｆｕｚｚｙ序滤子成为序滤子的充要条件及Ｆｕｚｚｙ序滤子的结构性质     

Fuzzy nilpotent algebras

We define the concept of fuzzy nilpotent algebra, prove that the homomorphic inverse image of a fuzzy nilpotent algebra is also nilpotent and study the intersection and union of fuzzy nilpotent algebras.     

一种完备完全分配格上矩阵方程的求解方法

模糊理论已经在决策、模式识别、故障诊断、过程控制等许多方面得到了广泛应用，在这些应用问题求解中往往要遇到求解模糊关系方程。本文从完备完全分配格的角度给出了一种求解模糊关系方程极小解的完备解法，并用计算机实现了提出的算法，为实际问题求解计算机化打下了基础。     

Fuzzy数的扩张运算及其性质

本文讨论了Ｆ数的扩张加法和扩张数乘运算的性质；并举反例说明这样的扩张运．算不能使Ｆ数全体Ｆ＊构成线性空间；最后对可列个Ｆ数的运算进行了讨论．     

The diameter of a fuzzy set

In pattern recognition one often wants to measure geometric properties of imprecisely defined subsets of an image. This paper proposes definitions of intrinsic and extrinsic diameter for fuzzy subsets which reduce to the ordinary definitions when the subsets are crisp. We also define height and width for a fuzzy subset and show how they relate to the area (i.e., integral of membership). For convex fuzzy subsets the intrinsic diameter cannot exceed the extrinsic diameter, but it can be smaller. Finally, for piecewise constant convex fuzzy subsets the intrinsic diameter cannot exceed half the fuzzy perimeter, but this need not be true in the nonconvex case.     

The systems approach and fuzzy set theory bridging the gap between mathematical and language-oriented economists

Ideas are presented to show how fuzzy mathematics can be applied in macro-economics in combination with the systems approach in order to bridge the gap between mathematical and language-oriented economists.Two reasons are given.From a mathematical point of view, fuzzy sets, fuzzy relations and fuzzy logic are not fuzzy at all. They are all well defined, but tend to be more complicated than traditional, mathematical concepts used in economics.From a language-oriented economist's point of view, fuzzy sets, etc. are used to express mathematically the type of concepts which are typical in language and most valuable in dealing with complex systems like an economy.The paper deals with economics in general terms, but examples are provided to illustrate the ideas.