由一种模糊代数上的模糊数值测度确定的不相似度量

给出全有限测度空间(X,,μ)中生成的模糊σ-代数上的模糊数值测度,模糊σ-代数上的不相似度量。对X为有限集的情形,计算了模糊子集间的距离,给出了一种模糊聚类工具。     

一种非可加测度上的拟积概率积分研究

给出了一种非可加测度的定义,其具有F可加性;并对Einstein算子进行了优化,设计了λ模糊拟积算子和λ模糊拟和算子,证明其满足T范数与S范数的条件;接下来基于这种非可加测度和模糊拟积算子给出了模糊拟积概率积分的定义,并将其积分整体看成一个集函数,研究并证明其满足的性质,由此丰富了模糊测度的理论.     

可信测度空间下的似乘算子模糊概率积分研究

模糊概率积分是模糊数学的一个重要部分,是将模糊概率与积分相结合的一种积分形式.通过t-模和s-模定义条件设计了一个似乘算子和似和算子,又构建了一个全新的可信测度,并在可信测度空间下结合似乘算子重新定义了Sugeno模糊概率积分,根据新的Sugeno模糊概率积分定义获得了该积分相应的线性和非线性性质,并给出相应的证明,这...     

Carleson测度和某些算子的关系

本文定义了几个算子，又给出了α阶Ｃａｒｌｅｓｏｎ测度（α〉的定义，利用算子理论方面的知识讨论了α阶Ｃａｒｌｅｓｏｎ测度与这些算子的有界性的紧密关系，这些算子在以后讨论α阶Ｃａｒｌｅｓｏｎ测度的等价命题的有很重要的作用。     

有界向量测度的一个新特征

设Ｘ是Ｂａｎａｃｈ空间，Σ是某集Ω的一此子集所作代数，μ：Σ→Ｘ是有界向量测度。本文利用向量级数来给出有界向量测度的一个新特征。     

模糊事件的概率测度熵

通过对模糊事件及其概率测度的定义引出有限集上模糊子集熵的概念。运用模糊事件及概率测度的基本性质,给出了模糊熵的一些基本定理。     

（B）值模糊测度的若干注记

文[1]中引入了取值向量格的模糊测度和模糊积分。在本文中,将考察由标量模糊测度产生的(B)值模糊测度以及由(B)值模糊积分诱导的(B)值模糊测度的若干性质。     

基于距离测度的三角模糊交互多属性决策方法

针对属性间存在交互作用的三角模糊多属性决策问题,基于可信性分布理论给出了关于三角模糊数新的排序方法。通过将区间数的Wasserstein距离测度进行推广,得到三角模糊数的距离测度;考虑到属性间存在的交互作用,定义了一种2可加Shapley三角模糊Choquet积分集结算子(2ASTFCA);针对属性权重部分已知的情形,以方案之间离差最大化为目标构建规划模型得到属性权重。最后,通过青岛市休闲农业综合信息服务平台开发方选择实例,说明所提方法的有效性。     

几种模糊测度之间的关系

本文讨论了人工智能中常用的五种模糊测度之间的关系。通过典型例证，指出了它们裼 异同，建立了它们之间正确的关系。     

模糊积分定义的模糊测度

利用［３］中的一种模糊积分定义了一种模糊测度，并讨论其性质及收敛性。     

若干新的贴近度公式

依据包含度和贴近度的公理化定义 ,讨论了由包含度诱导的贴近度 ,给出了一些具体的诱导公式。     

Similarity measure application to fault detection of flight system

Fault detection technique is introduced with similarity measure. The characteristics of conventional similarity measure based on fuzzy number are discussed. With the help of distance measure, similarity measure is constructed explicitly. The designed distance-based similarity measure is applicable to general fuzzy membership functions including non-convex fuzzy membership function, whereas fuzzy number-based similarity measure has limitation to calculate the similarity of general fuzzy membership functions. The applicability of the proposed similarity measure to general fuzzy membership structures is proven by identifying the definition. To decide fault detection of flight system, the experimental data (pitching moment coefficients and lift coefficients) are transformed into fuzzy membership functions. Distance-based similarity measure is applied to the obtained fuzzy membership functions, and similarity computation and analysis are obtained with the fault and normal operation coefficients.     

Quantitative comparison of similarity measure and entropy for fuzzy sets

Comparison and data analysis with the similarity measures and entropy for fuzzy sets were carried out. The distance proportional value between the fuzzy set and the corresponding crisp set was considered by the fuzzy entropy. The relation between the similarity measure and the entropy for fuzzy set was also analyzed. The fuzzy entropy was reformulated as the dissimilarity measure. Furthermore, crisp set having the minimum uncertainty with respect to the corresponding fuzzy set was also proposed. Finally, derivation of a similarity measure from entropy with the help of total information property was derived. A simple example shows the relation between similarity measure and fuzzy entropy, in which the summation of similarity measure and fuzzy entropy represents a constant value.     

Similarity measure design and similarity computation for discrete fuzzy data

The similarity computations for fuzzy membership function pairs were carried out. Fuzzy number related knowledge was introduced, and conventional similarity was compared with distance based similarity measure. The usefulness of the proposed similarity measure was verified. The results show that the proposed similarity measure could be applied to ordinary fuzzy membership functions, though it was not easy to design. Through conventional results on the calculation of similarity for fuzzy membership pair, fuzzy membership-crisp pair and crisp-crisp pair were carried out. The proposed distance based similarity measure represented rational performance with the heuristic point of view. Furthermore, troublesome in fuzzy number based similarity measure for abnormal universe of discourse case was discussed. Finally, the similarity measure computation for various membership function pairs was discussed with other conventional results.     

基于直觉模糊集相似度量的多属性决策方法

针对一个特定的由直觉模糊集刻划的决策问题进行研究。基于直觉模糊值的几何意义,提出一种新的直觉模糊值上的相似度量,并基于该度量提出一种直觉模糊集上的多属性决策方法。最后,以实例说明该决策方法的有效性。     

基于包含度理论的图像置乱程度评价研究

提出了基于包含度理论的图像置乱程度评价新方法。本文首先对置乱前后图像中任意像素所对应二阶邻域系统构造一个模糊集并定义其隶属度;其次计算图像中各像素所对应二阶邻域系统模糊集及其补集之间的包含度;最后根据置乱前后两图像的包含度来构造图像置乱程度评价函数。实验结果表明,本文提出的评价方法是能够较好地刻画图像的置乱程度,反映了加密次数与置乱程度之间的关系,与人的视觉基本相符。而且对于不同的图像,该评价方法能在一定程度上反映所用的置乱变换在各置乱阶段的效果。     

改进的广义模糊软集的贴近度

基于广义模糊软集在处理不确定性问题中的应用,本文对已有的广义模糊软集的贴近度进行了修正,并将其应用于医疗诊断问题中。通过比较得到,修正的贴近度更合理,因而有更好的适用性。     

Power interconnected system clustering with advanced fuzzy C-mean algorithm ＇~＂

An advanced fuzzy C-mean (FCM) algorithm was proposed for the efficient regional clustering of multi-nodes interconnected systems. Due to various locational prices and regional coherencies for each node and point, modified similarity measure was considered to gather nodes having similar characteristics. The similarity measure was needed to contain locational prices as well as regional coherency. In order to consider the two properties simultaneously, distance measure of fuzzy C-mean algorithm had to be modified. Regional clustering algorithm for interconnected power systems was designed based on the modified fuzzy C-mean algorithm. The proposed algorithm produces proper classification for the interconnected power system and the results are demonstrated in the example of IEEE 39-bus interconnected electricity system.     

Fuzzy entropy design for non convex fuzzy set and application to mutual information

Fuzzy entropy was designed for non convex fuzzy membership function using well known Hamming distance measure. The proposed fuzzy entropy had the same structure as that of convex fuzzy membership case. Design procedure of fuzzy entropy was proposed by considering fuzzy membership through distance measure, and the obtained results contained more flexibility than the general fuzzy membership function. Furthermore, characteristic analyses for non convex function were also illustrated. Analyses on the mutual information were carried out through the proposed fuzzy entropy and similarity measure, which was also dual structure of fuzzy entropy. By the illustrative example, mutual information was discussed.