The classification of statistically recursive sets

The main aim of this paper is to make a classification of random setsK _m (ω) constructed in theorem 2. 1 and theorem 2. 1′ in [1]. We provide five criterions for the classification. Many kinds of random sets such as Hawkes constructed in [2], Graf constructed in [3] and Mauldin constructed in [4] are the special cases ofK _m (ω) constructed in [1], and then these random sets belong to some model respectively according to our classification. Supported by the National Natural Science Fundation and the Doctal Programme Fundation of China Hu Dihe: born in May 1935, Professor     

Rough算子求解不一致信息系统的约简算法

为求解不一致信息系统的属性约简,在经典粗集理论模型的基础上,许多学者提出了上、下分布约简等方法,但是,这些方法尽可能保持了原决策系统的决策分布情况并且当数据集基数较大时,时间空间复杂度都较大。本文从另一个视角将大数据库中记录看成概率事件,利用粗集理论导出规则的模糊性度量方法—Rough算子,在多数优先的原则的基础上,将不一致信息系统转化为一致信息系统,并基于此提出了递增式反向求解方法。这种反向求解思想也为在大数据库中求解约简提供了可能。     

粗糙依赖约简技术在网络课程评价中的研究

介绍了粗糙集的概念和约简的相关定义,提出了基于粗糙依赖的属性约简算法.通过差别矩阵求核,并计算非核属性粗糙依赖值,从而确定相对属性约简.以远程教学网络课程等级评价为例进行算法验证,并通过基于值核的值约简算法提取决策规则,实践证明得到了满意的结果.     

模糊划分的一个新定义及其应用

提出了模糊划分的一个新定义。可以证明它蕴含了Ruspini的定义,并且具有与直观及其实际应用相符的性质。而且根据此定义,可以定义模糊集合的相对清晰度及模糊划分的平均清晰度。实验证明,模糊划分的平均清晰度可以衡量FCM算法的聚类效果。     

一种基于关联矩阵的直觉模糊聚类算法

文章首先定义一种新的直觉模糊集之间的关联系数,利用此关联系数给出关联矩阵;其次,通过平方法把关联矩阵转化为等价关联矩阵,形成聚类原则,得出聚类算法;最后,通过实例对算法进行验证.     

基于一类完备格诱导的直觉模糊集的多元扩展运算

基于一种二元序完备格引入了直觉模糊集的截集的概念,给出了直觉模糊集的加、减和乘法等算术运算,获得了这种截集的算术运算性质,并通过实例说明这些包含关系可以严格成立.此外,在完备格诱导的直觉模糊集的截集基础上,得到了直觉模糊集的多元扩展原理,进而讨论了多元扩展运算的2个基本性质.     

结构智能的调节器:符号化及示范实现

通过三种控制功能,将调节问题层层归约,并利用拓广了的调节问题归约与或图,来显式地表示出结构智能调节器的逻辑推理和数值计算的细节和过程。整套方法直观形象,避免了逻辑上的冗余性或(和)不完备性,容易理解和分析。     

基于粗糙集理论的系统建模方法

根据粗糙集理论，提出了粗糙集建模的方法，并给出了建模步骤：首先采集系统的输入输出样本集，建立决策表，然后根据相对约简求出属性的重要性，由其重要性得出决策的最简形式，从而得到系统的粗糙集模型。以线性系统为例建立了粗糙集仿真模型，验证了模型的有效性。仿真结果表明，在开环条件下建立的一阶系统粗糙集模型，能适应于开环和闭环，也能适应于可变的输入信号；二阶系统模型只能适应于建模时的情况。该建模方法可以推广到非线性系统的建模中。     

基于遗传优化的粗糙神经网络模式识别器及应用

通过粗糙集获取知识表达系统的分类规则，用产生的规则对神经网络进行编码，并利用遗传算法对初步学习后的神经网络的权值进行优化，最终得到一个神经网络模式识别器。举例说明了采用这种方法得到模式识别器的过程及其对待识别对象的学习和分类效果。结果表明：采用粗糙规则对神经网络编码可以缩短神经网络的训练过程，遗传算化对神经网络权值的优化可在一定程度上提高模式识别的精度。     

A Testable Theory for the Emergence of the Classical World

The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2^N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2^N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments.