单向S-粗模糊集及其特性

提出动态的模糊集,即单向S-模糊集。由此提出了单向S-粗模糊集概念,给出了单向S-粗模糊集结构。定义了单向S-粗模糊集的截集概念,讨论了单向S-粗模糊集的特性。分析了单向S-粗模糊集与Z.Pawlak 粗集、Dubois粗模糊集以及单向S-粗集之间的关系。给出了单向S-粗模糊集的背景和意义解释,单向S-粗模糊集是具有动态特性的粗模糊集。     

双向S-模糊粗糙集及其应用

以Z.Pawlak粗集理论为基础,将动态模糊近似概念引入Dubois模糊粗糙集中。提出了双向S-模糊粗糙集概念,给出了双向S-模糊粗糙集的结构与性质。分析了双向S-模糊粗糙集与Z.Pawlak粗集、Dubois模糊粗集、S-粗集、S-粗糙模糊集及单向S-模糊粗糙集之间的关系。给出了双向S-模糊粗糙集的应用及存在价值。     

The deviation of a set of strings

This paper introduces the concept of set deviation as a tool to characterise the deviation of a set of strings around its set median. The set deviation is defined as the set median of the positive edit sequences between any string and the set median. We show that the set deviation has the same properties as the classic second-order statistical moment. This approach is generalised to higher-order-moments of a set of strings. We then show how the set deviation can be efficiently used in well-known statistical algorithms to improve the computation of the set median of a set of strings, illustrating this concept with several examples, particularly in post-processing of texts extracted from video sequences.     

A New Fuzzy Set Theory Satisfying All Classical Set Formulas

A new fuzzy set theory,C-fuzzy set theory,is introduced in this paper.It is a particular case of the classical set theory and satisfies all formulas of the classical set theory.To add a limitation to C-fuzzy set system,in which all fuzzy sets must be"non-uniform inclusive"to each other,then it forms a family of sub-systems,the Z-fuzzy set family.It can be proved that the Zo-fuzzy set system,one of Z-fuzzy set systems,is equivalent to Zadeh's fuzzy set system.Analysis shows that 1) Zadeh's fuzzy set syste...     

Mining Informative Rule Set for Prediction

Mining transaction databases for association rules usually generates a large number of rules, most of which are unnecessary when used for subsequent prediction. In this paper we define a rule set for a given transaction database that is much smaller than the association rule set but makes the same predictions as the association rule set by the confidence priority. We call this rule set informative rule set. The informative rule set is not constrained to particular target items; and it is smaller than the non-redundant association rule set. We characterise relationships between the informative rule set and non-redundant association rule set. We present an algorithm to directly generate the informative rule set without generating all frequent itemsets first that accesses the database less frequently than other direct methods. We show experimentally that the informative rule set is much smaller and can be generated more efficiently than both the association rule set and non-redundant association rule set.     

粗糙集的阶梯式近似

首先,利用基于边界域粗糙近似算子,给出n阶边界集的定义,引入n阶粗糙近似算子的定义,构造粗糙集理论的一套阶梯式近似方法.然后,通过实例和相关证明表明,无论二元关系还是在覆盖环境中,总存在正整数n,对于任意对象集,n阶上下近似集完全等于该对象集,即该对象集是此意义下的精确集,或其n阶上下近似集趋近于某一固定的对象集,即n阶粗糙集总能使对象集合趋近于它本身或某一固定的集合.     

集合代数是经典命题演算形式系统的语义解释

经典命题演算形式系统(CPC)中的公式只是一些形式符号,其意义是由具体的解释给出的.逻辑代数和集合代数都是布尔代数,都是CPC的解释.集合代数是CPC的集合语义,其中对联结词的解释就是集合运算;对形式公式的解释就是集合函数;对逻辑蕴涵.逻辑等价的解释就是集合包含和集合相等=.标准概率逻辑是在标准概率空间上建立的逻辑体系,命题表示随机事件,随机事件是集合,概率空间中的事件域是集合代数,概率逻辑就是CPC集合语义的实际应用.CPC完全适用于概率命题演算.     

Soft rough fuzzy sets and soft fuzzy rough sets

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.     

可调节模糊粗糙集:模型与属性约简

模糊粗糙集是经典粗糙集为适应实际应用需求所进行的拓展,然而目前很多的模糊粗糙集模型都仅仅使用多个二元关系的简单融合方式,不具备调节功能。为解决这一问题,使用参数化的二元算子,提出了一种可调节的模糊粗糙集模型。在此基础上,将近似质量作为度量标准,使用启发式算法来求解可调节模糊粗糙集的约简。最后对可调节模糊粗糙集的近似质量和约简与强模糊粗糙集、弱模糊粗糙集的结果进行了比较分析。实验结果表明,可调节模糊粗糙集通过使用不同的参数,具有很好的调节作用,是强模糊粗糙集和弱模糊粗糙集的一种泛化形式。     

Flou值模糊集的表现定理

为了弥补区间值模糊集和三参数模糊集在模糊信息表达方面的不足,在Flou集的基础上,提出了一种新的L模糊集,Flou值模糊集,并用投票模型对其作出解释。引入Flou嵌套集的概念,结合Flou值模糊集截集的定义及分解定理,建立了Flou值模糊集的表现定理,并用一个实际算例验证了表现定理的有效性。它揭示了Flou集和Flou值模糊集的联系,提供了一种利用Flou嵌套集拼成Flou值模糊集的方法。为处理模糊信息提供了一种新的工具,并为Flou值模糊集的研究和应用奠定了初步的理论基础。     

新型ε-不敏感损失函数支持向量诱导回归算法及售后服务数据模型预测系统

对含有噪声的数据序列根据预测置信度进行去噪处理,将训练集和测试集及预测数据共同作为训练向量集,以此建立新型支持向量诱导回归算法。本文利用该算法对实时售后服务的“千车故障数”进行了时间序列分析,并建立了新型的ε-不敏感损失函数小样本模型预测系统。预测显示误差小于5．3％的值占了总体的98．1％,其预测置信度达到0．983,与二次和Huber损失函数相比其MAPE值只有2．3％。用计算机模拟仿真单批次预测显,当时间参量t→＋∞,“千车故障数”将收敛于定值74．0601,这和实际相当吻合,表明所建预测模型的有效性。文章最后还和传统神经网络模型作了比较,说明新型SVM机比神经网络处理小样本能力更强。     

Transitive closures and orderings on soft sets

In this paper an attempt is made to extend some standard results in set theory on the basis of soft set relations. Antisymmetric relation and transitive closure of a soft set relation are introduced and an analogue of Warshall’s algorithm is proposed for calculating the transitive closure of a soft set relation. Ordering on a soft set is defined and some set theoretical results based on this are proved.     

用演化算法求解高校排课的问题

根据排课问题的有效性约束,建立了基于实际情况的数学模型,提出课元、资源等概念模型。采用演化算法来解决排课问题,根据教师集、班级集、课程集、教室集、时间集、课元集、资源集等概念定义了约束集,再设计了相应的编码和评价方法,采用轮盘选择、单点交叉、随机变异、μ＋λ淘汰等策略进行计算．实验结果表明,用演化算法解决排课问题是可行的。     

基于排序的非劣集合快速求解算法

提出一种快速算法求解非劣集合，它采用两种技术加速求解：①它不直接求原集合的非劣集合而是转化成求一个整型集合的非劣集合；②它制定一个总体上非劣元素在前、劣元素在后的检查序列，并以尽可能少的比较次数检查一个元素的非劣性，一旦发现后面的元素全劣，终止搜索．理论和实验结果表明，当非劣集合较大时新算法的性能明显优于当前所知的较快算法(KLP)．     

Defuzzification of spatial fuzzy sets by feature distance minimization

We present a novel defuzzification method, i.e., a mapping from the set of fuzzy sets to the set of crisp sets, and we suggest its application to image processing. Spatial fuzzy sets are, e.g., useful as information preserving representations of objects in images. Defuzzification of such a spatial fuzzy set can be seen as a crisp segmentation procedure. With the aim to provide preservation of selected quantitative features of the fuzzy set, we define the defuzzification of a fuzzy set to be a crisp set which is as close as possible to the fuzzy set, where the distance measure on the set of fuzzy sets, that we propose for defuzzification, incorporates selected local and global features of the fuzzy sets. The distance measure is based on the Minkowski distance between feature representations of the sets. The distance minimization, performed in the suggested defuzzification method, provides preservation of the selected quantitative features of the fuzzy set. The method utilizes the information contained in the fuzzy representation for defining a mapping from the set of fuzzy sets to the set of crisp sets. If the fuzzy set is a representation of an unknown crisp original set, such that the selected features of the original set are preserved in the fuzzy representation, then the defuzzified set may be seen as an approximate reconstruction of the crisp original. We present four optimization algorithms, exhibiting different properties, for finding the crisp set closest to a given discrete fuzzy set. A number of examples, using both synthetic and real images, illustrate the main properties of the proposed method. An evaluation of both theoretical aspects of the method, and its results, is given.     

动态描述逻辑的可拓集合扩展

通过对可拓集合与经典集合、模糊集合的分析比较,说明可拓集合的特点和优点,用可拓集合代替经典集合或模糊集合作为动态描述逻辑DDL的集合论基础,对DDL进行扩展,生成了一种新的描述逻辑DDES,并给出了DDLES中概念、关系和实例的描述形式以及它们的语义解释,最后对传统描述逻辑ALC、模糊DDL和DDES中的Abox形式进行了比较.     

S-粗Vague集合及应用

在原始Vague集基础上提出动态的Vague集,即Ｓ-Vague集,由此提出了Ｓ-粗Vague集概念。接着给出了Ｓ-粗Vague集结构与性质,分析了Ｓ-粗Vague集与Z.Pawlak粗集、Dubois粗糙模糊集以及S-粗集之间的关系,给出了Ｓ-粗Vague集的应用。     

粗糙集与FI代数

在粗糙集的代数刻画方面,一个重要方法是在偶序对<■(X),■(X)>构成的集合中,通过定义基本运算,寻找刻画偶序对所构成集合的代数结构。本文在偶序对<■(X),■(X)>构成的集合中定义二元运算→,证明了偶序对<■(X),■(X)>所构成的集合构成FI代数,并给出几个简单性质。     

Ⅱ-型模糊集截集的定义及特征研究

经典模糊集的截集概念是经典模糊集合与经典集合联系的桥梁,对于II-型模糊集,该文在分析II-型模糊集、区间值II-型模糊集、I-型模糊集以及经典集合之间关系的基础上,定义了II-型模糊集的截集概念,分析了II-型模糊集截集的特征,仿真证明了II-型模糊集截集的有效性,为基于II-型模糊集的决策、聚类等实际应用提供了新的方法。