蕴涵算子族及其应用

提出了模糊蕴涵算子族的新概念,给出了两族蕴涵算子:L-λ-R0(λ∈[1-2,1])族算子与L-λ-G(λ∈[0,1])族算子.L-λ-R0(λ∈[1-2,1])族算子包括Lukasiewicz(简称Rlu)算子与R0算子,L-λ-G(λ∈[0,1])族算子包括Rlu算子与G(o)del(RG))算子.重点讨论了L-λ-Ro(λ∈[1-2,1])族算子的伴随算子及其正则性.结果表明,在蕴涵算子族L-λ-Ro(λ∈[1-2,1])中,只有RLu算子与R0算子有伴随算子且具有正则性,从而说明这两种算子是较理想的蕴涵算子.最后讨论了其应用,同时提出了命题的置信区间及其可信度的新概念.     

正则蕴涵算子族G-λ-R0及其三Ⅰ支持算法

首先给出了一个新的蕴涵算子族:G-λ-R0(λ∈[0,1])(它包括Gsdel(简称RG)算子与R0算子).然后重点讨论了G-λ-R0(λ∈[0,1])族算子的伴随算子及其正则性.结果表明,在该算子族中,每一个算子都具有伴随算子且具有正则性.从而说明了此算子是较理想的蕴涵算子.最后讨论了基于此蕴涵算子族的三Ⅰ支持算法.     

基于效用评估算子的装甲装备作战效能评估

装甲装备作战效能评估适合采用效用函数评估方法.软件实现层次上的算子是定义了输入和输出,封装了一定操作的功能元件.从评估方法到评估算子元件的映射称为评估方法的算子化,生成的算子元件称为评估算子.基于评估算子的评估建模灵活方便,而且容易扩展和理解,是一种较好的评估建模途径.文中将效用函数评估方法算子化为效用评估算子,运用效用评估算子建立装甲装备作战效能评估的算子树模型,并给出了应用实例.     

正则蕴涵算子族G-λ-R_0及其三I支持算法

首先给出了一个新的蕴涵算子族:G-λ-R(0λ∈[0,1])(它包括G觟de(l简称RG)算子与R0算子)。然后重点讨论了G-λ-R0(λ∈[0,1])族算子的伴随算子及其正则性。结果表明,在该算子族中,每一个算子都具有伴随算子且具有正则性。从而说明了此算子是较理想的蕴涵算子。最后讨论了基于此蕴涵算子族的三I支持算法。     

求解TSP的启发式顺序交叉算子

旅行商问题是经典的NP难组合优化问题之一.在用遗传算法求解旅行商问题时,顺序交叉算子是一种较为常用的遗传交叉算子.使用顺序交叉算子时的交叉点位置是随机指定的,不能反映关键遗传信息,导致算法执行效率较低.在顺序交叉算子的基础上,提出了一种启发式顺序交叉算子.该算子结合顺序交叉算子和启发式算法以得到双亲中交叉点位置,保留了双亲中关键的城市顺序信息.该算子改善了使用顺序交叉算子执行效率低的问题.实验结果表明了该算子的有效性.     

CD格上的近似算子

Pawlak近似算子具有多种推广形式。讨论了完全分配格上的近似算子。通过近似空间中的不确定性映射,分别引入了三种形式的上近似算子及下近似算子,讨论了它们的基本性质及其与已有近似算子之间的关系。研究结果表明,目前文献中出现的多种近似算子可以作为完全分配格上近似算子的特例。     

遗传算子的分析

阐述了遗传算法的特点,分析了遗传算法中选择算子、交叉算子和变异算子的特性,讨论了不同遗传算子对算法最优结果的获得所起的作用,提出了改善算法性能的措施,并设计了切实可行的选择算子、交叉算子和变异算子。模拟结果表明,遗传算法能在较短的时间内提供优化解,为解决复杂的优化问题提供了可行方案。     

变权缓冲算子及其作用强度的研究

针对传统缓冲算子不能实现作用强度的微调,从而导致缓冲作用效果过强或过弱的问题,构造了变权弱化缓冲算子和变权强化缓冲算子.研究了缓冲算子调节度与可变权重之间的关系,并用遗传算法探讨该类缓冲算子的优化问题.研究结果表明,可变权重在功能上类似于高阶作用算子,但控制缓冲算子作用强度的灵活性则明显优于高阶缓冲算子.最后以我国能源消费总量的预测问题为例,验证了变权缓冲算子的有效性和优越性.     

基于改进反序-杂交算子的免疫克隆选择算法

反序-杂交算子在求解TSP时容易陷入局部最优。为了优化电路板布局,提高计算快速性,对反序-杂交算子进行了改进,设计了1st-Inver-over算子和2nd-Inver-over算子。采用1st-Inver-over算子和2nd-Inver-over算子作为主要免疫基因操作算子实现了求解TSP的免疫克隆算法,在算法前期,只采用1st-Inver-over算子来保证算法的收敛速度,在算法后期,根据种群的多样性自适应的选取1st-Inver-over算子和2nd-Inver-over算子来协调算法的收敛速度和种群的多样性。仿真结果表明,Inver-over ICSA比经典的GT算法具有更好的收敛性和搜索效率。     

基于MATLAB的芒果边缘检测的研究

本文介绍了图像边缘检测的基本原理和常用的检测方法：Robert算子,Sobel算子,Prewitt算子,Canny算子和Log算子等,将这些方法应用于芒果的边缘检测,并给出了相应的MATLAB边缘检测的具体实现方法和检测结果,结果表明：Canny算子和Log算子检测得到的效果较好。     

广义粗糙近似算子的拓扑性质

粗糙集理论是一种处理不确定性问题的数学工具。粗糙近似算子是粗糙集理论中的核心概念,基于等价关系的Pawlak粗糙近似算子可以推广为基于一般二元关系的广义粗糙近似算子。近似算子的拓扑结构是粗糙集理论的重点研究方向。文中主要研究基于一般二元关系的广义粗糙近似算子诱导拓扑的性质,给出了基于粒和基于子系统的广义粗糙近似算子诱导的4种拓扑,研究了它们之间的关系;通过对象的右邻域系统给出了基于粒的广义近似算子诱导的拓扑的基,研究了相应拓扑的正规性与正则性;通过分析基于子系统的广义上近似算子的性质,证明了基于子系统的广义上近似算子诱导的拓扑可以转化为基于对象的广义下近似算子诱导的拓扑。     

基于ε-修正的直觉模糊信息集成方法及其在决策中的应用

已有的一些直觉模糊集成算子在处理一些特殊直觉模糊数时会出现反直觉现象。首先介绍了两个直觉模糊集成算子和直觉模糊数的比较方法。接着,举例说明了这些集成算子在某些情况下出现的反直觉现象。然后提出了基于ε-修正的直觉模糊集成算子,并讨论了ε取值对此算子结果的影响。之后建立了一种基于ε-修正的直觉模糊集成算子的决策方法。最后通过一个实例比较了原集成算子和本文提出的修正集成算子的集成结果,验证基于ε-修正的直觉模糊集成算子可以修正这些反直觉现象,这也拓宽了原集成算子的使用范围。     

加权模糊聚集算子研究

在数据挖掘、模糊专家系统和多Agent协同决策过程中，要经常面对信息聚集技术和对多个模糊数据来源进行聚集运算，一般用得最多的是合取、析取及加权平均等算子，但是不同的领域有着不同的需求，本文着重对加权聚集算子进行研究。首先，提出了加权平均关系与析取关系结合后的析取-加权平均算子，该算子解决了加权平均算子不能区分析取与合取的关系。然后，提出了一种最大加权平均算子和最小加权平均算子，该算子将最大最小值算子与加权平均算子进行了泛化，解决了同时考虑信息局部性特征与信息整体性特征的问题。理论分析表明，本文提出的加权模糊聚集算子对于模糊信息源的聚集运算起到了很好的补充和完善的功能。     

Multilevel Training of Binary Morphological Operators

The design of binary morphological operators that are translation-invariant and locally defined by a finite neighborhood window corresponds to the problem of designing Boolean functions. As in any supervised classification problem, morphological operators designed from training sample also suffer from overfitting. Large neighborhood tends to lead to performance degradation of the designed operator. This work proposes a multi-level design approach to deal with the issue of designing large neighborhood based operators. The main idea is inspired from stacked generalization (a multi-level classifier design approach) and consists in, at each training level, combining the outcomes of the previous level operators. The final operator is a multi-level operator that ultimately depends on a larger neighborhood than of the individual operators that have been combined. Experimental results show that two-level operators obtained by combining operators designed on subwindows of a large window consistently outperforms the single-level operators designed on the full window. They also show that iterating two-level operators is an effective multi-level approach to obtain better results.     

The structure of pan-addition operator with pre-determined pan-multiplication

Based on the structure of general pan-multiplication operators and the theory of first order linear partial differential equations, we study the structure of pan-addition operators with pre-determined pan-multiplication operators. At first, we describe the structure of pan-addition operators under the ordinary multiplication. Then, with this structure in place, we derive the general representation for the structure of pan-addition operators.     

Fuzzy information retrieval based on geometric-mean averaging operators

Fuzzy sets are very useful in information retrieval. In this paper, we point out that there are some drawbacks in the existing averaging operators (i.e., P-norm operators, infinite-one operators, and Waller-Kraft operators) to deal with AND and OR operations of fuzzy information retrieval. Furthermore, we present new averaging operators based on geometric-mean averaging (GMA) operators to deal with these drawbacks. We use some examples to compare the proposed GMA operators with the existing averaging operators. We also prove some properties of the proposed GMA operators. The proposed GMA operators can overcome the drawbacks of the existing averaging operators and easily determine an appropriate value of the parameter α, where α is either 0 or 1, for handling AND and OR operations of fuzzy information retrieval.     

粗糙近似算子的公理化刻画:综述

从近似空间导出的一对下近似算子与上近似算子是粗糙集理论研究与应用发展的核心基础,近似算子的公理化刻画是粗糙集的理论研究的主要方向.文中回顾基于二元关系的各种经典粗糙近似算子、粗糙模糊近似算子和模糊粗糙近似算子的构造性定义,总结与分析这些近似算子的公理化刻画研究的进展.最后,展望粗糙近似算子的公理化刻画的进一步研究和与其它数学结构之间关系的研究.     

A unified approach to aggregation based upon mom and mam operators

The focus of this article is on the issue of information aggregation. We introduce two new aggregation operators, called MOM and MAM operators, which are, respectively, generalized and and or operators. We describe their relationship to the multivalued logic triangular norm operators and show how they generalize these operators by weakening the associativity property. We provide a duality theorem between these new operators. We present some special classes of these operators. We extend these operators to allow for weighted aggregations, which enable us to include importances. We introduce some families of these weighted MOM and MAM operators. We show how the typical neural aggregation is a special class of these weighted MOM and MAM operators. This generalization allows us to consider neural network and fuzzy logic methods in the same framework. © 1995 John Wiley & Sons, Inc.     

Rough fuzzy approximations on two universes of discourse

In rough set theory, the lower and upper approximation operators can be constructed via a variety of approaches. Various fuzzy generalizations of rough approximation operators have been made over the years. This paper presents a framework for the study of rough fuzzy sets on two universes of discourse. By means of a binary relation between two universes of discourse, a covering and three relations are induced to a single universe of discourse. Based on the induced notions, four pairs of rough fuzzy approximation operators are proposed. These models guarantee that the approximating sets and the approximated sets are on the same universes of discourse. Furthermore, the relationship between the new approximation operators and the existing rough fuzzy approximation operators on two universes of discourse are scrutinized, and some interesting properties are investigated. Finally, the connections of these approximation operators are made, and conditions under which some of these approximation operators are equivalent are obtained.     

Nonmonotonic OWA operators

 The basic properties of the Ordered Weighted Averaging (OWA) operator are recalled. The role of these operators in the formulation of multi-criteria decision functions, using the concept of quantifier guided aggregation, is discussed. An extended class of OWA operators, one based upon a relaxation of the requirements on the OWA operators, is introduced. This relaxation allows us to consider a new branch of OWA operators, NOMOWA operators, which have negative weights and which exhibit nonmonotonicity. Some special cases of these operators are discussed and then we investigate the role of these nonmonotonic operators in the formulation of multi-criteria decision functions.