基于k-means和邻域粗糙集的航空客户价值分类研究

对客户价值进行分类, 识别重要价值客户, 对航空公司获利至关重要。本文提出了基于k-means和邻域粗糙集的航空客户价值分类模型。首先, 从客户的当前价值和潜在价值双视角出发, 建立了航空客户综合价值评价指标体系; 之后, 采用基于Elbow的k-means方法对航空客户进行聚类, 采用邻域粗糙集方法对决策系统进行指标约简, 根据约简后的决策系统完成客户价值初筛。评估前先使用SMOTE方法消除数据的不平衡性, 而后采用网格搜索组合分类器的方法对航空客户价值分类的效果进行评估和检验。最后, 根据评估结果对航空客户价值细分。文末, 对国内某航空公司的62988条真实客户记录进行了实证分析和验证, 其中, 潜在VIP客户群的分类准确率达到了92%, 从而为航空客户价值分类提供了一种新思路。     

Topology vs generalized rough sets

This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology.     

不完备信息下的灰色粗糙集成决策模型侯亚林

In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.     

集值映射及其应用

考虑集值映射的动力学,证明了对于上半连续的集值映射在一定条件下吸引子的存在性及吸引子在扰动下的上半连续性,进一步考虑集值映射在微分方程数值模拟中的应用．利用集值映射的吸引子在扰动下的上半连续性,阐明微分方程数值模拟中的次分算法及区间算法的合理性．     

基于粗糙集理论的知识约简及应用实例

在保持分类能力不变的前提下 ,通过利用粗糙集理论中的知识约简方法 ,在保护知识库分类不变的条件下 ,删除其中不相关或不重要的知识 ,从而导出问题的决策 .利用基于决策表的粗糙集模型算法 ,实例分析如何数字化表示决策表 ,并对其进行属性约简和属性值的约简 ,从而提取决策规则 .     

Using fuzzy set theory in a scheduling problem: A case study

This paper deals with a real scheduling problem where it seems interesting to use fuzzy sets The question of knowing how and when it is possible to use fuzzy sets (rather than probabilities for instance) is discussed in great detail for the studied case. Fuzzy concepts are shown to be very useful and easy to work with in this decision-aid problem.     

可用性观点下的烟叶质量粗糙集评价方法

通过对现代卷烟产业中烟叶质量新需求的理解和归纳,构建了可用性观点下的烟叶质量综合评价新指标体系。考虑到实际烟叶质量评价中的数据的复杂性和问题求解的特殊性,将基于等价关系的Pawlak粗糙集模型扩展为基于上、下近似相似关系的扩展粗糙集模型,并设计了相应的可用性观点下烟叶质量粗糙集智能评价模型,在实现了不依赖主观先验信息求取各指标客观权重的同时,进一步引入了专家的主观权重信息,以达到对烟叶“可用性”需求的动态调整。文章首次尝试了基于定量化解决途径来应用和阐释烟叶的“可用性”概念,文末的实证分析验证了本文方法的可行性和一定程度的优越性。     

多集值信息表中的多粒度模糊决策论粗糙集

多粒度粗糙集和决策论粗糙集是Pawlak粗糙集的重要推广,目前已成为人工智能研究的热点.然而,它们大多处理的都是单值信息系统中的问题.而实际生活中绝大多数都是处理多值问题,为了解决这一问题,在多集值信息表中将多粒粗糙集与模糊决策论粗糙集相结合进行研究,提出了其在乐观,悲观情形下的上下近似,研究了一些相关性质并给出了多集值信息表中的多粒度模糊决策论粗糙集精度、粗度的概念,最后通过一个具体例子验证其有效性.     

不确定规划的研究现状及其发展前景

本文简要介绍不确定规划理论、算法以及应用研究的现状，描绘了不确定规划理论的基本框架。首先介绍处理各种不确定性的数学工具；接着阐述不确定规划的建模机理与求解方法，然后提出了不确定规划中值得进一步研究的一些问题，最后展望了不确定规划的发展前景。     

集合对策边缘解的公理化方法

本文将单调集合对策边缘解推广到一般集合对策上,利用三个公理,确定了集合对策边缘解的唯—性．在证明唯—性的过程中,引进了单调集合对策将集合对策进行分解．证明过程与Aarts等人的方法完全不一样,在某些地方吸收了Young的有关思想．     

Probabilistic graded rough set and double relative quantitative decision-theoretic rough set

The probabilistic rough set (PRS) model ignores absolute quantitative information i.e., overlap between equivalence class and basic set. And graded rough set (GRS) model cannot reflect the distinctive degrees of information. In order to overcome these defects, this paper proposes the probabilistic graded rough set (PGRS), which is an extension of Pawlak's rough set and GRS. What is more, we propose double relative quantitative decision-theoretic rough set (Drq-DTRS) models, which essentially indicate the relative and absolute quantification.     

Mathematical programming in rough environment

Classical mathematics is usually crisp while most real-life problems are not; therefore, classical mathematics is usually not suitable for dealing with real-life problems. In this article, we present a systematic and focused study of the application of rough sets (Z. Pawlak, Rough sets, In. J. Comput. Informa. Sci. 11 (1982), pp. 341–356.) to a basic area of decision theory, namely ‘mathematical programming’. This new framework concerns mathematical programming in a rough environment and is called ‘rough programming’ (L. Baoding, Theory and Practice of Uncertain Programming, 1st ed., Physica-Verlag, Heidelberg, 2002; E.A. Youness, Characterizing solutions of rough programming problems, Eut. J. Oper. Res. 168 (2006), pp. 1019–1029). It implies the existence of the roughness in any part of the problem as a result of the leakage, uncertainty and vagueness in the available information. We classify rough programming problems into three classes according to the place of the roughness. In rough programming, wherever roughness exists, new concepts like rough feasibility and rough optimality come to the front of our interest. The study of convexity for rough programming problems plays a key role in understanding global optimality in a rough environment. For this, a theoretical framework of convexity in rough programming and conceptualization of the solution is created on the lines of their crisp counterparts.     

程度下近似算子与变精度上近似算子的差运算模型

目的是探讨精度与程度的复合,建立并研究新的粗糙集拓展模型.基于程度与精度的逻辑差需求,提出了程度下近似算子与变精度上近似算子的差运算模型,得到了程度下近似算子与变精度上近似算子的差运算的宏观本质、精确描述与基本性质.并用一个医疗实例说明了模型的意义和应用.程度下近似算子与变精度上近似算子的差运算模型,部分的拓展了程度粗糙集模型和经典粗糙集模型.     

程度与精度的逻辑差近似算子的性质

目的是结合精度与程度,探索新的粗糙集拓展模型.从程度与精度的逻辑差运算出发,定义了程度与精度的逻辑差粗糙集模型.模型中,通过变精度近似与程度近似的转化公式,研究了程度与精度的逻辑差近似算子,并得到了近似算子的幂作用等性质.用程度与精度的逻辑差粗糙集模型拓展了程度粗糙集模型、经典粗糙集模型,并在这些模型中得到了近似算子幂作用的相应性质.     

推广的积分第一中值定理的再改进

研究推广的积分第一中值定理成立的条件,弱化该定理成立应满足的基本要求,并进而得到被积函数连续性替代条件的相关推论.     

基于多Agent的车间任务招投标粗模糊集建模研究

首先通过相识集、招标集、投标集和任务集的概念 ,描述制造执行系统中的调度 Agent与资源 A-gent间任务招投标过程模型 ;基于任务的属性和资源 Agent完成任务的成本、质量、负荷和时间等属性 ,定义论域上的模糊集 ,将模糊集中的隶属度函数作为粗集的属性 ,在模糊集上作截集 ,从而获得系统的分类知识 ;收集样本数据 ,构造并分析决策表 ,进而获得调度 Agent调度决策知识 ;应用调度知识进行推理 ,从争取获得招标任务的若干个资源 Agent中 ,选出最适合招标任务的中标者 .     

基于RST/IAHP的航空维修人因可靠性评估模型研究

针对航空维修人因可靠性定量评估这一难点问题,提出了一种基于粗糙集理论(RST)和区间层次分析法(IAHP)的人因可靠性评估模型.根据大量统计数据,运用决策树法建立分层次的航空维修科目人因可靠性指标评价体系.综合采用区间层次分析法和粗糙集方法确定指标权重,提出了采用区间型加权算法对指标进行聚合.以某航空维修系统更换发动机科目为例,对所提方法进行案例验证.结果表明,该方法具有实用、可操作性强等特点,为航空维修系统科目的人因可靠性评估提供了理论参考.     

半环上的粗糙集

利用同余关系把粗糙集理论引入到半环里,给出了半环中的一个子集的上,下近似的概念,并研究了其一系列性质;另外我们还讨论了半环中的粗糙理想及性质.     

基于Vague粗糙集信息熵的属性约简算法

针对复杂系统分析中的数据信息冗余问题,提出一种基于Vague粗糙集信息熵的属性约简算法。首先,对Vague粗糙集相关概念进行拓展,提出Vague粗糙集的扩展信息熵和广义信息熵的模型;其次,对基于信息熵的属性重要性度量和属性约简原理进行研究,进而提出了一种基于Vague粗糙集信息熵的监督式属性约简算法;最后,选取UCI数据库对算法性能进行验证,计算结果表明该算法实用有效。