Generalized ordered weighted averaging operators based methods for MADM in intuitionistic fuzzy set setting

Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.

A minimal axiom group for rough set based on quasi-ordering

Rough set axiomatization is one aspect of rough set study to characterize rough set theory using dependable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. The classic rough set theory is based on equivalent relation, but rough set theory based on reflexive and transitive relation (called quasi-ordering) has wide applications in the real world. To characterize topological rough set theory, an axiom group named RT, consisting of 4 axioms, is proposed. It is proved that the axiom group reliability in characterizing rough set theory based on similar relation is reasonable. Simultaneously, the minimization of the axiom group, which requires that each axiom is an equation and each is independent, is proved. The axiom group is helpful for researching rough set theory by logic and axiom system methods.

SOME EQUAL DIVISIONS ON ORDERED TREE SET

We say a divisien (S = SA or SB, g) is equal if it divides set S into two subsets SA and SB satisfying f (SA) = f (SB), where f is som attribute function on these sets and SA or SB need not be empty. In the present paper, we have obtained some equal divisions on set of ordered tree with n modes: two equal divisions on tree set; two equal divisions on node set; two divisions on leaf set, one is equal, another one is ''asymptotically'' equal. We conclude that, ordered tree set is on its good behavior in equal dividing.

The Fractal Structures of the Sample Path of a General Subordinator and the Random Re-orderings of the Cantor Set

In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.

The Counting Problem of an Order N-group of Set

In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.

The Normal Meromorphic Functions Family Concerning Higher Order Derivative and Shared Set by One-Way

Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.

REAIZATION OF THE NEIGHBORING LOGIC SYMMETRY FOR BOOLEAN ORDERED SET

By means of Logic symmetric relation,the single neighboring Logic path for Ndimensions Boolean ordered set is solved.A new method of determining any logic neighboringsubset in limited dimension is proposed.Its results are intuitional and realizable for computer.

Higher-order Optimality Conditions for Henig Effcient Solution in Set-valued Optimization under Cone-convexlike Maps

This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.

Results of Associated Implication Algebra on a Partial Ordered Set

Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.

Optimality conditions in set optimization employing higher-order radial derivatives

There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.

Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.

基于组合赋权-偏序集的应急供应链可靠性评价

为协调好应急供应链中物资的分配与使用,基于文献分析等方法提炼应急供应链可靠性评价指标,建立由组织保障可靠性、系统制度可靠性以及运作流程可靠性3个一级指标及其对应的17个二级指标组成的应急供应链可靠性评价指标体系;利用层次分析法(AHP)、熵权法(EWM)和三角模糊数计算指标权重,将蕴含权重信息的偏序关系引入评价研究中,构建组合赋权-偏序集模型评价应急供应链的可靠性,并应用该模型评价分析C市5个县级城市的应急供应链可靠性水平。结果表明:5个县级城市的应急供应链可靠性程度可分为4类,其中,地区03的可靠性水平高,地区04、02的可靠性水平较高,地区05的可靠性水平中等,而地区01的可靠性水平低;通过对比分析,获取各地区的优势环节和薄弱环节以及需改进的地方。该评价模型可有效评估应急供应链可靠性水平。

汉英表征顺序认知定势差异及其对外语教学的启示

中国“崇尚和合、取法自然”的哲学思想和英美民族“天人各一、主客二分”的思维方式导致汉英在句法结构上的显著差异。句法结构差异在认知表征顺序上体现为汉语是“背景——前景”,英语是“前景——背景”的认知定势差异。现代汉语在时间表征顺序上临摹自然时间顺序,而英语则相反;汉语在组词上受“损——益”价值取向制约,而英语组词并不受“损——益”价值约束。研究汉英表征顺序认知定势规律,有助于跨文化外语学习和教学减少盲目性,提高针对性,最大限度地提高外语理解、记忆的效率。

基于Roughset的有序信息表的排序问题研究

针对有序信息表的排序问题,提出了总体排序的过程框架。将有序信息表转化为二进制信息表,运用粗糙集理论对信息表进行简化,在对属性值标准化的基础上构造有序信息表中实体的排序度量函数,根据度量函数值的大小进行排序。实例表明该过程框架在误差允许范围内是有效可行的。

‘京白梨’果形及果重差异影响因素分析

为解决‘京白梨’品质退化的问题,以北京地区‘京白梨’结果树为试材,比较不同秋子梨授粉品种、坐果序位和立地条件(丘陵和平地果园)对‘京白梨’果形和果重的影响。结果表明,利用‘子母梨’、‘山梨’、‘鸭广梨’、‘金香水’和‘寒红’分别给‘京白梨’授粉,‘山梨’、‘寒红’授粉效果最佳,获得的‘京白梨’果重分别为113.60、110.80 g,果形指数均为0.82;3~5序位坐果率高、果重大,优于1~2序位和6~9序位坐果;山地丘陵果园‘京白梨’果重100.77 g、果形指数0.82,而平地果园果重125.08 g、果形指数0.87,果形指数受立地条件影响。综上所述,为保证‘京白梨’果形的典型性,可配置‘山梨’和‘寒红’为授粉品种,疏果保留3~5序位,并在冷凉山区环境种植。

7元素集合上T_(0)拓扑数计算

主要借助序与拓扑交叉的方法,得出拓扑空间上的T_(0)拓扑数与偏序之间的一一对应关系,通过对极小元和极大元的个数进行分类讨论,结合Hasse图和层级配比数,进而采用纯数学的方法计算得出7元素集合上T_(0)拓扑数为7544798.

基于模糊集理论和序关系分析法的电力市场指标体系研究

随着我国电力市场改革工作逐步深入,电力市场建设和运营过程中一些问题渐渐显露。合理、高效的电力市场评价体系是市场参与者进行市场分析和建设的重要工具,也是政府部门制定监管政策的科学依据。在充分考虑电力市场评价体系原则及SCP范式理论的基础上,构建了包含市场结构、市场运营、市场效益和市场可持续发展四个维度的三级指标体系;并基于序关系分析法和模糊集理论,研究分析电力市场综合指标评估方法。针对传统模糊集理论中“最大隶属度”原则的不足,提出群聚隶属度方法。通过实例计算分析,验证所构建评价体系的有效性和实用性。

利用到达定义集计算流依赖和def-order依赖

针对生成程序系统依赖图时语句顶点之间的流依赖和def-order依赖计算问题,给出了定义清晰的路径以及到达定义集的概念,描述了利用到达定义集进行计算的方法步骤,有助于确立语句之间的流依赖和def-order依赖关系。

基于不完备混合序信息系统的增量式属性约简

由于大数据环境下数据呈现出动态更新的特征,因此,增量式属性约简已成为粗糙集理论的重点研究方向。不完备混合型有序信息系统是一种常见的信息系统类型,然而,目前少有增量式属性约简方面的相关研究,针对这一问题,本文在不完备混合型有序信息系统下提出一种对象更新情形的增量式属性约简算法。首先,针对不完备混合型有序信息系统提出了邻域容差优势关系,基于该二元关系建立了一种新的邻域优势粗糙集模型。其次,在其基础上定义了邻域优势条件熵,并利用邻域优势条件熵作为启发式函数设计出一种不完备混合型有序信息系统的非增量式属性约简算法。然后,利用矩阵的形式重构了邻域容差优势关系和邻域优势条件熵,针对不完备混合型有序信息系统对象的动态变化,基于矩阵的计算策略分别研究了邻域优势条件熵随信息系统对象增加和对象减少时的增量式更新。最后,利用邻域优势条件熵的更新机制分别提出了不完备混合型有序信息系统对象增加和对象减少时属性约简的增量式更新算法。实验结果表明:(1)与非增量式算法相比,所提出的增量式算法约简属性数量平均降低了3.6%,分类精度平均提升了2.4%,属性约简的效率平均提升了约10倍;(2)与同类型增量式算法相比,所提出的增量式算法约简属性数量平均降低了9.0%,分类精度平均提升了2.1%,属性约简的平均效率提升了94%。因此,本文所提出增量式算法无论在属性约简结果和属性约简效率上都有着更高的性能。

Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator

The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.