A state of the art literature review of VIKOR and its fuzzy extensions on applications

Multi criteria decision making (MCDM) is one of the research areas of operations research and management science which has widely studied by researchers and practitioners. It finds a compromise solution for evaluating and ranking alternatives from the best to the worst under conflicting criteria with respect to decision maker(s) preferences. In a compromise approach, the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR; that means multi-criteria optimization and compromise solution) continues to be applied satisfactorily across different application areas. This paper conducts a state-of-the-art literature review to categorize, analyze and interpret the current research on VIKOR applications. It also discusses the extensions of VIKOR applied in fuzzy environments. A total of 343 papers are classified into 13 different application areas and a number of sub-application areas. Furthermore, all papers are also categorized with respect to publication year, published journal, country of origin, application type (real case study vs empirical study), and version of fuzzy sets used. This comprehensive literature review provides an insight for researchers and practitioners on VIKOR applications in terms of showing current state and potential areas for future attempts to be focused in the future.     

A Survey of Methods for Scaling Up Inductive Algorithms

One of the defining challenges for the KDD research community is to enable inductive learning algorithms to mine very large databases. This paper summarizes, categorizes, and compares existing work on scaling up inductive algorithms. We concentrate on algorithms that build decision trees and rule sets, in order to provide focus and specific details; the issues and techniques generalize to other types of data mining. We begin with a discussion of important issues related to scaling up. We highlight similarities among scaling techniques by categorizing them into three main approaches. For each approach, we then describe, compare, and contrast the different constituent techniques, drawing on specific examples from published papers. Finally, we use the preceding analysis to suggest how to proceed when dealing with a large problem, and where to focus future research.     

基于频繁主题集偏好的学术论文推荐算法

针对学术论文推荐中项目冷启动问题,提出了一种基于频繁主题集偏好的协同主题回归模型。该算法考虑到用户在选择学术论文时对研究热点的偏好,使用频繁主题集代表研究热点,将用户对研究热点的偏好表示成用户对频繁主题集的偏好。通过潜在狄利克雷分布主题模型挖掘得到论文—主题概率分布矩阵,并筛选出论文中概率较高的主题;然后挖掘出频繁出现的主题集合,并得到论文—频繁主题集矩阵;最后在预测未知评分时融入用户对频繁主题集的偏好。在CiteULike数据集上的实验表明,相比于矩阵分解模型和协同主题回归模型,该算法在召回率、准确率和RMSE三个指标上都有所提升。     

基于二元决策系统的粗集知识获取方法研究

提出一种新的粗集知识获取方法,首先将事例集表示成二元决策系统,然后奖其分解成一系列单一二元决策子系统。利用粗集理论对每一子系统进行分析,推理出最优规则。在对决策系统进行条件属性和规则简化时,提出了概率最佳简约准则和概率最小规则准则,按照这两种最优准则可以获得概率意义上数目最小规则集。通过实例分析,具体说明了该方法的实现步骤,结果表明该方法具有明显的优越性。     

基于拓展粗糙集的不完备表的规则挖掘及应用

实际应用中常存在缺省属性值的不完备信息系统,如何从不完备信息系统中挖掘有用规则是一个非常有价值的问题。粗糙集理论是一种有效的数据挖掘手段,但经典粗糙集缺乏对不完备信息系统的处理能力。在粗糙集拓展的基础上,设计出从不完备决策表中挖掘出有用规则的算法,并将其应用到银行贷款决策中不完备决策表的实例分析中。     

A Comparison of the Rough Sets and Recursive Partitioning Induction Approaches: An Application to Commercial Loans

Credit scoring is the term used to describe methods utilized for classifying applicants for credit into classes of risk. This paper evaluates two induction approaches, rough sets and decision trees, as techniques for classifying credit (business) applicants. Inductive learning methods, like rough sets and decision trees, have a better knowledge representational structure than neural networks or statistical procedures because they can be used to derive production rules. If decision trees have already been used for credit granting, the rough sets approach is rarely utilized in this domain. In this paper, we use production rules obtained on a sample of 1102 business loans in order to compare the classification abilities of the two techniques. We show that decision trees obtain better results with 87.5% of good classifications with a pruned tree, against 76.7% for rough sets. However, decision trees make more type–II errors than rough sets, but fewer type–I errors.     

基于Delphi的组卷系统

该文给出了一种组卷系统的设计,介绍了从题库中组卷的方法。系统选题时将按章节和题型分布,当有多套试卷生成时自动保证各套试卷中的试题不重复。按指定的难度要求组卷,系统的效率和试卷质量可以得到大幅度的提高。     

对方案有偏好的Vague集互补判断矩阵决策法

研究指标权重信息未知且对方案有偏好的Vague集多属性决策问题。首先将决策信息和偏好信息的Vague值转化为模糊值,进一步将偏好信息转化为互补判断矩阵,从而建立目标规划模型,通过求解该模型得各指标的权重,并通过求解各方案综合属性值对方案进行排序和择优。最后给出算例。     

基于软区分矩阵的模糊软集决策方法及其应用

通过在模糊软集中引入水平软集,用软区分矩阵来处理决策问题。首先,利用模糊软集的水平软集,将模糊软集转化为经典软集。其次,在软集中引入软区分矩阵的概念,提出了一种基于软区分矩阵解决模糊软集的新算法来处理决策问题。最后,通过实例说明了该算法的可行性。     

A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings

The purpose of this paper was to conduct a comparative study of score functions in multiple criteria decision analysis based on intuitionistic fuzzy sets. The concept of score functions has been conceptualized and widely applied to multi-criteria decision-making problems. There are several types of score functions that can identify the mixed results of positive and negative parts in a bi-dimensional framework of intuitionistic fuzzy sets. Considering various perspectives on score functions, the present study adopts an order of preference based on similarity to the ideal solution as the main structure to estimate the importance of different criteria and compute optimal multi-criteria decisions in intuitionistic fuzzy evaluation settings. An experimental analysis is conducted to examine the relationship between the results yielded by different score functions, considering the average Spearman correlation coefficients and contradiction rates. Furthermore, additional discussions clarify the relative differences in the ranking orders obtained from different combinations of numbers of alternatives and criteria as well as different importance conditions.     

三枝决策粗糙集

从贝叶斯理论出发,介绍基于三枝决策粗集理论。首先讨论在期望风险最小决策的语义下决策粗集理论基本模型的构建过程。其次,分析决策粗集三枝决策方法在不同概率区间犯错的可能性,并通过其与二枝决策及Pawlak粗集三枝决策的差异,给出决策粗集三枝决策方法优于其他两种决策方法的成立条件。最后,提供一种利用决策粗集三枝决策解决实际问题的方法。     

基于熵权Vague集的多目标决策方法

针对目前基于Vague集的多目标决策中目标权重的主观任意性以及评价函数的单一性问题,提出一种基于熵权Vague集的多目标决策方法。首先,将决策矩阵转化为目标优属度矩阵,再利用熵权系数法计算各个目标的客观权重,综合考虑客观权重和主观权重得到各个目标的权重向量区间;然后,通过计算方案的支持目标集、反对目标集和中立目标集得出方案的Vague估计值;最后,定义新的评价函数对方案进行排序并选出最优方案。通过算例验证了所提方法的合理性和有效性。     

基于二进制的决策表求核算法

决策表属性约简是粗糙集理论中的核心内容之一,其中求核运算是决策表属性约简的基础,提出了基于二进制的新的决策表求核算法,将求核运算转化为数值的比较运算,并给出了属性绝对必要性和相对必要性的新的判定规则,与传统算法相比,其速度更快,效率更高,易于计算机实现,为扩展粗糙集的应用提供了理论基础。     

一种基于二叉判定图的包过滤规则设计方法

提出了一种采用二叉判定图来表示规则集的新的算法。通过仿真实验证明：对于较大规模的规则集,基于BDD的包过滤规则设计方法简沽可行,且在存储空间和查询性能上要优于传统的线性顺序方法。     

Decision‐theoretic rough sets under Pythagorean fuzzy information

Decision‐theoretic rough sets (DTRSs), which provide a classical model of three‐way decisions (3WDs), play an important role in risk decision‐making problems. The risk is associated with the loss function of DTRSs, which is evaluated by the decision makers. As a new extension of fuzzy sets, Pythagorean fuzzy sets can handle uncertain information more flexibly than intuitionistic fuzzy sets in the process of decision making and it gives a new measure for the determination of loss functions of DTRSs. More specifically, we take into account the loss functions of DTRSs with Pythagorean fuzzy numbers and propose a Pythagorean fuzzy decision‐theoretic rough set (PFDTRS) model. Some properties of the expected losses are carefully investigated. Then we further design three approaches for deriving 3WDs with the PFDTRS model. The group decision making (GDM) based on the PFDTRS model is also discussed. It provides a novel interpretation for the determination of loss functions. With the aid of the Pythagorean fuzz weighted averaging operator, we aggregate the loss functions, as suggested by the all experts, which support a coherent way of designing information granules in the presence of numerics. An algorithm for 3WDs in GDM based on the PFDTRS model is designed. Then, an example is presented to elaborate on 3WDs with the PFDTRS model.     

一种新的直觉模糊集距离及其在决策中的应用

首先针对直觉模糊集距离中是否包含直觉模糊集通过隶属度、非隶属度以及犹豫度这三种信息,以及直觉模糊集距离是否满足相应距离度量的条件对其进行了详细分析,发现现有方法都是直接将犹豫度直接引入到直觉模糊集距离中,从而会产生不一致性。鉴于此,定义了一种新的直觉模糊集距离度量方法,其不仅考虑隶属度和非隶属度信息,同时还考虑犹豫度对隶属度和非隶属度的分配,从而间接地将犹豫度也引入到直觉模糊集距离中。其次,证明了所提距离度量满足距离度量条件,并结合实例将其与现有距离度量方法进行比较分析,说明了新方法的合理性。最后,将所提出方法应用于多准则模糊决策中,进一步说明了新方法的有效性和可行性。     

Multiple criteria decision making and decision support systems — Guest editor's introduction

Integration of MCDM with DSS brings benefit to both fields. MCDM tools are useful in identifying and evaluating incompatible alternatives for DSS, while DSS can implement MCDM approaches and help maintain and retrieve MCDM models. Over the years, MCDM has made considerable contribution to the development of various DSS subspecialties. This special issue on Multiple Criteria Decision Making and Decision Support Systems consists of 9 selected papers from the 20th International Conference on Multiple Criteria Decision Making. The guest editors highlight the key ideas and contributions of the papers in the special issue.     

Cycle elimination for invocation graph-based context-sensitive pointer analysis

Context

Pointer analysis is an important building block of optimizing compilers and program analyzers for C language. Various methods with precision and performance trade-offs have been proposed. Among them, cycle elimination has been successfully used to improve the scalability of context-insensitive pointer analyses without losing any precision.

Objective

In this article, we present a new method on context-sensitive pointer analysis with an effective application of cycle elimination.

Method

To obtain similar benefits of cycle elimination for context-sensitive analysis, we propose a novel constraint-based formulation that uses sets of contexts as annotations. Our method is not based on binary decision diagram (BDD). Instead, we directly use invocation graphs to represent context sets and apply a hash-consing technique to deal with the exponential blow-up of contexts.

Result

Experimental results on C programs ranging from 20,000 to 290,000 lines show that applying cycle elimination to our new formulation results in 4.5 ×speedup over the previous BDD-based approach.

Conclusion

We showed that cycle elimination is an effective method for improving the scalability of context-sensitive pointer analysis.     

基于粗糙集理论的协同训练算法

为了提升风险决策环境下协同训练的效果, 提出了一种基于粗糙子空间的协同决策算法。首先利用粗糙集属性约简的概念, 将部分标记数据属性空间分解为两差异性较大的粗糙子空间; 在各子空间上训练分类器, 并依据各分类器决策风险代价及隶属度将无标记数据划分为可信、噪声和待定样本。综合两分类器的分类结果, 标注少量可信无标记样本后重复协同训练。从理论上分析了算法性能提升的区间界, 并在UCI数据集上进行实验, 验证了模型的有效性及效率。