Neighborhood based decision-theoretic rough set models

As an extension of Pawlak rough set model, decision-theoretic rough set model (DTRS) adopts the Bayesian decision theory to compute the required thresholds in probabilistic rough set models. It gives a new semantic interpretation of the positive, boundary and negative regions by using three-way decisions. DTRS has been widely discussed and applied in data mining and decision making. However, one limitation of DTRS is its lack of ability to deal with numerical data directly. In order to overcome this disadvantage and extend the theory of DTRS, this paper proposes a neighborhood based decision-theoretic rough set model (NDTRS) under the framework of DTRS. Basic concepts of NDTRS are introduced. A positive region related attribute reduct and a minimum cost attribute reduct in the proposed model are defined and analyzed. Experimental results show that our methods can get a short reduct. Furthermore, a new neighborhood classifier based on three-way decisions is constructed and compared with other classifiers. Comparison experiments show that the proposed classifier can get a high accuracy and a low misclassification cost.     

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.     

三角直觉模糊决策的变权方法

研究了属性值为三角直觉模糊数的多属性决策问题,提出了一种基于变权综合的决策方法。首先,针对三角直觉模糊数,提出一种新的三角直觉模糊排序方法;其次,定义了三角直觉模糊变权加权算术平均算子和三角直觉模糊变权加权几何平均算子;然后,提出一种基于三角直觉模糊变权集成算子的多属性决策方法;最后,数值算例说明了该方法的有效性。     

基于区间粗糙直觉模糊数的多属性决策方法

研究了区间粗糙直觉模糊多属性决策。探讨了区间粗糙直觉模糊数的运算法则及其性质;定义了区间粗糙直觉模糊数的得分函数和精确函数,进而给出其排序方法;给出了区间粗糙直觉模糊数的变权算术平均和变权几何平均算子,并且建立了区间粗糙直觉模糊数的多属性决策模型;实例验证了所提出决策方法的有效性。     

Multi-objective optimization method for learning thresholds in a decision-theoretic rough set model

For decision-theoretic rough sets, a key issue is determining the thresholds for the probabilistic rough set model by setting appropriate cost functions. However, it is not easy to obtain correct cost functions because of a lack of prior knowledge and few previous studies have addressed the determination of learning thresholds and cost functions from datasets. In the present study, a multi-objective optimization model is proposed for threshold learning. In our model, we integrate an objective function that minimizes the decision cost with another that decreases the size of the boundary region. The ranges of the thresholds and two types of F_measure are used as constraints. In addition, a multi-objective genetic algorithm is employed to obtain the Pareto optimal set. We used 12 UCI datasets to validate the performance of our method, where the experimental results demonstrated the trade-off between the two objectives as well as showing that the thresholds obtained by our method were more intuitive than those obtained using other methods. The classification abilities of the solutions were improved by the F_measure constraints.     

一个模糊层次分析法在方案排序中的应用

给出了一个模糊层次分析法(FAHP).该方法的决策矩阵的元素为三角模糊数.结合三角模糊数比较的可能度理论,提出了一个基于模糊层次分析法的有限方案决策方法,最后的实例说明方法的有效性和合理性.     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.     

三角模糊数互补判断矩阵排序的目标规划法

针对决策者以三角模糊数互补判断矩阵形式给出的多目标决策问题.给出三角模糊数加性一致性互补判断矩阵的判定定理.利用该定理基于最小偏差建立一个目标规划模型而解得三角模糊数互补判断矩阵的权重向量,从而使用三角模糊数排序公式对方案排序,提出了基于目标规划的三角模糊数互补判断矩阵排序法.最后,将模型与方法应用于项目投资决策中.     

A dominance intuitionistic fuzzy-rough set approach and its applications

Although the rough set and intuitionistic fuzzy set both capture the same notion, imprecision, studies on the combination of these two theories are rare. Rule extraction is an important task in a type of decision systems where condition attributes are taken as intuitionistic fuzzy values and those of decision attribute are crisp ones. To address this issue, this paper makes a contribution of the following aspects. First, a ranking method is introduced to construct the neighborhood of every object that is determined by intuitionistic fuzzy values of condition attributes. Moreover, an original notion, dominance intuitionistic fuzzy decision tables (DIFDT), is proposed in this paper. Second, a lower/upper approximation set of an object and crisp classes that are confirmed by decision attributes is ascertained by comparing the relation between them. Third, making use of the discernibility matrix and discernibility function, a lower and upper approximation reduction and rule extraction algorithm is devised to acquire knowledge from existing dominance intuitionistic fuzzy decision tables. Finally, the presented model and algorithms are applied to audit risk judgment on information system security auditing risk judgement for CISA, candidate global supplier selection in a manufacturing company, and cars classification.     

An approach to decision making based on intuitionistic fuzzy rough sets over two universes

Rough set theory has been combined with intuitionistic fuzzy sets in dealing with uncertainty decision making. This paper proposes a general decision-making framework based on the intuitionistic fuzzy rough set model over two universes. We first present the intuitionistic fuzzy rough set model over two universes with a constructive approach and discuss the basic properties of this model. We then give a new approach of decision making in uncertainty environment by using the intuitionistic fuzzy rough sets over two universes. Further, the principal steps of the decision method established in this paper are presented in detail. Finally, an example of handling medical diagnosis problem illustrates this approach.     

直觉模糊多属性的意见集中排序法

研究了属性权重信息不完全确定,属性值为直觉模糊集的多属性决策问题。首先根据直觉模糊数的得分函数和精确函数对决策矩阵中的评价值比较大小,进而按属性集中的每个属性对方案排成线性序;然后通过计算赋权模糊优先矩阵确定方案的优属度,建立规划模型确定属性的权重;再利用加权算术算子对方案集结,得到专家对方案的排序,从而得到一种新的意见集中排序的决策方法。数值实例说明该方法的有效性和实用性,可为解决直觉模糊多属性决策提供新方法     

基于VIKOR和关联系数的犹豫三角模糊语言多属性决策方法

针对属性评价值为犹豫三角模糊语言集的多属性决策问题,提出一种基于VIKOR方法的犹豫三角模糊语言多属性决策方法.首先定义了犹豫三角模糊语言集的相关概念.然后运用VIKOR和关联系数方法,在可接受优势和决策过程稳定的条件下对方案进行择优,在理论分析的基础上,提出了这种新方法的计算步骤.并构建了确定最优属性权重的非线性规划模型,研究了当专家权重和属性权重未知情况下的犹豫三角模糊语言多属性决策方法.最后通过实例说明了该方法的有效性和可行性.     

Ranking fuzzy numbers with integral value

Ranking fuzzy numbers is important in decision making. Since very often the alternatives are evaluated by fuzzy numbers in a vague environment, a comparison between these fuzzy numbers is indeed a comparison between alternatives. This paper proposes a method of ranking fuzzy numbers with integral value. The method, which is independent of the type of membership functions used and the normality of the functions, can rank more than two fuzzy numbers simultaneously. It is relatively simple in computation, especially in ranking triangular and trapezoidal fuzzy numbers. Further, an index of optimism is used to reflect the decision maker's optimistic attitude. Discussion on comparative advantages is included.     

基于粗糙集的模糊决策算法

给出一种从连续决策表中提取模糊决策规则的规则提取算法。首先,转化连续属性值为模糊值;然后,给出两个不同对象的模糊属性值关于相应连续属性的相似度;其次,给出了λ相似关系与λ相似类的定义。根据λ相似关系,给出粗糙-模糊空间中的下近似与上近似概念;最后,结合模糊集与粗糙集理论的思想,给出一种从连续值域决策表获取决策规则的算法,并通过实例说明该算法的有效性。     

基于新精确函数的区间直觉模糊多属性决策方法

基于区间直觉模糊数隶属度和非隶属度构成的二维几何图形特征给出区间直觉模糊数精确函数的新定义,并将其作为区间直觉模糊数的排序指标,区间直觉模糊数的精确函数值越大,则区间直觉模糊数就越大,进而提出一种权重信息不完全确定的区间直觉模糊多属性决策方法.通过算例分析说明所提出排序指标的有效性和决策方法的可行性.     

多粒度模糊粗糙集研究

本文研究了模糊粗糙集中属性约简问题.利用模糊粗糙集和多粒度粗糙集各自优点的结合,提出了两类多粒度模糊粗糙集模型,使得两类粗糙集中的上下近似算子关于负算子对偶.同时研究了多粒度模糊粗糙集的性质及与单粒度模糊粗糙集的关系.并通过构造区分函数的方法提出了一类多粒度模糊粗糙集模型的近似约简方法.最后用一个实例核对了该类多粒度模糊粗糙决策系统近似约简方法的有效性.     

An interval type-2 fuzzy sets-based TODIM method and its application to green supplier selection

With the increasing awareness and significant environmental pressures from various stakeholders, companies have realized the significance of selecting green suppliers to their supply chain activities, which involves multiple criteria with uncertainty and the decision makers’ behaviour with irrational. Interval type-2 fuzzy sets (IT2 FSs) have advantages in modelling uncertainty over type-1 fuzzy sets. And TODIM is an useful non-linear prospect model for selecting the irrationally determined alternatives, but the ratings and weights are crisp values. In this paper, we develop the IT2 FSs-based TODIM method to select green supplier. First, we introduce a new distance computing method for IT2 FSs to assist the dominance models to deal with gains (losses) computation. Second, we identify the gains (losses) computing expression through comparing the ranking values of the IT2 FSs evaluations, and obtain the dominance degree of one alternative over others. Third, we use the presented IT2 FSs ranking method using possibility mean and variation coefficient concepts to defuzzify the dominance degree, and obtain the crisp global performance to select the best alternative. Finally, we also apply the proposed IT2 FSs-based TODIM method to green supplier selection for automobile manufacturers.     

Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution

This paper discusses full fuzzy linear programming (FFLP) problems of which all parameters and variable are triangular fuzzy numbers. We use the concept of the symmetric triangular fuzzy number and introduce an approach to defuzzify a general fuzzy quantity. For such a problem, first, the fuzzy triangular number is approximated to its nearest symmetric triangular number, with the assumption that all decision variables are symmetric triangular. An optimal solution to the above-mentioned problem is a symmetric fuzzy solution. Every FLP models turned into two crisp complex linear problems; first a problem is designed in which the center objective value will be calculated and since the center of a fuzzy number is preferred to (its) margin. With a special ranking on fuzzy numbers, the FFLP transform to multi objective linear programming (MOLP) where all variables and parameters are crisp.     

基于Hausdorff距离的模糊数互补判断矩阵排序研究

基于Bonissone近似计算、Hausdorff距离和模糊折衷型决策方法,给出带有梯形模糊数互补判断矩阵的一种排序方法。同时给出精确值、三角模糊数的互补判断矩阵转化为梯形模糊数互补判断矩阵的方法,因此本文方法同样适合于处理精确值、三角模糊数的互补判断矩阵的排序问题。最后用算例说明了计算过程。     

双论域上的区间值直觉模糊粗糙集模型及其应用

基于区间值直觉模糊相容关系,给出了双论域上的区间值直觉模糊粗糙集模型并讨论了其相关性质,为粗糙集的应用提供了新的理论基础与操作手段。最后,通过一个例子阐述了本文提出的区间值直觉模糊粗糙集模型在临床诊断系统中的具体应用。