Fast assignment reduction in inconsistent incomplete decision systems

This paper focuses on fast algorithm for computing the assignment reduct in inconsistent incomplete decision systems. It is quite inconvenient to judge the assignment reduct directly ac-cording to its definition. We propose the judgment theorem for the assignment reduct in the inconsistent incomplete decision system, which greatly simplifies judging this type reduct. On such basis, we derive a novel attribute significance measure and construct the fast assignment reduction algorithm （F-ARA）, intended for com-puting the assignment reduct in inconsistent incomplete decision systems. Final y, we make a comparison between F-ARA and the discernibility matrix-based method by experiments on 13 Univer-sity of California at Irvine （UCI） datasets, and the experimental results prove that F-ARA is efficient and feasible.

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.

Maximizing deviation method for multiple attribute decision making under q-rung orthopair fuzzy environment

Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.

Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators

Two interval-valued intuitionistic uncertain linguistic hybrid operators cal ed the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging （I-IIULHSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley geometric （I-IIULHSG） operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among elements and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponentially complex. In order to simplify the complexity of solving a fuzzy measure, we further define the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley averaging （I-IIULHλSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley geometric （I-IIULHλSG） operator. Moreover, an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is developed. Finally, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibility.

Interval-Valued Neutrosophic Soft Expert Set from Real Space to Complex Space

A fuzzy system is a novel computing technique that accesses uncertain information by fuzzy representation.In the decision-making process,fuzzy system and soft computing are effective tools that are tolerant to imprecision,uncertainty,and partial truths.Evolutionary fuzzy systems have been developed with the appearance of interval fuzzy,dual fuzzy,hesitant fuzzy,neutrosophic,plithogenic representations,etc.Moreover,by capturing compound features and convey multi-dimensional data,complex numbers are utilized to generalize fuzzy and neutrosophic fuzzy sets.In this paper,a representation of neutrosophic soft expert systems based on the real and complex numbers in the interval form is proposed.The interval-valued neutrosophic soft expert set(I-VNSES)is defined,and the interval-valued complex neutrosophic soft expert set(I-VCNSES)is formally generalized from the concept of IVNSES.For both I-VNSES and I-VCNSES,we introduce the relevant basic theoretical operations and study their properties.Based on these new concepts,a generalized algorithm is proposed and applied to handle the imbedded indeterminacy in the two-dimensional interval data.The proposed algorithm is tested on the economic factors that affected the Malaysian economy in 2020 to see which ones are the most influential.Eventually,a comparison of three current approaches is used to back up this study.

基于信息粒的不协调决策形式背景的分布约简

粒计算和知识约简是知识发现和数据挖掘的两个重要课题。基于信息粒研究不协调决策形式背景的属性约简的定义和方法。首先,利用对象概念的内涵定义对象集上的拟序关系,并研究其相关性质。然后,利用拟序类定义分布函数和最大部分函数,进而提出不协调决策形式背景的(最大)分布协调集和(最大)分布约简的定义。最后,定义不协调决策形式背景的(最大)分布辨识矩阵及(最大)分布辨识公式,基于辨识矩阵给出(最大)分布协调集的判定定理,并提出计算分布约简和最大分布约简的方法。

A MULTI-ATTRIBUTE LARGE GROUP EMERGENCY DECISION MAKING METHOD BASED ON GROUP PREFERENCE CONSISTENCY OF GENERALIZED INTERVAL-VALUED TRAPEZOIDAL FUZZY NUMBERS

In this paper, a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by generalized interval-valued trapezoidal fuzzy numbers （GITFNs）. Firstly, a degree of similarity formula between GITFNs is presented. Secondly, expert preference information on different alternatives is clustered into several aggregations via the fuzzy clustering method. As the clustering proceeds, an index of group preference consistency is introduced to ensure the clustering effect, and then the group preference information on different alternatives is obtained. Thirdly, the TOPSIS method is used to rank the alternatives. Finally, an example is taken to show the feasibility and effectiveness of this approach. These method can ensure the consistency degree of group preference, thus decision efficiency of emergency response activities can be improved.

Dominance-based fuzzy rough approach to an interval-valued decision system

Though the dominance-based rough set approach has been applied to interval-valued information systems for knowledge discovery, the traditional dominance relation cannot be used to describe the degree of dominance principle in terms of pairs of objects. In this paper, a ranking method of interval-valued data is used to describe the degree of dominance in the interval-valued information system. Therefore, the fuzzy rough technique is employed to construct the rough approximations of upward and downward unions of decision classes, from which one can induce at least and at most decision rules with certainty factors from the interval-valued decision system. Some numerical examples are employed to substantiate the conceptual arguments.

Interval-Valued Dual Hesitant Fuzzy Hamacher Aggregation Operators for Multiple Attribute Decision Making

As an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given,and an numerical example is provided to demonstrate that the developed approach is both valid and practical.

Reducing Inconsistent Rules Based on Irregular Decision Table

In this paper, we study the problem of rule extraction from data sets using the rough set method. For inconsistent rules due to improper selection of split-points during discretization, and/or to lack of information, we propose two methods to remove their inconsistency based on irregular decision tables. By using these methods, inconsistent rules are eliminated as far as possible, without affecting the remaining consistent rules. Experimental test indicates that use of the new method leads to an improvement in the mean accuracy of the extracted rules.

基于时间偏好不一致的最优关系租金与银企估值

基于时间偏好不一致性的理论框架,构建了银企合作的关系贷款模型,模型中银行的最优停贷决策被视为一项实物期权。数值结果表明,时间偏好不一致性会导致代理人选择更低的违约门槛,但借款人的融资成本会更高。在项目估值方面,相比时间偏好一致情形,具有时间偏好不一致特征的银行和企业项目价值都大幅减少。此外,幼稚型和成熟型代理人对比结果显示,幼稚型代理人的错误信念能够抑制由于时间偏好不一致而导致的违约风险上升,并且能够降低最优关系租金,从而减轻具有财务约束的企业的融资成本。构建的贷款模型不仅丰富了银企关系型借贷的相关理论研究,而且指出在代理人具有时间偏好不一致的条件下最优关系租金(融资成本)更高,这从行为金融的认知偏差角度为中小企业融资难、融资贵的困境提供了新的解释。

不一致邻域决策信息系统的增量式属性约简研究

属性约简是数据挖掘、机器学习等研究领域中的一个非常重要的预处理步骤,其效率的高低会直接影响到数据挖掘、机器学习等相关任务的性能。针对目前已有的非增量式属性约简方法在处理不一致邻域信息系统动态变化时无法高效更新属性约简的问题,提出一种在不一致邻域决策信息系统中对象集发生变化时的增量式属性约简方法。首先,该文以不一致邻域决策信息系统为研究对象,结合不一致邻域的特点给出了一种新的不一致度的表示方法。在此基础上用不一致度来表征属性重要度,以属性重要度为启发式信息研究不一致邻域信息系统对象集发生变化条件下邻域类以及不一致度的更新机理。随后,以不一致度为启发信息构建了增量式属性约简算法。进一步,在UCI上选取6个数据集,通过分类精度测试实验精选出各个数据集的最佳邻域半径δ,最后,利用最佳邻域半径δ在各个数据集上执行增量式属性约简算法实验,实验结果表明该文提出的增量式属性约简算法在保持分类精度不变的前提下较其他算法更加快速和有效。

不一致决策表的知识约简方法研究

目前计算不一致决策表的分布约简、最大分布约简和分配约简的方法均基于可辨识属性矩阵,在大数据集下耗时较多.为此,提出转化算法,将计算原不一致决策表的上述3种约简转化为计算3种一致决策表的Paw lak约简.通过应用针对后者的高效启发式算法,有效地减少了计算时间.此外,引入λ-约简的概念,通过调节λ的值,能得到一族反映决策矢量不同水平相似程度的知识约简.该方法降低了分布约简对决策表区分能力的过高要求,较上述3种约简更为灵活.

基于简化分辨矩阵的粗糙集属性约简算法

针对改进的经典算法求取属性约简存在的时间和空间性能不理想问题,本文提出了一种新的属性约简算法ARSDM。该算法先将决策表按决策属性的类别划分,后采用边生成矩阵元素边约简边排序的思想求取属性约简,有效地加快了约简速度。实验表明ARSDM算法与经典算法相比具有较好的时间和空间性能。

基于粗集边界域的快速约简算法

属性约简是粗糙集研究的核心内容之一。已有的大多数属性约简算法都是采用基于正域的贪心算法求决策表的代数约简。事实上,对于不一致决策表,代数约简改变了决策类族原有的Pawlak拓扑结构,造成决策类的不确定性扩大。为此,提出了一种新的基于粗集边界域的约简模型,它能够保持决策类族原有的Pawlak拓扑结构。依据新模型,提出了一种高效率的基于粗集边界域的属性约简算法。理论分析和实验表明,所提算法是有效可行的。

基于多元组Rough集的不相容决策

Ｒｏｕｇｈ集理论是一种具有模糊边界的集合理论．它被广泛应用于不相容决策表中的规则提取．本文讨论了基于多元组Ｒｏｕｇｈ集的不相容决策方法，并给出了相应的算法，同时也对不相容规则的相容度作了分析．该方法比普通Ｒｏｕｇｈ集方法更简单、更有效．

不相容决策表的属性约简算法

对Skowron可辨识矩阵方法进行分析,并应用反例说明基于Skowron可辨识矩阵的属性约简算法对不相容决策表的属性约简,可能会导致错误的结果。针对这一问题,提出了一种基于改进可辨识矩阵的属性频率约简算法。该算法以改进的可辨识矩阵为基础,以属性频率作为启发信息,同时在算法中加入消除冗余属性二次约简过程。提供了实例分析,验证了该算法能够有效地对相容与不相容的决策表进行属性约简。

基于差别矩阵的不一致决策表规则获取算法

针对传统基于差别矩阵的不一致决策表规则获取算法效率不理想的情况,提出了一种快速的基于差别矩阵的规则获取算法。算法首先引入简化决策表思想,删除决策表中可能存在的许多重复对象;然后基于简化决策表构造不同决策类之间的子差别矩阵,以有效地解决对象分布的非平衡性问题和缩小算法的求解空间;且采用启发式向后贪心搜索策略求解相对最小属性约简;并根据规则可信度获取有效的决策规则,可信度可动态设置,使算法具有较好的适应性。最后通过算例分析和实验比较验证了算法能获取有效的决策规则。

基于信息观点的约简算法比较

在相关文献的基础上,给出了三种不同条件熵的性质,进而研究了基于三种条件熵的不同搜索策略的约简的算法之间的关系,包括对一致和不一致决策表约简的执行时间、约简质量和分类性能的比较。理论分析和实验结果表明三种条件熵不同性质导致了三种条件熵的约简算法存在各自的优缺点。上述工作为用户根据实际需要选择合适的约简算法提供了有益的参考。