Approach to stochastic multi-attribute decision problems using rough sets theory

Multi-attribute decision problems where the performances of the alternatives are random variables are considered. The suggested approach grades the probabilities of preference of one alternative over another with respect to the same attribute. Based on the graded probabilistic dominance relation, the pairwise comparison information table is defined. The global preferences of the decision maker can be seen as a rough binary relation. The present paper proposes to approximate this preference relation by means of the graded probabilistic dominance relation with respect to the subsets of attributes. At last, the method is illustrated by an example.

Immune algorithm for discretization of decision systems in rough set theory

Rough set theory plays an important role in knowledge discovery, but cannot deal with continuous attributes, thus discretization is a problem which we cannot neglect. And discretization of decision systems in rough set theory has some particular characteristics. Consistency must be satisfied and cuts for discretization is expected to be as small as possible. Consistent and minimal discretization problem is NP-complete. In this paper, an immune algorithm for the problem is proposed. The correctness and effectiveness were shown in experiments. The discretization method presented in this paper can also be used as a data pre- treating step for other symbolic knowledge discovery or machine learning methods other than rough set theory.

Matrix-based method for solving decision domains of neighbourhood multigranulation decision-theoretic rough sets

It is more and more important to analyse and process complex data for gaining more valuable knowledge and making more accurate decisions.The multigranulation decision theory based on conditional probability and cost loss has the advantage of processing decision-making problems from multi-levels and multi-angles,and the neighbourhood rough set model(NRS)can facilitate the analysis and processing of numerical or mixed type data,and can address the limitation of multigranulation decision-theoretic rough sets(MG-DTRS),which is not easy to cope with complex data.Based on the in-depth study of hybrid-valued decision systems and MG-DTRS models,this study analysed neigh-bourhood MG-DTRS(NMG-DTRS)deeply by fusing MG-DTRS and NRS;a matrix-based approach for approximation sets of NMG-DTRS model was proposed on the basis of the matrix representations of concepts;the positive,boundary and negative domains were constructed from the matrix perspective,and the concept of positive decision recognition rate was introduced.Furthermore,the authors explored the related properties of NMG-DTRS model,and designed and described the corresponding solving algorithms in detail.Finally,some experimental results that were employed not only verified the effectiveness and feasibility of the proposed algorithm,but also showed the relationship between the decision recognition rate and the granularity and threshold.

Softζ-Rough Set and Its Applications in Decision Making of Coronavirus

In this paper,we present a proposed method for generating a soft rough approximation as a modification and generalization of Zhaowen et al.approach.Comparisons were obtained between our approach and the previous study and also.Eventually,an application on Coronavirus(COVID-19)has been presented,illustrated using our proposed concept,and some influencing results for symptoms of Coronavirus patients have been deduced.Moreover,following these concepts,we construct an algorithm and apply it to a decision-making problem to demonstrate the applicability of our proposed approach.Finally,a proposed approach that competes with others has been obtained,as well as realistic results for patients with Coronavirus.Moreover,we used MATLAB programming to obtain the results;these results are consistent with those of theWorld Health Organization and an accurate proposal competing with the method of Zhaowen et al.has been studied.Therefore,it is recommended that our proposed concept be used in future decision making.

The Approach to Probabilistic Decision-Theoretic Rough Set in Intuitionistic Fuzzy Information Systems

For the moment, the representative and hot research is decision-theoretic rough set (DTRS) which provides a new viewpoint to deal with decision-making problems under risk and uncertainty, and has been applied in many fields. Based on rough set theory, Yao proposed the three-way decision theory which is a prolongation of the classical two-way decision approach. This paper investigates the probabilistic DTRS in the framework of intuitionistic fuzzy information system (IFIS). Firstly, based on IFIS, this paper constructs fuzzy approximate spaces and intuitionistic fuzzy (IF) approximate spaces by defining fuzzy equivalence relation and IF equivalence relation, respectively. And the fuzzy probabilistic spaces and IF probabilistic spaces are based on fuzzy approximate spaces and IF approximate spaces, respectively. Thus, the fuzzy probabilistic approximate spaces and the IF probabilistic approximate spaces are constructed, respectively. Then, based on the three-way decision theory, this paper structures DTRS approach model on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. So, the fuzzy decision-theoretic rough set (FDTRS) model and the intuitionistic fuzzy decision-theoretic rough set (IFDTRS) model are constructed on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. Finally, based on the above DTRS model, some illustrative examples about the risk investment of projects are introduced to make decision analysis. Furthermore, the effectiveness of this method is verified.

A New Method for Constructing Decision Tree Based on Rough Sets Theory

Decision trees induction algorithms have been used for classification in a wide range of application domains. In the process of constructing a tree, the criteria of selecting test attributes will influence the classification accuracy of the tree.In this paper,the degree of dependency of decision attribute to condition attribute,based on rough set theory,is used as a heuristic for selecting the attribute that will best separate the samples into individual classes.The result of an example shows that compared with the entropy-based approach,our approach is a better way to select nodes for constructing decision trees.

Variable precision rough set for multiple decision attribute analysis

A variable precision rough set (VPRS) model is used to solve the multi-attribute decision analysis (MADA) problem with multiple conflicting decision attributes and multiple condition attributes. By introducing confidence measures and a β-reduct, the VPRS model can rationally solve the conflicting decision analysis problem with multiple decision attributes and multiple condition attributes. For illustration, a medical diagnosis example is utilized to show the feasibility of the VPRS model in solving the MADA problem with multiple decision attributes and multiple condition attributes. Empirical results show that the decision rule with the highest confidence measures will be used as the final decision rules in the MADA problem with multiple conflicting decision attributes and multiple condition attributes if there are some conflicts among decision rules resulting from multiple decision attributes. The confidence-measure-based VPRS model can effectively solve the conflicts of decision rules from multiple decision attributes and thus a class of MADA problem with multiple conflicting decision attributes and multiple condition attributes are solved.

Rough Set Processing Model for Fuzzy Decision Tables with Weights

The classical rough set can not show the fuzziness and the importance of objects in decision procedure because it uses definite form to express each object. In order to solve this problem,this paper firstly introduces a special decision table in which each object has a membership degree to show its fuzziness and has been assigned a weight to show its importance in decision procedure. Then,the special decision table is studied and the relevant rough set model is provided. In the meantime,relevant definitions and theorems are proposed. On the above basis,an attribute reduction algorithm is presented. Finally,feasibility of the relevant rough set model and the presented attribute reduction algorithm are verified by an example.

Knowledge Discovery for Event Series Decision Based on Rough Set

To make decisions about event series is part of our life, and to discover knowledge from these decisions is of great significance in the field of controlling and decision-making. The paper takes event series as the exterior form of movements with the dynamic attributes, and gets the Markov transition probabilities matrix to express those attributes with statistics. First, according to the matrix, the decision table is constructed. Then, by reducing attributes based on rough set theory, the decision table is reduced, and the decision rules are acquired as well. Finally we make the decision through defining rule distance and taking the minimum rule distance as decision principle. Followed is an example, which proves that the algorithm is feasible and effective to the event series decision.

Process Auxiliary Decision-making Based on Rough Sets and Regulation Distance Computing

Computer aided process planning（CAPP） is an important content of computer integrated manufacturing, and intelligentizing is the orientation of development of CAPP. Process planning has characters of empirical and time-consuming to finalize, and the same technical aim always can be achieved by different process schemes, so intelligentizing of process decision making always be a difficult point of CAPP and computer integrated manufacturing （CIM）. For the purpose of intelligent aided process decision making and reuse of process resource, this paper proposed a decision making method based on rough sets（RS） and regular distance computing. The main contents and methods of process planning decision making are analyzed under agile response manufacturing environment, the concept of process knowledge granule is represented, and the methods of process knowledge granule partitioning and granularity analysis are put forward. Based on the theory of RS and combined the method of process attributes importance identification, the paper brought forward a computing model for process scheme regulation distance under the same attribute conditions, and conflict resolution strategy was introduced to acquire process scheme fit for actual situation of enterprise＇s manufacturing resources, so as to realize process resources＇ conflict resolution and quick excavate and reuse of enterprises＇ existing process knowledge, to advance measures of process decision making and improve the rationality and capability of agile response of process planning.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Pessimistic Rough Decision

With granular computing point of view,this paper first presents a novel rough set model with a multigranulation view,called pessimistic rough decision,where set approximations are defined through using consistent granules among multiple granular spaces on the universe.Then,we investigate several important properties of the pessimistic rough decision model.With introduction of the rough set model,we have developed two types of multigranulation rough sets(MGRS):optimistic rough decision and pessimistic rough decision. These multigranulation rough set models provide a kind of effective approach for problem solving in the context of multi granulations.

Three-way group decision making with linguistic evaluations

Based on linguistic evaluations, a linguistic threeway decision method is proposed. First, the alternatives are rated in linguistic forms and divided into acceptance, rejection and uncertainty regions. Secondly, the linguistic three-way group decision steps are provided. Specifically, the experts determine the lower bound and upper bound of the uncertainty region, respectively. When the evaluation is superior to the upper bound, the corresponding alternative is put into the acceptance region directly. Similarly, when the evaluation is inferior to the lower bound, the corresponding alternative is put into the rejection region directly, and the remaining alternatives are put into the uncertain region. Moreover, the objects in the uncertainty region are especially discussed. The linguistic terms are transformed into fuzzy numbers and then aggregated. Finally, a recommendation example is provided to illustrate the practicality and validity of the proposed method.

Emergency Decision-Making Based on q-Rung Orthopair Fuzzy Rough Aggregation Information

With the frequent occurrences of emergency events,emergency decision making(EDM)plays an increasingly significant role in coping with such situations and has become an important and challenging research area in recent times.It is essential for decision makers to make reliable and reasonable emergency decisions within a short span of time,since inappropriate decisions may result in enormous economic losses and social disorder.To handle emergency effectively and quickly,this paper proposes a new EDM method based on the novel concept of q-rung orthopair fuzzy rough(q-ROPR)set.A novel list of q-ROFR aggregation information,detailed description of the fundamental characteristics of the developed aggregation operators and the q-ROFR entropy measure that determine the unknown weight information of decision makers as well as the criteria weights are specified.Further an algorithm is given to tackle the uncertain scenario in emergency to give reliable and reasonable emergency decisions.By using proposed list of q-ROFR aggregation information all emergency alternatives are ranked to get the optimal one.Besides this,the q-ROFR entropy measure method is used to determine criteria and experts’weights objectively in the EDM process.Finally,through an illustrative example of COVID-19 analysis is compared with existing EDM methods.The results verify the effectiveness and practicability of the proposed methodology.

一种基于Rough Set理论的属性约简及规则提取方法

该文针对RoughSet理论中属性约简和值约简这两个重要问题进行了研究，提出了一种借助于可辨识矩阵（discernibilitymatrix）和数学逻辑运算得到最佳属性约简的新方法．同时，借助该矩阵还可以方便地构造基于RoushSet理论的多变量决策树．另外，对目前广泛采用的一种值约简策略进行了改进，最终使得到的规则进一步简化．

基于Rough Set的综合评价方法研究

目前诸多的综合评价方法在权重设置和单因素评价矩阵确定等方面的局限性制约了人们对评价对象的科学认识。论文根据RoughSet理论,提出了基于RoughSet的综合评价方法,旨在消除权重设置的主观性,有效削减指标体系规模。文章最后通过实例,验证该方法的实用性、可行性。

基于Rough set理论的增量式规则获取算法

从 Rough set理论出发 ,讨论在新增数据时 ,新数据与已有规则集的关系、属性约简以及值约简的变化规律 .并在此基础上提出一个新的基于 Rough Set理论的增量式算法 .从理论上和实验上对新算法和传统算法在算法复杂度上做了分析与比较 .

基于Rough Sets的传感器异常数据处理

在各种传感器的应用中,经常要对传感器的测量数据进行处理,以保证测量结果的可靠性．为了利用粗糙集理论处理不确定数据的优点,根据粗糙集理论的思想,先由已知测量数据提取出决策表,再进行补全、离散化等预处理,最后进行属性约简并提取出分类规则,对测量数据进行分类,剔除测量数据中的异常数据．实验结果显示该异常数据发现方法比常用的异常数据处理方法更为客观、精确和可靠．

基于Roughset理论的改进三比值故障诊断方法

本文提出一种基于粗糙集理论的三比值电力变压器故障诊断法。文中首先从IEC三比值诊断表出发,应用粗糙集理论构造决策表,然后对决策表进行约简,最后获得变压器故障三比值诊断决策表。实验结果表明,这种改进的三比值诊断方法扩展了原始IEC三比值的编码范围,提高了实际故障诊断能力,它的正确诊断率比IEC三比值诊断法较高,在实际工程中具有应用价值。

基于不完备信息系统的Rough Set决策规则提取方法

对象信息的不完备性是从实例中归纳学习的最大障碍。针对不完备的信息,研究了基于不完备信息系统的粗糙集决策规则提取方法,利用分层递减约简算法,通过实例有效地分析和处理了含有缺省数据和不精确数据的信息系统,扩展了粗糙集的应用领域。