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.

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.

On Multi-Granulation Rough Sets with Its Applications

Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.

Multi-Granularity Neighborhood Fuzzy Rough Set Model on Two Universes

The two universes multi-granularity fuzzy rough set model is an effective tool for handling uncertainty problems between two domains with the help of binary fuzzy relations. This article applies the idea of neighborhood rough sets to two universes multi-granularity fuzzy rough sets, and discusses the two-universes multi-granularity neighborhood fuzzy rough set model. Firstly, the upper and lower approximation operators are defined in the two universes multi-granularity neighborhood fuzzy rough set model. Secondly, the properties of the upper and lower approximation operators are discussed. Finally, the properties of the two universes multi-granularity neighborhood fuzzy rough set model are verified through case studies.

Pseudo-Semi-Overlap Functions-Based Fuzzy Rough Sets Applied to Image Edge Extraction

As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value.

Attribute Reduction of Neighborhood Rough Set Based on Discernment

For neighborhood rough set attribute reduction algorithms based on dependency degree,a neighborhood computation method incorporating attribute weight values and a neighborhood rough set attribute reduction algorithm using discernment as the heuristic information was proposed.The reduction algorithm comprehensively considers the dependency degree and neighborhood granulation degree of attributes,allowing for a more accurate measurement of the importance degrees of attributes.Example analyses and experimental results demonstrate the feasibility and effectiveness of the algorithm.

Mathematical Morphology View of Topological Rough Sets and Its Applications

This article focuses on the relationship between mathematical morphology operations and rough sets,mainly based on the context of image retrieval and the basic image correspondence problem.Mathematical morphological procedures and set approximations in rough set theory have some clear parallels.Numerous initiatives have been made to connect rough sets with mathematical morphology.Numerous significant publications have been written in this field.Others attempt to show a direct connection between mathematical morphology and rough sets through relations,a pair of dual operations,and neighborhood systems.Rough sets are used to suggest a strategy to approximatemathematicalmorphology within the general paradigm of soft computing.A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology.This paper examines rough set theory from the viewpoint of mathematical morphology to derive rough forms of themorphological structures of dilation,erosion,opening,and closing.These newly defined structures are applied to develop algorithm for the differential analysis of chest X-ray images from a COVID-19 patient with acute pneumonia and a health subject.The algorithm and rough morphological operations show promise for the delineation of lung occlusion in COVID-19 patients from chest X-rays.The foundations of mathematical morphology are covered in this article.After that,rough set theory ideas are taken into account,and their connections are examined.Finally,a suggested image retrieval application of the concepts from these two fields is provided.

Two-Layer Information Granulation:Mapping-Equivalence Neighborhood Rough Set and Its Attribute Reduction

Attribute reduction,as one of the essential applications of the rough set,has attracted extensive attention from scholars.Information granulation is a key step of attribute reduction,and its efficiency has a significant impact on the overall efficiency of attribute reduction.The information granulation of the existing neighborhood rough set models is usually a single layer,and the construction of each information granule needs to search all the samples in the universe,which is inefficient.To fill such gap,a new neighborhood rough set model is proposed,which aims to improve the efficiency of attribute reduction by means of two-layer information granulation.The first layer of information granulation constructs a mapping-equivalence relation that divides the universe into multiple mutually independent mapping-equivalence classes.The second layer of information granulation views each mapping-equivalence class as a sub-universe and then performs neighborhood informa-tion granulation.A model named mapping-equivalence neighborhood rough set model is derived from the strategy of two-layer information granulation.Experimental results show that compared with other neighborhood rough set models,this model can effectively improve the efficiency of attribute reduction and reduce the uncertainty of the system.The strategy provides a new thinking for the exploration of neighborhood rough set models and the study of attribute reduction acceleration problems.

A Neighborhood Rough Set Attribute Reduction Method Based on Attribute Importance

Attribute reduction is a hot topic in rough set research. As an extension of rough sets, neighborhood rough sets can effectively solve the problem of information loss after data discretization. However, traditional greedy-based neighborhood rough set attribute reduction algorithms have a high computational complexity and long processing time. In this paper, a novel attribute reduction algorithm based on attribute importance is proposed. By using conditional information, the attribute reduction problem in neighborhood rough sets is discussed, and the importance of attributes is measured by conditional information gain. The algorithm iteratively removes the attribute with the lowest importance, thus achieving the goal of attribute reduction. Six groups of UCI datasets are selected, and the proposed algorithm SAR is compared with L2-ELM, LapTELM, CTSVM, and TBSVM classifiers. The results demonstrate that SAR can effectively improve the time consumption and accuracy issues in attribute reduction.

Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

Approximation Maintenance When Adding a Conditional Value in Set-Valued Ordered Decision Systems

The integration of set-valued ordered rough set models and incremental learning signify a progressive advancement of conventional rough set theory, with the objective of tackling the heterogeneity and ongoing transformations in information systems. In set-valued ordered decision systems, when changes occur in the attribute value domain, such as adding conditional values, it may result in changes in the preference relation between objects, indirectly leading to changes in approximations. In this paper, we effectively addressed the issue of updating approximations that arose from adding conditional values in set-valued ordered decision systems. Firstly, we classified the research objects into two categories: objects with changes in conditional values and objects without changes, and then conducted theoretical studies on updating approximations for these two categories, presenting approximation update theories for adding conditional values. Subsequently, we presented incremental algorithms corresponding to approximation update theories. We demonstrated the feasibility of the proposed incremental update method with numerical examples and showed that our incremental algorithm outperformed the static algorithm. Ultimately, by comparing experimental results on different datasets, it is evident that the incremental algorithm efficiently reduced processing time. In conclusion, this study offered a promising strategy to address the challenges of set-valued ordered decision systems in dynamic environments.

基于Rough Set的规则自动抽取设计方案

知识获取是专家系统的重要研究领域,而理论以理论的独特之处成为这一领域的有效工具。文章针对一具体专家系统Rough Set--专家系统在知识获取方面能力的不足,简要介绍其知识表示和知识获取的方法后,提出了一种基于理论的规则自动抽取OTCA-ES--Rough Set的设计方案。

基于Rough Set理论的铁路货运量预测

利用RoughSet理论通过对数据进行分析和推理发现隐含知识的优点,在结合该理论与铁路货运量预测要求的基础上,提出一个基于RoughSet理论的铁路货运量预测流程;合理选择统计指标并将相关原始数据代入预测流程涉及的各步骤后,得出预测我国铁路货运量发展水平的规则集;利用该规则集预测了"十五"期间我国铁路货运量的发展水平;该规则集有望在我国"十一五"规划的制定中发挥一定的参考作用。

基于Rough Set的电子邮件分类系统

随着电子邮件的广泛使用,通过它进行不良信息传播的事件不断发生.电子邮件分类问题成为了网络安全研究的热点。本文通过对电子邮件头进行分析,运用Rough Set理论中相关的数据分析技术,建立了电子邮件分类系统的模型,并进行了实验测试,得到了满意的结果。

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 Set理论的摩擦学诊断知识获取系统

摩擦学系统诊断知识的获取本质上是一个模式分类和识别的问题。本文结合摩擦学系统和RoughSet理论的特点 ,提出了一种基于RoughSet理论的摩擦学诊断知识获取方法。这种方法能够用于模糊和不确定知识的获取和处理。并给出了具体的示例 。

基于Roughset知识获取的故障数据表聚类离散化方法研究

为了从故障诊断实例的数据资源中知识获取,对具有连续属性值的故障实例数据表转化为Rough set(RS)理论离散数据类型的决策表的正确映射进行了研究。将改进的k-means聚类算法用于故障实例数据表的离散映射方案设计。在设置故障实例的导师决策类别数为聚类数k对论域划分的基础上,提出了根据均值聚类中心排序序号构造离散映射符号集、相对均值聚类中心由相似测度确定连续属性值映射编码的离散化方案。实例表明,该方法反映了转子振动故障特征的一般规律,断点设置具有动态自适应和抗干扰特性。获得的决策规则可用于构造和扩充故障诊断知识库。

基于Rough Set理论的“数据浓缩”

本文讨论了基于RoushSet（RS）理论数据浓缩的几个问题．首先，介绍了一个基于差别矩阵的属性约简策略，并给出了数据浓缩的测量；然后分析了对UCI机器学习数据库40余个例子的数据浓缩的结果；最后，我们强调了在数据浓缩中例外的重要性，并讨论了不一致数据浓缩．

基于Rough Set的油液故障诊断系统的知识发现

结合RoughSet理论和摩擦学系统的特点,讨论了油液故障诊断系统的不协调性.在包含度方法的基础上,将普通二元关系进行推广,提出了一种不协调油液故障诊断系统知识发现模型,给出具体的运算方法,并通过试验实例验证了该模型的有效性.结果表明,该模型在最大分布约简的基础上进行油液诊断知识获取,能够很好地完成不确定性问题的推理,并且可以推导出具有最大可信度的油液诊断知识规则.

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。