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.

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.

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.

Definability and Textural Rough Set Algebras

In this paper,a counterpart of definability is studied in texture spaces.The concept of textural complete field is defined and the relations with textural definable sets are investigated.If a texture is discrete,then textural definability coincides with definability.Using this fact,we obtain some basic results for definability in rough set algebras.Further,we discuss on definability for fuzzy rough sets considering textural fuzzy direlations.

Function S-Rough sets and its applications

Based on S-rough sets（singular rough sets）, this paper presents function S-rough sets （function singular rough sets）and its mathematical structures and features. Function S-rough sets has two forms： function one direction S-rough sets （function one direction singular rough sets） and function two direction S-rough sets （function two direction singular rough sets）. This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special ease of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.

Function S-rough sets and mining-discovery of rough law in systems

Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.

Intuitionistic Fuzzy Rough Sets Based on Two Intuitionistic Fuzzy Implicators

This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.

On uniqueness of (fuzzy) relation in some generalized rough set model

In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.

Cost Sensitive Multi-Granulation Preference Relation Rough Set for Ordinal Decision System

The preference analysis is a class of important issues in multi-criteria ordinal decision making.The rough set is an effective approach to handle preference analysis.In order to solve the multi-criteria preference analysis problems,this paper improves the preference relation rough set model and expands it to multi-granulation cases.Cost is also an important issue in the field of decision analysis.Taking the cost into consideration,we also expand the model to the cost sensitive multi-granulation preference relation rough set.Some theorems are represented,and the granule structure selection based on approximation quality is investigated.The experimental results show that the multi-granulation preference rough set approach with the consideration of cost has a better performance in granule structure selection than that without cost consideration.

Representation Theorem of Fuzzy Rough Set

This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.

Dominance-based rough set approach as a paradigm of knowledge discovery and granular computing

Dominance-based rough set approach(DRSA) permits representation and analysis of all phenomena involving monotonicity relationship between some measures or perceptions.DRSA has also some merits within granular computing,as it extends the paradigm of granular computing to ordered data,specifies a syntax and modality of information granules which are appropriate for dealing with ordered data,and enables computing with words and reasoning about ordered data.Granular computing with ordered data is a very general paradigm,because other modalities of information constraints,such as veristic,possibilistic and probabilistic modalities,have also to deal with ordered value sets(with qualifiers relative to grades of truth,possibility and probability),which gives DRSA a large area of applications.

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.

Intrusion detection based on rough set and artificial immune

In order to increase intrusion detection rate and decrease false positive detection rate,a novel intrusion detection algorithm based on rough set and artificial immune( RSAI-IDA) is proposed.Using artificial immune in intrusion detection,anomaly actions are detected adaptively,and with rough set,effective antibodies can be obtained. A scheme,in which antibodies are partly generated randomly and others are from the artificial immune algorithm,is applied to ensure the antibodies diversity. Finally,simulations of RSAI-IDA and comparisons with other algorithms are given. The experimental results illustrate that the novel algorithm achieves more effective performances on anomaly intrusion detection,where the algorithm's time complexity decreases,the true positive detection rate increases,and the false positive detection rate is decreased.

Properties and Relations of Several Operators Based on Covering Rough Sets

The coveting rough sets theory is a generalization of traditional rough set theory, and can also describe information with incompleteness and fuzziness in information systems. In this paper, we first provide the definitions of several upper and lower covering approximation operators on the covering approximation space. Then, we study the properties of these operators. Finally, we propose the mutual relations between approximation operators and similar relations of the operator （ I ） based on the covering rough sets.

A Survey of Software Packages Used for Rough Set Analysis

Soft computing is a combination of methods that complement each other when dealing with ambiguous real life decision systems. Rough Set Theory (RST) is a technique used in soft computing that enhances the idea of classical sets to deal with incomplete knowledge and provides a mechanism for concept approximation. It uses reducts to isolate key attributes affecting outcomes in decision systems. The paper summarizes two algorithms for reduct calculation. Moreover, to automate the application of RST, different software packages are available. The paper provides a survey of packages that are most frequently used to perform data analysis based on Rough Sets. For benefit of researchers, a comparison of based on functionalities of those software is also provided.

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．

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．