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.

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.

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.

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.

IMPROVED ACCURACY AND ROUGHNESS MEASURES FOR ROUGH SETS

Accuracy and roughness, proposed by Pawlak(1982), might draw a conclusion inconsistent with our intuition in some cases. This letter analyzes the limitations in these measures and proposes improved accuracy and roughness measures based on information theory.

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.

NEW METHOD FOR MEASURING FUZZINESS IN ROUGH SETS

A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.

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.

Variable Precision Rough Set and a Fuzzy Measure of Knowledge Based on Variable Precision Rough Set

Variable precision rough set (VPRS) is an extension of rough set theory (RST). By setting threshold value β , VPRS looses the strict definition of approximate boundary in RST. Confident threshold value for β is discussed and the method for deriving decision making rules from an information system is given by an example. An approach to fuzzy measures of knowledge is proposed by applying VPRS to fuzzy sets. Some properties of this measure are studied and a pair of lower and upper approximation operato...

Two kinds of average approximation accuracy

Rough set theory places great importance on approximation accuracy,which is used to gauge how well a rough set model describes a target concept.However,traditional approximation accuracy has limitations since it varies with changes in the target concept and cannot evaluate the overall descriptive ability of a rough set model.To overcome this,two types of average approximation accuracy that objectively assess a rough set model’s ability to approximate all information granules is proposed.The first is the relative average approximation accuracy,which is based on all sets in the universe and has several basic properties.The second is the absolute average approximation accuracy,which is based on undefinable sets and has yielded significant conclusions.We also explore the relationship between these two types of average approximation accuracy.Finally,the average approximation accuracy has practical applications in addressing missing attribute values in incomplete information tables.

Document classification approach by rough-set-based corner classification neural network

A rough set based corner classification neural network, the Rough-CC4, is presented to solve document classification problems such as document representation of different document sizes, document feature selection and document feature encoding. In the Rough-CC4, the documents are described by the equivalent classes of the approximate words. By this method, the dimensions representing the documents can be reduced, which can solve the precision problems caused by the different document sizes and also blur the differences caused by the approximate words. In the Rough-CC4, a binary encoding method is introduced, through which the importance of documents relative to each equivalent class is encoded. By this encoding method, the precision of the Rough-CC4 is improved greatly and the space complexity of the Rough-CC4 is reduced. The Rough-CC4 can be used in automatic classification of documents.

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.

Multi-granularity feature enhancement network for maritime ship detection

Due to the characteristics of high resolution and rich texture information,visible light images are widely used for maritime ship detection.However,these images are suscep-tible to sea fog and ships of different sizes,which can result in missed detections and false alarms,ultimately resulting in lower detection accuracy.To address these issues,a novel multi-granularity feature enhancement network,MFENet,which includes a three-way dehazing module(3WDM)and a multi-granularity feature enhancement module(MFEM)is proposed.The 3WDM eliminates sea fog interference by using an image clarity automatic classification algorithm based on three-way decisions and FFA-Net to obtain clear image samples.Additionally,the MFEM improves the accuracy of detecting ships of different sizes by utilising an improved super-resolution reconstruction con-volutional neural network to enhance the resolution and semantic representation capa-bility of the feature maps from YOLOv7.Experimental results demonstrate that MFENet surpasses the other 15 competing models in terms of the mean Average Pre-cision metric on two benchmark datasets,achieving 96.28%on the McShips dataset and 97.71%on the SeaShips dataset.

Attribute Reduction on Decision Tables Based on Hausdorff Topology

Attribute reduction through the combined approach of Rough Sets(RS)and algebraic topology is an open research topic with significant potential for applications.Several research works have introduced a strong relationship between RS and topology spaces for the attribute reduction problem.However,the mentioned recent methods followed a strategy to construct a new measure for attribute selection.Meanwhile,the strategy for searching for the reduct is still to select each attribute and gradually add it to the reduct.Consequently,those methods tended to be inefficient for high-dimensional datasets.To overcome these challenges,we use the separability property of Hausdorff topology to quickly identify distinguishable attributes,this approach significantly reduces the time for the attribute filtering stage of the algorithm.In addition,we propose the concept of Hausdorff topological homomorphism to construct candidate reducts,this method significantly reduces the number of candidate reducts for the wrapper stage of the algorithm.These are the two main stages that have the most effect on reducing computing time for the attribute reduction of the proposed algorithm,which we call the Cluster Filter Wrapper algorithm based on Hausdorff Topology.Experimental validation on the UCI Machine Learning Repository Data shows that the proposed method achieves efficiency in both the execution time and the size of the reduct.

Fault Diagnosis of Vehicle Transmission System Based on Rough Set Theory

Rough set theory is used to treat the data of vehicle transmission system faults. The minimum fault feature vector can be obtained by calculating the importance and dependency of each attribute. Real time diagnosis, as a result, can be actualized. Ultimate decision making can be done by analyzing the consistency of decision information. The result shows that rough set theory is useful and possesses its unique merits in this field.

On-Line Monitoring of Grinding Status Based on Rough Set Theory

This paper focuses on the new approach of on line monitoring of grinding burn and wheel wear based on the rough set theory. This method adopts the grinding chip flow thermal signal, and acquires identification rules by establishing sensitive characteristic parameters and constructing the knowledge system through continuum attribute discretization, attribute reduction and knowledge acquisition, and then monitors grinding burn and wheel wear in accordance with the acquired rules. The experiment results show that the new method is effective.

A Multi-Tuple Rough Set Approach for Information Retrieval

How to deal with the imprecise information retrieval has become more and more important in the present information society. An efficient and effective method of information retrieval based on multi tuple rough set is discussed in this paper. The new approach is considered as a generalization of the original rough set model for flexible information retrieval. The imprecise query results can be obtained by multi tuple approximations.