Covering-based rough sets process data organized by a covering of the universe. A soft set is a parameterized family of subsets of the universe. Both theories can deal with the uncertainties of data. Soft sets have no...Covering-based rough sets process data organized by a covering of the universe. A soft set is a parameterized family of subsets of the universe. Both theories can deal with the uncertainties of data. Soft sets have not any restrictions on the approximate description of the object,and they might form a covering of the universe. From this viewpoint,we establish a connection between these two theories. Specifically,we propose a complementary parameter for this purpose. With this parameter,the soft covering approximation space is established and the two theories are bridged. Furthermore,we study some relations between the covering and the soft covering approximation space and obtain some significant results. Finally,we define a notion of combine parameter which can help us to simplify the set of parameters and reduce the storage requirement of a soft covering approximation space.展开更多
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 classificati...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.展开更多
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 neighborho...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.展开更多
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 furth...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.展开更多
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 u...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.展开更多
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 p...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.展开更多
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 significa...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.展开更多
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 gr...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 L<sub>2</sub>-ELM, LapTELM, CTSVM, and TBSVM classifiers. The results demonstrate that SAR can effectively improve the time consumption and accuracy issues in attribute reduction.展开更多
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 inves...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.展开更多
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 transfor...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.展开更多
基金supported by National Natural Science Foundation of China under Grant No. 60873077/F020107the Science Research Project of Zhangzhou Normal University under Grant No. SK09002
文摘Covering-based rough sets process data organized by a covering of the universe. A soft set is a parameterized family of subsets of the universe. Both theories can deal with the uncertainties of data. Soft sets have not any restrictions on the approximate description of the object,and they might form a covering of the universe. From this viewpoint,we establish a connection between these two theories. Specifically,we propose a complementary parameter for this purpose. With this parameter,the soft covering approximation space is established and the two theories are bridged. Furthermore,we study some relations between the covering and the soft covering approximation space and obtain some significant results. Finally,we define a notion of combine parameter which can help us to simplify the set of parameters and reduce the storage requirement of a soft covering approximation space.
文摘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.
文摘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.
文摘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.
基金Anhui Provincial University Research Project(Project Number:2023AH051659)Tongling University Talent Research Initiation Fund Project(Project Number:2022tlxyrc31)+1 种基金Tongling University School-Level Scientific Research Project(Project Number:2021tlxytwh05)Tongling University Horizontal Project(Project Number:2023tlxyxdz237)。
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China (Nos.62006099,62076111)the Key Laboratory of Oceanographic Big Data Mining&Application of Zhejiang Province (No.OBDMA202104).
文摘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.
文摘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 L<sub>2</sub>-ELM, LapTELM, CTSVM, and TBSVM classifiers. The results demonstrate that SAR can effectively improve the time consumption and accuracy issues in attribute reduction.
基金funded by King Khalid University through a large group research project under Grant Number R.G.P.2/449/44.
文摘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.
文摘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.
