Topological characterizations of covering for special covering-based upper approximation operators

Ge, Xun; Bai, Xin; Yun, Ziqiu

doi:10.1016/j.ins.2012.04.005

Cited by 34 publications

(14 citation statements)

References 65 publications

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“…The covering generated by a reflexive and symmetric relation is characterized. It establishes the equivalence of the unary covering and the covering with the property that the intersection of any two elements is the union of finite elements in this covering [18][19][20][21][22][23][24][25][26][27][28].…”

Section: Covering Rough Setsmentioning

confidence: 99%

“…upper approximation) as the union of covering components intersecting the set. It is multi-mapping items for inadequate information about the genuine characteristic [18][19][20][21][22][23][24][25][26][27][28]. Hybrid rough set systems have been used in different applications for feature selections [29][30][31][32][33][34], classifications [35][36][37][38][46][47][48] and image segmentation [39].…”

Section: Introductionmentioning

confidence: 99%

“…The proposed classification method at first perceives approximation spaces of the classes by setting up an arrangement of named data exploring the traits of the recognized upper and lower approximation space for every one of the classes. Right when that happens, the fitting principle is to isolate the most legitimate class executed to perceive the most appropriate class [17][18][19][20][21][22][23][24][25][26][27][28]. Covering rough set methodology is proposed for the productive classification of medical information.…”

Section: Introductionmentioning

confidence: 99%

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RETRACTED ARTICLE: Covering-based rough set classification system

Kumar

Inbarani

Azar

et al. 2016

Neural Comput & Applic

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Medical data classification is applied in intelligent medical decision support system to classify diseases into different categories. Several classification methods are commonly used in various healthcare settings. These techniques are fit for enhancing the nature of prediction, initial identification of sicknesses and disease classification. The categorization complexities in healthcare area are focused around the consequence of healthcare data investigation or depiction of medicine by the healthcare professions. This study concentrates on applying uncertainty (i.e. rough set)-based pattern classification techniques for UCI healthcare data for the diagnosis of diseases from different patients. In this study, covering-based rough set classification (i.e. proposed pattern classification approach) is applied for UCI healthcare data. Proposed CRS gives effective results than delicate pattern classifier model. The results of applying the CRS classification method to UCI healthcare data analysis are based upon a variety of disease diagnoses. The execution of the proposed covering-based rough set classification is contrasted with other approaches, such as rough set (RS)-based classification methods, Kth nearest neighbour, improved bijective soft set, support vector machine, modified soft rough set and back propagation neural network methodologies using different evaluating measures.

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Section: Covering Rough Setsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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RETRACTED ARTICLE: Covering-based rough set classification system

Kumar

Inbarani

Azar

et al. 2016

Neural Comput & Applic

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“…Chen and Li defined open sets, closed sets, rough inclusion, rough equality on covering rough sets and studied some of their properties [7][8][9]. Ge, Bai, Yun, Bian and Wang gave topological characterizations of the covering C for covering upper approximation operators to be closure operators [2,12]. Restrepo and Gómez investigated properties of covering approximation operators being closure and topological closure in a framework of sixteen pairs of dual approximation operators [28].…”

Section: Introductionmentioning

confidence: 99%

Topological structures of a type of granule based covering rough sets

Zhang¹,

Li²

2018

Filomat

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Rough set theory is one of important models of granular computing. Lower and upper approximation operators are two important basic concepts in rough set theory. The classical Pawlak approximation operators are based on partition and have been extended to covering approximation operators. Covering is one of the fundamental concepts in the topological theory, then topological methods are useful for studying the properties of covering approximation operators. This paper presents topological properties of a type of granular based covering approximation operators, which contains seven pairs of approximation operators. Then, topologies are induced naturally by the seven pairs of covering approximation operators, and the topologies are just the families of all definable subsets about the covering approximation operators. Binary relations are defined from the covering to present topological properties of the topological spaces, which are proved to be equivalence relations. Moreover, connectedness, countability, separation property and Lindelöf property of the topological spaces are discussed. The results are not only beneficial to obtain more properties of the pairs of covering approximation operators, but also have theoretical and actual significance to general topology.

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“…Naturally, it is a significative work to investigate Question 1.3 by using rough-set theory. In the past years, with development of information sciences and computer science, applications of rough-set theory have been extended from Pawlak approximation spaces to covering approximation spaces (see [1,[9][10][11]20,33,36,46,[50][51][52][53][54][55][56], for example).…”

Section: Introductionmentioning

confidence: 99%

Connectivity of covering approximation spaces and its applications on epidemiological issue

2014

Applied Soft Computing

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Topological characterizations of covering for special covering-based upper approximation operators

Cited by 34 publications

References 65 publications

RETRACTED ARTICLE: Covering-based rough set classification system

RETRACTED ARTICLE: Covering-based rough set classification system

Topological structures of a type of granule based covering rough sets

Connectivity of covering approximation spaces and its applications on epidemiological issue

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