Measuring roughness of generalized rough sets induced by a covering

Xu, Weihua; Zhang, Wenxiu

doi:10.1016/j.fss.2007.03.018

Cited by 197 publications

(78 citation statements)

References 15 publications

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“…This set is characterized by a pair of precise concepts called the lower and upper approximations. The lower and upper approximation operators are related to the necessity (box) and possibility (diamond) operators of modal logic [5], and the interior and closure operators in topological space [9,12,16,17,19,38,39,44]. Zakowski [47] studied a set of axioms on approximation operators, and Comer [10] investigated axioms on approximation operators in relation to cylindric algebras within the context of Pawlak information systems [28].…”

Section: Introductionmentioning

confidence: 99%

“…Also, Cattaneo [8] used a special class of relations to obtain two kinds of approximations. Wei and Wen [39] defined a measure of roughness based on generalized rough sets with the new approximations and proved some properties of the measure. Pawlak and Skowron [22] presented approximation spaces based on the neighborhood of objects and on inclusion measures of the neighborhood into concepts and defined the inductive extensions of approximation spaces.…”

Section: Introductionmentioning

confidence: 99%

“…The classical rough set theory is based on equivalence relations, but it has been extended to relation based rough sets [34,41,42,43,56], covering based rough sets [18,49,51,52,53,54,55] and fuzzy rough sets [13,30,41,42]. In [5,38,39,40], an extensive research on the binary relation based rough sets was done. These authors started from the properties of binary relations, for example, reflexivity, symmetry, and transitivity, to investigate the essential properties of the lower and upper approximation operations generated by such relations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximation operators by using finite family of reflexive relations

Abu-Donia¹,

Salama²

2015

IJAMR

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximation operators by using finite family of reflexive relations

Abu-Donia¹,

Salama²

2015

IJAMR

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“…Much study on this area had been reported and many useful results were obtained until now [2][3][4][5][6][7]. However, most work was based on consistent information systems, and the main methodology has been developed under equivalence relations (indiscernibility relations).…”

Section: Introductionmentioning

confidence: 99%

Rough Computational Approach to UAR based on Dominance Matrix in IOIS

Zhang¹,

Xu²

2011

IIM

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Rough set theory is a new mathematical tool to deal with vagueness and uncertainty. The classical rough set theory based on equivalence relation has made a great progress, while the equivalence relation is too harsh to meet and is extended to dominance relation in real world. It is important to investigate rough computational methods for rough set theory, which is one of the bottleneck problems in the development of rough set theory. In this article, rough computational approach to upper approximation reduction (UAR) is discussed based on dominance matrix in inconsistent ordered information systems (IOIS). The algorithm of upper approximation reduction is obtained, from which we can provide approach to upper approximation reduction operated simply in inconsistent systems based on dominance relations. Finally, an example illustrates the validity of this method, and shows the method is excellent to a complicated information system.

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“…Bonikowski, 1998), the authors studied the reduct of covering of generalized rough sets; In (Z. Bonikowski, 1998;Z.Bonikowski, 2003), the authors mainly studied the structure of cover, authors proposed a representative approximation spaces, that is, discussed the point x of universe U (i.e.x ∈ U) by covering, they defined the description of x and the minimal description of x; In (Xu WeiHua, 2007), the authors considered some new concepts and main results in generalized rough sets induced by a covering; In (Qiu Weigen, 2006), the author discussed fined covering fuzzy generalized rough sets; In (Eric C.C.Tsang, 2008), the authors defined the induced cover and the intersection of a family of covers by using the induced cover in covering generalized rough sets.…”

mentioning

confidence: 99%

The Minimal Description of Formal Concept Analysis

Fu¹

2010

JMR

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In rough sets, there were some of results of minimal description formed by covering, this paper gives some remarks about them.Using the idea of minimal description in formal concept analysis, discusses the corresponding relation between the covering of objects set and the attributes set.Keywords: Rough set, Formal concept analysis, Minimal description, Covering, PartitionIn 1982, R.Wille (1999) proposed a new model to represent the formal concepts associated to a context (G, M, I), named formal concept analysis based on the formal context, which is a pair consisting of a set of objects (the extension) and a set of attributes (the intension) such that the intension consists of exactly those attributes that the objects in the extension have in common, and the extension contains exactly those objects that share all attributes in the intension. The extension and the intension of a concept uniquely determine each other. The main goal is to reveal the hierarchical structure of formal concepts and to investigate the dependencies among attributes. It provides a theoretical framework for the discovery and design of concept hierarchies from relational information systems. It serves as a basis for conceptual data analysis and knowledge processing. The family of all formal concepts is a complete lattices, which is an effective method for several real-world applications in data analysis, such as object-oriented databases, inheritance lattices, mining for association rules, generating frequent sets (F.M. Baltasar, 1998;J.S. Deogun, 2004;So Kuznetsov, 2002;R.Godin, 1995) etc, one of the important challenges in data handling is generating or navigating the concept lattice of binary relation.The theory of rough sets as a tool for processing uncertain and incomplete information, proposed by Z. Pawlak (1991) in 1982, in which the lower approximation and upper approximation of an arbitrary subset of universe U are the basic operators.The concepts of the lower and upper approximations in rough sets theory are fundamental to the examination of granularity in knowledge, and are an effective way of studying imprecision, vagueness, and uncertainty, and rough set has been successed using all kinds of artificial intelligence fields, such as: data mining , machine learning. There are many authors studying rough sets and formal concept analysis, the readers can see (Zhang wenxiu, 2006; A

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Measuring roughness of generalized rough sets induced by a covering

Cited by 197 publications

References 15 publications

Approximation operators by using finite family of reflexive relations

Approximation operators by using finite family of reflexive relations

Rough Computational Approach to UAR based on Dominance Matrix in IOIS

The Minimal Description of Formal Concept Analysis

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