A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets

Meng, Zhaozong; Shi, Zhongzhi

doi:10.1016/j.ins.2009.04.002

Cited by 143 publications

(73 citation statements)

References 30 publications

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“…This technique has led to many practical applications in various areas such as, but not limited to, medicine learning, knowledge discovery, economics, finance, engineering and even arts and culture [18,22,23,27,30,31,32,33,40,41,44]. Combined with other complementary concepts such as fuzzy sets, statistics, and logical data analysis, rough sets have been exploited in hybrid approaches to improve the performance of data analysis tools.…”

Section: Introductionmentioning

confidence: 99%

Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms

Mirvakili

Anvariyeh

Davvaz

2017

Foundations of Computing and Decision Sciences

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Abstract. The initiation and majority on rough sets for algebraic hyperstructures such as hypermodules over a hyperring have been concentrated on a congruence relation. The congruence relation, however, seems to restrict the application of the generalized rough set model for algebraic sets. In this paper, in order to solve this problem, we consider the concept of set-valued homomorphism for hypermodules and we give some examples of set-valued homomorphism. In this respect, we show that every homomorphism of the hypermodules is a set-valued homomorphism. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximations of a hypermodule, are provided. We also propose the notion of generalized lower and upper approximations with respect to a subhypermodule of a hypermodule discuss some significant properties of them.

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Section: Introductionmentioning

confidence: 99%

Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms

Mirvakili

Anvariyeh

Davvaz

2017

Foundations of Computing and Decision Sciences

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“…There are two main methods to generalize it. One method is to extend an equivalence relation to other binary relations, such as a similarity relation, a tolerance relation, and dominance relation [2][3][4][5]12,[21][22][23]26,27,[31][32][33][34][35][37][38][39][40]42,43,51,[54][55][56]. The other is to replace a partition of the universe with a covering and obtained the covering rough sets [1,19,52,[57][58][59].…”

Section: Introductionmentioning

confidence: 99%

NMGRS: Neighborhood-based multigranulation rough sets

Lin

Qian

2012

International Journal of Approximate Reasoning

205

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“…However, diverse problems in covering-based rough sets are NP-hard and therefore those algorithms to solve them are almost greedy ones [8,20], especially heuristic ones [22]. In order to establish applicable mathematical structures for these problems, covering-based rough sets are combined with some other theories and methods, such as fuzzy sets [7,27], topology [25,40] and lattice theory [6].…”

Section: Introductionmentioning

confidence: 99%

Four matroidal structures of covering and their relationships with rough sets

Wang

Zhu

et al. 2013

International Journal of Approximate Reasoning

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Covering is a common form of data representation, and covering-based rough sets serve as an efficient technique to process this type of data. However, many important problems such as covering reduction in covering-based rough sets are NP-hard so that most algorithms to solve them are greedy. Matroids provide well-established platforms for greedy algorithm foundation and implementation. Therefore, it is necessary to integrate covering-based rough set with matroid. In this paper, we propose four matroidal structures of coverings and establish their relationships with rough sets. First, four different viewpoints are presented to construct these four matroidal structures of coverings, including 1-rank matroids, bigraphs, upper approximation numbers and transversals. The respective advantages of these four matroidal structures to rough sets are explored. Second, the connections among these four matroidal structures are studied. It is interesting to find that they coincide with each other. Third, a converse view is provided to induce a covering by a matroid. We study the relationship between this induction and the one from a covering to a matroid. Finally, some important concepts of covering-based rough sets, such as approximation operators, are equivalently formulated by these matroidal structures. These interesting results demonstrate the potential to combine covering-based rough sets with matroids.

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A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets

Cited by 143 publications

References 30 publications

Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms

Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms

NMGRS: Neighborhood-based multigranulation rough sets

Four matroidal structures of covering and their relationships with rough sets

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