Rough sets: Some extensions

Pawlak, Zdzisław; Skowron, Andrzej

doi:10.1016/j.ins.2006.06.006

Cited by 1,081 publications

(441 citation statements)

References 56 publications

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“…Rough set [1,2], proposed by Pawlak, is a powerful tool, which can be used to deal with the inconsistency problems by separation of certain and doubtful knowledge extracted from the exemplary decisions. Though Pawlak's rough set theory has been demonstrated to be useful in the fields such as knowledge discover [3,4], decision analysis [5,6], data mining [7,8], pattern recognition [9], artificial intelligence [10], medical diagnosis [11] and so on.…”

Section: Introductionmentioning

confidence: 99%

Incomplete Variable Multigranulation Rough Sets Decision

Zhang¹,

Wang²,

Yang³

et al. 2014

Appl. Math. Inf. Sci.

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Abstract:Recently, a multigranulation rough set (MGRS) has become a new direction in rough set theory, which is different from the Pawlake's rough set since the former takes multiple granulations on the universe into account. In this paper, by analyzing the limitations of optimistic multigranulation rough set (OMGRS) and pessimistic multigranulation rough set (PMGRS) in incomplete information system, the incomplete variable multigranulation rough set (VMGRS) is proposed, and the relationships among VMGRS, OMGRS and PMGRS are deeply explored, From the properties, it can be found that OMGRS and PMGRS are the special cases compared to our VMGRS. Furthermore, several important measurements are introduced into the VMGRS; it is shown that the measurements of the VMGRS are between the measurements of OMGRS and PMGRS. Finally, some numerical examples are employed to substantiate the conceptual arguments.

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Section: Introductionmentioning

confidence: 99%

Incomplete Variable Multigranulation Rough Sets Decision

Zhang¹,

Wang²,

Yang³

et al. 2014

Appl. Math. Inf. Sci.

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“…The equivalence classes are called ε-elementary sets. They can be viewed as sets of indiscernible objects characterized by the same available information about them [21,24]. Definable sets are any unions of ε-elementary sets.…”

Section: Introductionmentioning

confidence: 99%

An Adequate Representation of Medical Data Based on Partial Set Approximation

Csajbók

Mihálydeák

Ködmön

2013

Computer Information Systems and Industrial Management

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Abstract. Computer aided medical diagnosis and treatment require an adequate representation of uncertain or imperfect medical data. There are many approaches dealing with such type of data. Pawlak proposed a new method called rough set theory. In this paper, beyond classical and recent methods, the authors propose a basically new approach. It relies on a generalization of rough set theory, namely, the partial covering of the universe of objects. It adequately reflects the partial nature of real-life problems. This new approach called the partial approximation of sets is presented as well as its medical informatics application is demonstrated.

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“…Rough set theory 1,2,3,4 , proposed by Pawlak, has been demonstrated to be useful in pattern recognition, knowledge discovery 5,6 , decision support 7,8 , data mining, feature selection, medical diagnosis and so on. Pawlak's rough set, is constructed on the basis of an indiscernibility relation, which is an equivalence relation and then such model can be used to unravel decision rules from the information system with decision attributes, such system can also be referred to as decision system in many rough set literatures.…”

Section: Introductionmentioning

confidence: 99%

Local and Global Measurements of MGRS Rules

Yang¹,

Zhang²,

Yang³

2012

IJCIS

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Since the multigranulation rough sets (MGRS) can be considered as the compositions of multiindependent Pawlak's rough sets, the multigranulation rough set rules (MGRS rules) are then the compositions of decision rules, which are supported by multi-independent Pawlak's rough sets. To measure MGRS rules, both the local and global views are employed in this paper. In local view, the support, certainty and coverage factors are proposed to measure MGRS rules, which are support by an object; while in global view, these three factors are proposed to measure MGRS rules, which are coexisting in a decision system. The necessary conditions for these factors to achieve maximal and minimal values are also addressed. Some numerical examples are employed to substantiate the conceptual arguments.

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Rough sets: Some extensions

Abstract: In this article, we present some extensions of the rough set approach and we outline a challenge for the rough set based research.

Cited by 1,081 publications

References 56 publications

Incomplete Variable Multigranulation Rough Sets Decision

Incomplete Variable Multigranulation Rough Sets Decision

An Adequate Representation of Medical Data Based on Partial Set Approximation

Local and Global Measurements of MGRS Rules

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