Multigranulation rough sets: From partition to covering

Lin, Guoping; Liang, Jiye; Qian, Yuhua

doi:10.1016/j.ins.2013.03.046

Cited by 155 publications

(33 citation statements)

References 47 publications

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“…Recently, the multigranulation approach attracts more and more researchers [16][17][18][19]27,28,52] . Furthermore, multi-scale information systems can be explained as an application of Model RI in a multigranulation space in [52] , whereas it has some differences from a multigranulation rough set, which is a Model A in [52] .…”

Section: Introductionmentioning

confidence: 99%

A new approach of optimal scale selection to multi-scale decision tables

2017

Information Sciences

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Section: Introductionmentioning

confidence: 99%

A new approach of optimal scale selection to multi-scale decision tables

2017

Information Sciences

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“…The optimistic multigranulation rough set model and the pessimistic multigranulation rough set model are presented [4,5]. Recently, more attentions have been paid to multigranulation rough sets [6,7,8,9,10]. …”

Section: Pessimistic Multigranulation Rough Setsmentioning

confidence: 99%

On the connections between multigranulation rough sets and generalized rough sets

Jiao¹,

Wan²,

Qin³

2017

Proceedings of the 2016 2nd International Conference on Materials Engineering and Information Technology Applications (MEITA 20

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Abstract. This note makes a comparative study of multigranulation rough set model and generalized rough set model. It is pointed out that the pessimistic multigranulation rough set model (PMGRS) is a kind of generalized rough set model, it is induced by a reflexive and symmetric relation on the universe. On the contrary, the optimistic multigranulation rough set model (OMGRS) is not a generalized rough set model. In other words, OMGRS can not be induced by a binary relation in general. Furthermore, some mistakes in the existing papers are pointed out. Pessimistic multigranulation rough setsRough set theory, proposed by Pawlak [1], is a well-established mechanism for dealing with vagueness and uncertainty in data analysis. Rough set model is constructed on the basis of an approximation space ( , ) U R , where U is a non-empty set of objects (also called the universe of discourse) and R is an equivalence relation imposed upon U . An arbitrary subset of the universe (or target concept) is approximated by a pair of lower and upper approximations constructed by the equivalence classes associated with the equivalence relation R . The concepts of upper and lower approximations in rough set theory allow us to discover the knowledge hidden in information systems and express it in the form of decision rules.In Pawlaks rough set model, equivalence relation is a key and primitive notion. The equivalence classes are building blocks for constructing the lower and upper approximations. This equivalence relation, however, seems to be a very stringent condition that may limit the application domain of the rough set model. To solve this problem, Pawlak's rough set model has been generalized to arbitrary binary relation based rough set model, covering based rough set model, fuzzy rough set model, etc, to meet the needs of some real application problems. Yao [2] proposed generalized rough set model and investigated the constructive and algebraic approaches in the study of rough sets. In the constructive approach, one starts from a binary relation on the universe and defines a pair of lower and upper approximation operators using the binary relation. In the algebraic approach, one defines a pair of dual approximation operators and states axioms that must be satisfied by the operators. The axioms of approximation operators guarantee the existence of certain types of binary relations producing the same operators.Definition 1 [1] Let U be a finite universe and R an equivalence relation on U . The pair ( , ) U R is referred to as a Pawlak approximation space. For any X U ⊆ , the lower approximation

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“…In this paper, we will stick to the first approach, the multigranulation rough set models. Using the concept of S-approximation spaces, we generalize the concept of neighborhood-based multigranulation rough set theory [18], or the neighborhood systems [44] to S-approximation spaces which are independent of the inclusion relation, i.e., deciders of any type, and also relaxing the compatibility assumption [25], i.e., knowledge mappings of any type, e.g., covering or tolerance rather than partitions [19,41]. This approach might be a better fit to multi-source decision makings on two universes where the knowledge mappings are different due to different experimental conditions and/or sampling strategies.…”

Section: Introductionmentioning

confidence: 99%

Neighborhood system S-approximation spaces and applications

Shakiba

Hooshmandasl

2015

Knowl Inf Syst

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In this paper, we will study neighborhood system S-approximation spaces, i.e., combination of S-approximation spaces with identical elements except that they have different knowledge mappings, e.g., the knowledge mappings differ due to different experimental conditions and/or sampling methodology. In such situations, there is a risk of contradictory knowledge sets which can lead to different decisions by the same query. These situations are studied in this paper in detail. Moreover, neighborhood system S-approximation spaces are investigated from a three-way decisions viewpoint with respect to different deciders. In addition, completeness results are shown for optimistic and pessimistic neighborhood system S-approximation spaces, i.e., these constructions can be represented by an ordinary S-approximation space. Also, the concept of knowledge significance is proposed and studied in detail, and we have shown that computing a minimal set of knowledge mappings for a neighborhood system S-approximation space is NP-hard. Finally, the paper is concluded by two illustrative medical examples.

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Multigranulation rough sets: From partition to covering

Cited by 155 publications

References 47 publications

A new approach of optimal scale selection to multi-scale decision tables

A new approach of optimal scale selection to multi-scale decision tables

On the connections between multigranulation rough sets and generalized rough sets

Neighborhood system S-approximation spaces and applications

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