Constructive methods of rough approximation operators and multigranulation rough sets

Zhang, Xiao­hong; Miao, Duoqian; Liu, Caihui; Le, Meilong

doi:10.1016/j.knosys.2015.09.036

Cited by 107 publications

(27 citation statements)

References 31 publications

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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%

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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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Section: Pessimistic Multigranulation Rough Setsmentioning

confidence: 99%

“…Zhang [10] proposed an algebraic approach for the rough approximation operators in the multiple approximation spaces. Four kinds of constructive methods of rough approximation operators from existing rough sets are established, and some important properties are investigated.…”

Section: U ⊆mentioning

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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“…Rough sets, a new-style mathematical tools, are widely applied to handle incertitude and incomplete data in many fields, such as cognitive science, patter recognition, machine learning, and so on; for example in [2][3][4] the applications of rough sets were given. In addition, an equivalence relation (briefly, ER), as an indispensable part in Pawlak rough sets, is also investigated highly by many researchers.…”

Section: Introductionmentioning

confidence: 99%

A study on soft rough semigroups and corresponding decision making applications

2017

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Abstract:In this paper, we study a kind of soft rough semigroups according to Shabir's idea. We define the upper and lower approximations of a subset of a semigroup. According to Zhan's idea over hemirings, we also define a kind of new C -soft sets and C C -soft sets over semigroups. In view of this theory, we investigate the soft rough ideals (prime ideals, bi-ideals, interior ideals, quasi-ideals, regular semigroups). Finally, we give two decision making methods: one is for looking a best a parameter which is to the nearest semigroup, the other is to choose a parameter which keeps the maximum regularity of regular semigroups.

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“…Rough set theory, proposed by Pawlak [34,35] has been conceived as an excellent tool to analyze and handle intelligent systems characterized by imprecise, vague and uncertain information in many fields, such as data mining, knowledge discovery, decision making and so on [5,6,8,9,12,19,21,24,26,37,38,43,44,49,50,54,57] .…”

Section: Introductionmentioning

confidence: 99%

Catoptrical rough set model on two universes using granule-based definition and its variable precision extensions

Dai

Han

Zhang

et al. 2017

Information Sciences

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Constructive methods of rough approximation operators and multigranulation rough sets

Cited by 107 publications

References 31 publications

On the connections between multigranulation rough sets and generalized rough sets

On the connections between multigranulation rough sets and generalized rough sets

A study on soft rough semigroups and corresponding decision making applications

Catoptrical rough set model on two universes using granule-based definition and its variable precision extensions

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