Some topological properties of rough sets and their applications

Tripathy, B. K.; Mitra, Anirban

doi:10.1504/ijgcrsis.2010.036978

Cited by 22 publications

(14 citation statements)

References 6 publications

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“…Definition 2.5:Let (U, C) be a covering approximation, 12 , CC C be covers in C, for any X  U, its first type lower and upper approximations with respect to C1 and C2 are defined as follows …”

Section: Basics Of Covering Based Multi Granular Rough Setsmentioning

confidence: 99%

“…After its inception by Pawlak [5] the study of topological criterion was not attended by researchers until in [12] Tripathy et al studied the kinds of complement of a rough set, kinds of union and intersection of two rough sets. Similar study has been carried for different generalised rough sets including those for multigranular rough sets.…”

Section: Topological Properties Of Cbmgrsmentioning

confidence: 99%

“…As mentioned by Pawlak himself [5], in practical applications of rough sets we need to combine both types of information about the borderline region, that is, of the accuracy measure as well as the information about the topological classification of the set under consideration. Keeping this in mind, Tripathy and Mitra [12] have studied the kinds of rough sets by finding out the kinds of union and intersection of rough sets of different types. This characterization of basic rough sets has been extended to the context of both types of multigranular rough sets and their properties have been studied [10,13].…”

Section: Introductionmentioning

confidence: 99%

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Study of Covering Based Multi Granular Rough Sets and Their Topological Properties

Nagaraju¹,

Tripathy²

2015

IJITCS

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Abstract-The notions of basic rough sets introduced by Pawlak as a model of uncertainty, which depends upon a single equivalence relation has been extended in many directions. Over the years, several extensions to this rough set model have been proposed to improve its modeling capabilities. From the granular computing point of view these models are single granulations only. This single granulation model has been extended to multi-granulation set up by taking more than one equivalence relations simultaneously. This led to the notions of optimistic and pessimistic multi-granulation. One direction of extension of the basic rough set model is dependent upon covers of universes instead of partitions and has better modeling power as in many real life scenario objects cannot be grouped into partitions but into covers, which are general notions of partitions. So, multigranulations basing on covers called covering based multi-granulation rough sets (CBMGRS) were introduced. In the literature four types of CBMGRSs have been introduced. The first two types of CBMGRS are based on minimal descriptor and the other two are based on maximal descriptor. In this paper all these four types of CBMGRS are studied from their topological characterizations point of view. It is well known that there are four kinds of basic rough sets from the topological characterisation point of view. We introduce similar characterisation for CBMGRSs and obtained the kinds of the complement, union, and intersection of such sets. These results along with the accuracy measures of CBMGRSs are supposed to be applicable in real life situations. We provide proofs and counter examples as per the necessity of the situations to establish our claims.

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Section: Basics Of Covering Based Multi Granular Rough Setsmentioning

confidence: 99%

Section: Topological Properties Of Cbmgrsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Study of Covering Based Multi Granular Rough Sets and Their Topological Properties

Nagaraju¹,

Tripathy²

2015

IJITCS

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“…However the other types of classifications reduce either direct ly or indirectly to the five cases considered by Busse. Another important aspect of these results in [10,11] is the enumerat ion of possible types [8,12,13] of elements in a classification, which is based upon the types of rough sets introduced by Pawlak [8] and carried out further by Tripathy et al [10,11].…”

Section: Introductionmentioning

confidence: 99%

On Some Comparison Properties of Rough Sets Based on Multigranulations and Types of Multigranular Approximations of Classifications

Raghavan¹,

Tripathy²

2013

IJISA

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Abstract-In this paper we consider the inclusion properties for upper and lo wer appro ximation of union and intersection of sets for both pessimistic and optimistic mult igranulations. We find that two inclusions for pessimistic cases are actually equalities. For other six cases we provide examples to show that actually the proper inclusions hold true. On the approximation of classifications a theorem was proved in Tripathy et al to establish sufficient type properties. We establish here that actually the result is both necessary and sufficient one. Also, we consider types of elements in classifications with respect to both types of mu ltigranulat ions and establish a general theorem on them.

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“…As mentioned by Pawlak h imself [6], in practical applications of rough sets we combine both types of information about the borderline region, that is, of the accuracy of measure as well as the information about the topological classificat ion of the set under consideration. Keeping this in mind, Tripathy and Mitra [16] have studied the types of rough sets by finding out the types of union and intersection of rough sets of different types. These results were extended to the context of optimistic mult i granular rough sets by Tripathy et al [17].…”

Section: Introductionmentioning

confidence: 99%

On Some Topological Properties of Pessimistic Multigranular Rough Sets

Tripathy¹,

Nagaraju²

2012

IJISA

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Abstract-Rough set theory was introduced by Pawlak as a model to capture imp reciseness in data and since then it has been established to be a very efficient tool for this purpose. The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several equivalence relations taken one each at a time. There have been several extensions to the basic rough sets introduced since then in the literature. Fro m the granular computing point of view, research in classical rough set theory is done by taking a single granulation. It has been extended to mu ltigranular rough set (MGRS) model, where the set approximations are defined by taking mu ltip le equivalence relat ions on the universe simultaneously. Multigranular rough sets are of two types; namely optimistic M GRS and pessimistic M GRS. Topological properties of rough sets introduced by Pawlak in terms of their types were studied by Tripathy and Mitra to find the types of the union, intersection and complement of such sets. Tripathy and Raghavan have extended the topological properties of basic single granular rough sets to the optimistic M GRS context. Inco mplete informat ion systems take care of missing values for items in data tables. MGRS has also been extended to such type of incomplete information systems. In this paper we have carried out the study of topological properties of pessimistic M GRS by finding out the types of the union, intersection and complement of such sets. Also, we have provided proofs and examples to illustrate that the multip le entries in the table can actually occur in practice. Our results hold for both complete and incomp lete information systems. The mu ltip le entries in the tables occur due to imp reciseness and ambiguity in the informat ion. This is very common in many of the real life situations and needed to be addressed to handle such situations in efficient manner.

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Some topological properties of rough sets and their applications

Cited by 22 publications

References 6 publications

Study of Covering Based Multi Granular Rough Sets and Their Topological Properties

Study of Covering Based Multi Granular Rough Sets and Their Topological Properties

On Some Comparison Properties of Rough Sets Based on Multigranulations and Types of Multigranular Approximations of Classifications

On Some Topological Properties of Pessimistic Multigranular Rough Sets

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