Algebric properties of rough sets using topological characterisations and approximate equalities

Tripathy, B. K.; Mitra, Anirban

doi:10.1109/iccic.2013.6724196

Cited by 2 publications

(1 citation statement)

References 8 publications

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“…Validity of similar properties has been verified for all the other three types of approximate equalities. Algebraic properties involving rough sets using approximate equalities have been considered in [16,18]. As far as mu ltigranular rough sets are concerned, the rough equality and the rough equivalence have been extended to define the corresponding approximate equalities so far [14,17].…”

Section: E Other Approximate Equalitiesmentioning

confidence: 99%

Approximate Reasoning through Multigranular Approximate Rough Equalities

Tripathy¹,

Rawat²,

.Y³

et al. 2014

IJISA

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Abstract-The notion of rough set was introduced by Pawlak as an uncertainty based model, which basically depends upon single equivalence relations defined over a universe or a set of equivalence relations, which are not considered simultaneously. Hence, from the granular computing point of view it is unigranular by nature. Qian et al in 2006 and in 2010 introduced two types of multigranular rough sets (MGRS) called the optimistic and pessimistic M GRS respectively. The stringent notion of mathematical equality of sets was extended by introducing a kind of approximate equality, called rough equality by Novotny and Pawlak, which uses basic rough sets. Later three more related types of such approximate equalities have been introduced by Tripathy et al. He has also provided a comparative analysis of these four types of approximate equalities of sets leading to approximate reasoning in real life situations. Two of these four types of approximate equalities; namely the rough equality and rough equivalence have been extended to the context of multigranulations by Tripathy et al very recently. In this paper we carry out this study further by introducing the notion of approximate rough equalities for multigranulations and establish their properties. We use a real life example to illustrate the results in the paper and also to construct examples in support of some parts of the properties.

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Section: E Other Approximate Equalitiesmentioning

confidence: 99%

Approximate Reasoning through Multigranular Approximate Rough Equalities

Tripathy¹,

Rawat²,

.Y³

et al. 2014

IJISA

Self Cite

View full text Add to dashboard Cite

show abstract

Topological Properties of Multigranular Rough sets on Fuzzy Approximation Spaces

Tripathy

Parida²,

Parida

2019

International Journal of Rough Sets and Data Analysis

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One of the extensions of the basic rough set model introduced by Pawlak in 1982 is the notion of rough sets on fuzzy approximation spaces. It is based upon a fuzzy proximity relation defined over a Universe. As is well known, an equivalence relation provides a granularization of the universe on which it is defined. However, a single relation defines only single granularization and as such to handle multiple granularity over a universe simultaneously, two notions of multigranulations have been introduced. These are the optimistic and pessimistic multigranulation. The notion of multigranulation over fuzzy approximation spaces were introduced recently in 2018. Topological properties of rough sets are an important characteristic, which along with accuracy measure forms the two facets of rough set application as mentioned by Pawlak. In this article, the authors introduce the concept of topological property of multigranular rough sets on fuzzy approximation spaces and study its properties.

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Algebric properties of rough sets using topological characterisations and approximate equalities

Cited by 2 publications

References 8 publications

Approximate Reasoning through Multigranular Approximate Rough Equalities

Approximate Reasoning through Multigranular Approximate Rough Equalities

Topological Properties of Multigranular Rough sets on Fuzzy Approximation Spaces

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