On Rough Equalities and Rough Equivalences of Sets

Tripathy, B. K.; Mitra, Anirban; Ojha, J.

doi:10.1007/978-3-540-88425-5_10

Cited by 23 publications

(19 citation statements)

References 6 publications

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“…However, it was shown by Tripathy et al [13] that some of the rep lacement properties hold true and others hold true under suitable sufficient conditions. Validity of similar properties has been verified for all the other three types of approximate equalities.…”

Section: E Other Approximate Equalitiesmentioning

confidence: 99%

“…A much more generalised approximate equality which is almost independent of equality of sets, called the rough equivalence was introduced by Tripathy et al [13]. Later on two more types of appro ximate equalit ies called the approximate rough equality and approximate rough equivalence were introduced by Tripathy [15].…”

Section: E Other Approximate Equalitiesmentioning

confidence: 99%

“…So, they introduced the notion of rough equivalence, which is free fro m such deficiencies. Later on Tripathy [13] combined the conditions of rough equality and rough equivalence to define two more types of approximate equalities; called the approximate rough equality and approximate rough equivalence. In a sense, this completes the group of approximate equalities using the concepts of lower and upper appro ximat ions of sets.…”

Section: Introductionmentioning

confidence: 99%

“…In a sense, this completes the group of approximate equalities using the concepts of lower and upper appro ximat ions of sets. Also, a nice co mparative analysis of relat ive strengths and weaknesses of these four types of approximate equalities has been made in [13] and it is established that the notion of appro ximate rough equivalence is the most general among the four. Recently, two of the four types of rough equalities; namely the rough equality and rough equivalence, have been extended to the context of mu ltig ranulations by Tripathy et al [12,14].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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%

Section: E Other Approximate Equalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximate Reasoning through Multigranular Approximate Rough Equalities

Tripathy¹,

Rawat²,

.Y³

et al. 2014

IJISA

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show abstract

“…That is, basing upon our knowledge and requirement we can assume that the two sets are indistinguishable. Three more types of approximate equalities basing upon rough sets have been proposed and studied [11,21,23]. A comparative analysis of these approximate equalities is provided [11] This paper is further organized into five sections.…”

Section: Introductionmentioning

confidence: 99%

Covering Based Pessimistic Multigranular Rough Equalities and their Properties

Tripathy¹,

Parida²

2016

IJITCS

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Abstract-The basic rough set theory introduced by Pawlak as a model to capture imprecision in data has been extended in many directions and covering based rough set models are among them. Again from the granular computing point of view, the basic rough sets are unigranular by nature. Two types of extensions to the context of multigranular computing are done; called the optimistic and pessimistic multigranulation by Qian et al in 2006 and 2010 respectively. Combining these two concepts of covering and multigranulation, covering based multigranular models have been introduced by Liu et al in 2012. Extending the stringent concept of mathematical equality of sets rough equalities were introduced by Novotny and Pawlak in 1985. Three more types of such approximate equalities were introduced by Tripathy in 2011. In this paper we study the approximate equalities introduced by Novotny and Pawlak from the pessimistic multigranular computing point of view and establish several of their properties. These concepts and properties are shown to be useful in approximate reasoning.

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On Approximation of Classifications, Rough Equalities and Rough Equivalences

Tripathy

2009

Studies in Computational Intelligence

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On Rough Equalities and Rough Equivalences of Sets

Cited by 23 publications

References 6 publications

Approximate Reasoning through Multigranular Approximate Rough Equalities

Approximate Reasoning through Multigranular Approximate Rough Equalities

Covering Based Pessimistic Multigranular Rough Equalities and their Properties

On Approximation of Classifications, Rough Equalities and Rough Equivalences

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