Rough equivalence and algebraic properties of rough sets

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

doi:10.1504/ijaisc.2009.027296

Cited by 11 publications

(4 citation statements)

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“…An interesting analysis on the effectiveness of these four types of appro ximate equalities have been carried out in [15], which shows that the notion of rough equivalence is the most general among the four; where as the notion of approximate rough equivalence is the most natural one fro m the applicat ion point of view. So me algebraic properties of rough equivalence have been established in [16].…”

Section: E Other Approximate Equalitiesmentioning

confidence: 99%

“…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%

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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%

Approximate Reasoning through Multigranular Approximate Rough Equalities

Tripathy¹,

Rawat²,

.Y³

et al. 2014

IJISA

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“…Let us consider the example of a stock exchange dealing with shares of different companies [10]. The shares of different companies are of different denomination and are related to branches of the companies at different locations.…”

Section: Examplementioning

confidence: 99%

“…So, it is expected that the ordinary equalities may be replaced by any one of the four types of approximate equalities using rough sets. The first attempt in this direction was taken by Tripathy et al [10], where rough equivalence was considered instead of ordinary equality of sets. In this paper, we make a comparative analysis of applicability of all the four kinds of approximate equalities through rough sets and establish the results.…”

Section: Introductionmentioning

confidence: 99%

Algebric properties of rough sets using topological characterisations and approximate equalities

Tripathy

Mitra²

2013

2013 IEEE International Conference on Computational Intelligence and Computing Research

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The notion of rough sets [4] was used by Novotny and Pawlak [1, 2, 3] to introduce the concept of rough equality, in order to incorporate user knowledge in determining the equality of sets, which is a natural phenomenon in day to day life. Even this notion was shown to be deficient and was extended by Tripathy et al [6,9] to define the notion of rough equivalence of sets, which is more suitable in real life situations. Tripathy [7] added two more approximate equalities to this list in order to complete the kinds of approximate equalities. Algebraic properties of sets with mathematical equality have very little meaning when sets are replaced with rough sets. As a consequence, replacing equality by rough equivalence the algebraic properties were studied by Tripathy et al [10]. In our present work, we have made an analysis of the validity of the algebraic properties with respect to the four kinds of approximate equalities and provide a comparative study to establish that rough equivalence is the best and rough equality is the worst among these approximate equalities with respect to the algebraic properties involving rough sets. The topological characterisations of rough sets leading to four types of rough sets and operations on them [8] are being used in the sequel. We support our descriptions with a running real life example of shares.

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