Covering Based Rough Equivalence of Sets and Comparison of Knowledge

Rough set approach is a very useful tool to handle the unclear and ambiguous data. In this approach, a set's boundary region is used to express the incorrectness. Based on an equivalence relation, we can have upper and lower approximations for rough set. As rough sets make use of the equivalence relation property, they remain rigid. Rough set theory becomes a time consuming process because we need to find all the equivalence classes. It is unreliable and inefficient for real time applications where the data sets may be very large. In this paper, we provide a solution to this problem with covering based rough set approach. Covering based rough set is an extension of rough set approach in which the equivalence relation has been relaxed. This method is based on coverings rather than partitions. This makes it more flexible than rough sets and it is more convenient for dealing with complex applications. The purpose of covering based rough set is to get more number of overlapping. We uses covering based similarity measure which gives better results as compared to rough set which uses set and sequence similarity measure.

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“…Let (V,C) be a covering approximation space, and X, Y ,we define (12) where are rough membership functions and is an inclusion degree on…”

Section: Theoremmentioning

confidence: 99%

“…To find the similarity between objects, a similarity measure is also presented in [7]. In [11] [12], the authors have studied the covering rough models and also their properties. In [13] the relationship between covering based rough set and general rough set is discussed.…”

Section: Introductionmentioning

confidence: 99%

Covering based rough clustering of sequential data

Dhaduk

Kamle

Venkatesan

et al. 2014

2014 IEEE International Conference on Computational Intelligence and Computing Research

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“…Interchangeable notions are used to define the classification of universe and equivalence relations. [2,9] A rough set represented by a pair of crisp sets, is classified into lower and upper approximations of the set. The lower approximation of a rough set comprises of those elements of the universe, which can be said as those who belongs definitely with the available knowledge.…”

Section: Introductionmentioning

confidence: 99%

“…Such relations are found more abundant in real life situations. [2,9] Joseph Fiksel [6] defined the term societal network instead of social network to denote a mathematical system having well defined properties, where node represents individual people and arcs represent directed relations. Thus, societal network is defined as labelled directed network ( , , ) N A T where ' ' N is a finite set of nodes, ' ' T is a finite set of relational type, and…”

Section: Introductionmentioning

confidence: 99%

Clustering analysis in social network using Covering Based Rough Set

Mitra¹,

Satapathy²,

Paul³

2013

2013 3rd IEEE International Advance Computing Conference (IACC)

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This paper focuses on solving the problem of classification and clustering in social network by using Rough Set. When the data set consists of missing or uncertain data then the Rough set is proved to be an efficient tool. To solve a problem under the domain of social network, the problem must satisfy the fundamental property of rough set i.e., the attribute of the problem must holds true for equivalence relation. Hence, before implementing rough set to the specific problem of social network, it must be redefined in a way that properties of transitive, symmetric and reflexive should holds true. In this paper, we have studied on the concept of Fiksel's societal network and used it for redefining the social network problem in terms of equivalence relationships. Further, we had defined the Social network in terms of graph theory and mathematical relations. We had proceeded further in defining the Fiksel's societal network and social network with respect to rough set. Fiksel had defined the social network in terms of structural equivalence. We have discussed on the limitation of Rough set and observed that use of Covering Based Rough Set as an extension of Pawlak's rough set seems to be a better alternative. There are six types of covering based rough set. To keep continuity in this paper, we have mentioned about Covering based rough sets. Covering based rough set extends from partitioning in rough sets to covering of the universe and is flexible, when compared with rigid equivalence relation.

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“…So, in a sense the definition of rough equality incorporates user knowledge about the universe in arriving at approximate equality of sets or domains. Some more types of such approximate equalities have been introduced by Tripathy (see for instance [11,12,13,20,21,22]). These notions are more general and more applicable in real life situations.…”

Section: Properties Of Covering Based Pessimistic Multigranular Roughmentioning

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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Covering Based Rough Equivalence of Sets and Comparison of Knowledge

Cited by 9 publications

References 9 publications

Covering based rough clustering of sequential data

Covering based rough clustering of sequential data

Clustering analysis in social network using Covering Based Rough Set

Covering Based Pessimistic Multigranular Rough Equalities and their Properties

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