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Proceedings ArticleDOI

On some properties of covering based approximations of classifications of sets

24 Nov 2009-pp 1227-1232
TL;DR: Deriving results for all the five types of covering based rough sets can be used to derive rules for information systems with domains of attributes values being covers instead of partitions.
Abstract: Approximations of classifications, introduced and studied by Grzymala Busse [4] is a notion different from the notion of approximations of sets (Pawlak [9]). In fact the equivalence classes of approximate classifications cannot be arbitrary sets. Busse [4] had established properties of approximations of classifications which were recently extended to necessary and sufficient type theorems by Tripathy et. al ([12]). Four types of covering based rough sets have been obtained as generalization of basic rough sets. Also another covering rough set from a topological point of view has been obtained (14, 15, 16, 17, 18, 19]. Attempts have been made in [13] to extend the above results to covering based rough sets. In this paper we carry out this study further by deriving results for all the five types of covering based rough sets. These results can be used to derive rules for information systems with domains of attributes values being covers instead of partitions.
Citations
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Journal Article
TL;DR: Covering-based rough fuzzy set clustering approach is proposed to resolve the uncertainty of sequence data and uses covering-based similarity measure which gives better results as compared to rough set which uses set and sequence similarity measure.
Abstract: Clustering is categorised as hard or soft in nature. Soft clusters may have fuzzy or rough boundaries. Rough clustering can help researchers to discover overlapping clusters in many applications such as web mining and text mining. Rough set approach is a very useful tool to handle the unclear and ambiguous data. As rough sets make use of the equivalence relation property, they remain rigid and it is unreliable and inefficient for real time applications where the datasets 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. Clustering sequential data is one of the vital research tasks. We uses covering-based similarity measure which gives better results as compared to rough set which uses set and sequence similarity measure. In this paper, covering-based rough fuzzy set clustering approach is proposed to resolve the uncertainty of sequence data.

3 citations


Cites background from "On some properties of covering base..."

  • ...One such extension is the motion of coveringbased rough sets introduced by Shi and Gong (2010) and Tripathy and Panda (2009)....

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01 Jan 2015
TL;DR: This paper assesses the impact of rough set approach in classification of universe and applies roughest based classification process using MATLAB functions to the raw dataset before data pre-processing and shows that precompiled rouGhest classification has better accuracy and outperforms than some of earlier studies.
Abstract: Sentiment Analysis (SA) is an ongoing research in the field of text mining and classification. SA finds a computational domain from opinions and subjectivity of text data in online social media. Sentiments are inherited in the form of simple lexicons with symbols and texts having noise of irregular texts in complex forms. It is also seen that the high dimensional growth of lexical blends used by online users while expressing or responding their responses. These blends differ according to demographics and on the context of topics. The simplest approach to get rid of the noise data, adapted by number of studies is by simply removing the irregular lexicons, stopwords, emoticons and lexical blends. This paper investigates such effectiveness in sentiment classification. We assess the impact of rough set approach in classification of universe and apply to the raw datasets. Our earlier study on covering based approximation of classifications outperforms the general classification of universe. We apply roughest based classification process using MATLAB functions to the raw dataset before data pre-processing. Our results show that precompiled roughest classification has better accuracy and outperforms than some of earlier studies.

2 citations


Cites background from "On some properties of covering base..."

  • ...SA has been handled as a natural language processing (NLP) at many levels of granularity....

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Book ChapterDOI
01 Jan 2023
TL;DR: In this paper , the applicability of Rough Set Theory (RST) has been explored in the field of knowledge discovery, machine learning, expert systems, data analysis, and data mining.
Abstract: As many social network studies have been made public in recent years, maintaining privacy while publishing social network data has become a major challenge. Individual traits in social networks are characterized as being less essential than their relationships and links with other participants in the network. An adversary can simply target the privacy of some victims if they have some local knowledge about them. The majority of past readings on privacy preservation have only dealt with relational records and may not be prolonged to data from social networks. In this article, mainly examine privacy difficulties in social networks utilizing anonymization and l-diversity approaches, as well as the applicability of Pawlak’s Rough Set Theory (RST), which has dominated as a powerful tool in the field of knowledge discovery, machine learning, expert systems, data analysis, and data mining.
References
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Book
31 Oct 1991
TL;DR: Theoretical Foundations.
Abstract: I. Theoretical Foundations.- 1. Knowledge.- 1.1. Introduction.- 1.2. Knowledge and Classification.- 1.3. Knowledge Base.- 1.4. Equivalence, Generalization and Specialization of Knowledge.- Summary.- Exercises.- References.- 2. Imprecise Categories, Approximations and Rough Sets.- 2.1. Introduction.- 2.2. Rough Sets.- 2.3. Approximations of Set.- 2.4. Properties of Approximations.- 2.5. Approximations and Membership Relation.- 2.6. Numerical Characterization of Imprecision.- 2.7. Topological Characterization of Imprecision.- 2.8. Approximation of Classifications.- 2.9. Rough Equality of Sets.- 2.10. Rough Inclusion of Sets.- Summary.- Exercises.- References.- 3. Reduction of Knowledge.- 3.1. Introduction.- 3.2. Reduct and Core of Knowledge.- 3.3. Relative Reduct and Relative Core of Knowledge.- 3.4. Reduction of Categories.- 3.5. Relative Reduct and Core of Categories.- Summary.- Exercises.- References.- 4. Dependencies in Knowledge Base.- 4.1. Introduction.- 4.2. Dependency of Knowledge.- 4.3. Partial Dependency of Knowledge.- Summary.- Exercises.- References.- 5. Knowledge Representation.- 5.1. Introduction.- 5.2. Examples.- 5.3. Formal Definition.- 5.4. Significance of Attributes.- 5.5. Discernibility Matrix.- Summary.- Exercises.- References.- 6. Decision Tables.- 6.1. Introduction.- 6.2. Formal Definition and Some Properties.- 6.3. Simplification of Decision Tables.- Summary.- Exercises.- References.- 7. Reasoning about Knowledge.- 7.1. Introduction.- 7.2. Language of Decision Logic.- 7.3. Semantics of Decision Logic Language.- 7.4. Deduction in Decision Logic.- 7.5. Normal Forms.- 7.6. Decision Rules and Decision Algorithms.- 7.7. Truth and Indiscernibility.- 7.8. Dependency of Attributes.- 7.9. Reduction of Consistent Algorithms.- 7.10. Reduction of Inconsistent Algorithms.- 7.11. Reduction of Decision Rules.- 7.12. Minimization of Decision Algorithms.- Summary.- Exercises.- References.- II. Applications.- 8. Decision Making.- 8.1. Introduction.- 8.2. Optician's Decisions Table.- 8.3. Simplification of Decision Table.- 8.4. Decision Algorithm.- 8.5. The Case of Incomplete Information.- Summary.- Exercises.- References.- 9. Data Analysis.- 9.1. Introduction.- 9.2. Decision Table as Protocol of Observations.- 9.3. Derivation of Control Algorithms from Observation.- 9.4. Another Approach.- 9.5. The Case of Inconsistent Data.- Summary.- Exercises.- References.- 10. Dissimilarity Analysis.- 10.1. Introduction.- 10.2. The Middle East Situation.- 10.3. Beauty Contest.- 10.4. Pattern Recognition.- 10.5. Buying a Car.- Summary.- Exercises.- References.- 11. Switching Circuits.- 11.1. Introduction.- 11.2. Minimization of Partially Defined Switching Functions.- 11.3. Multiple-Output Switching Functions.- Summary.- Exercises.- References.- 12. Machine Learning.- 12.1. Introduction.- 12.2. Learning From Examples.- 12.3. The Case of an Imperfect Teacher.- 12.4. Inductive Learning.- Summary.- Exercises.- References.

7,826 citations

Journal ArticleDOI
TL;DR: Some extensions of the rough set approach are presented and a challenge for the roughSet based research is outlined and it is outlined that the current rough set based research paradigms are unsustainable.

1,161 citations

Journal ArticleDOI
TL;DR: It has been proved that the reduct of a covering is the minimal covering that generates theSame covering lower approximation or the same covering upper approximation, so this concept is also a technique to get rid of redundancy in data mining.

699 citations


"On some properties of covering base..." refers background in this paper

  • ...Several properties of the different types of CBrough sets have been derived by different researchers [1, 2, 3, 14, 15, 16, 17, 18, 19]....

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Journal ArticleDOI
TL;DR: This paper explores the topological properties of covering-based rough sets, studies the interdependency between the lower and the upper approximation operations, and establishes the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation.

588 citations


"On some properties of covering base..." refers background or methods in this paper

  • ...We require the following theorems from Zhu and Wang ([16]) and Zhu [18] for proving the results of this paper:...

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  • ...COVERING ROUGH SETS FROM A TOPOLOGICAL POINT OF VIEW A new type of CB – rough sets from the topological point of view (CB – rough set of T - type) was introduced by Zhu [18]....

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  • ...Several properties of the different types of CBrough sets have been derived by different researchers [1, 2, 3, 14, 15, 16, 17, 18, 19]....

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Journal ArticleDOI
TL;DR: The approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension, which makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets, which are analogous to classical operations on sets.

567 citations


Additional excerpts

  • ...Several properties of the different types of CBrough sets have been derived by different researchers [ 1 , 2, 3, 14, 15, 16, 17, 18, 19]....

    [...]