scholarly journals Efficient Rule Set Generation using Rough Set Theory for Classification of High Dimensional Data

2011 ◽  
pp. 129-136
Author(s):  
Prasanta Gogoi ◽  
Ranjan Das ◽  
B Borah ◽  
D K. Bhattacharyya
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Network Flow ◽  
Rough Set Theory ◽  
Real Life ◽  
Local Network ◽  
Upper Approximation ◽  
Inconsistent Data ◽  
Network Intrusion ◽  
Rule Set

In this paper, a rough set theory (RST) based approach is proposed to mine concise rules from inconsistent data. The approach deals with inconsistent data. At first, it computes the lower and upper approximation for each concept, then adopts a learning from an algorithm to build concise classification rules for each concept satisfying the given classification accuracy. Lower and upper approximation estimation is designed for the implementation, which substantially reduce the computational complexity of the algorithm. UCI ML Repository datasets are used to test and validate the proposed approach. We have also used our approach on network intrusion dataset captured using our local network from network flow. The results show that our approach produces effective and minimal rules and provide satisfactory accuracy over several real life datasets.

Analysis of Time-Series Data by Merging Decision Rules

2017 ◽  
Vol 21 (6) ◽  
pp. 1026-1033
Author(s):  
Yoshiyuki Matsumoto ◽  
Junzo Watada ◽  
◽  
Keyword(s):  
Time Series ◽  
Decision Rule ◽  
Set Theory ◽  
Rough Set ◽  
Time Series Data ◽  
Rough Set Theory ◽  
Decision Rules ◽  
Series Data ◽  
Rule Set ◽  
Analysis Of Time Series

Rough set theory was proposed by Z. Pawlak in 1982. This theory enables the mining of knowledge granules as decision rules from a database, the web, and other sources. This decision rule set can then be used for data analysis. We can apply the decision rule set to reason, estimate, evaluate, or forecast an unknown object. In this paper, rough set theory is used for the analysis of time-series data. We propose a method to acquire rules from time-series data using regression. The trend of the regression line can be used as a condition attribute. We predict the future slope of the time-series data as decision attributes. We also use merging rules to further analyze the time series data.

scholarly journals Covering-Based Rough Sets on Eulerian Matroids

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bin Yang ◽  
Ziqiong Lin ◽  
William Zhu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Closure Operator ◽  
Matroid Theory ◽  
Upper Approximation ◽  
Significant Generalization ◽  
Eulerian Matroid ◽  
Vital Structure

Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids.

Model of Covering Rough Sets in the Machine Intelligence

2012 ◽  
Vol 548 ◽  
pp. 735-739
Author(s):  
Hong Mei Nie ◽  
Jia Qing Zhou
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Machine Intelligence ◽  
Upper Approximation ◽  
Generalized Rough Sets

Rough set theory has been proposed by Pawlak as a useful tool for dealing with the vagueness and granularity in information systems. Classical rough set theory is based on equivalence relation. The covering rough sets are an improvement of Pawlak rough set to deal with complex practical problems which the latter one can not handle. This paper studies covering-based generalized rough sets. In this setting, we investigate common properties of classical lower and upper approximation operations hold for the covering-based lower and upper approximation operations and relationships among some type of covering rough sets.

ON ATTRIBUTE REDUCTION WITH INTUITIONISTIC FUZZY ROUGH SETS

2012 ◽  
Vol 20 (01) ◽  
pp. 59-76 ◽  
Author(s):  
ZHIMING ZHANG ◽  
JINGFENG TIAN
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Theoretical Foundation ◽  
Attribute Reduction ◽  
Upper Approximation ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Rough Sets ◽  
Axiomatic Approaches

Intuitionistic fuzzy (IF) rough sets are the generalization of traditional rough sets obtained by combining the IF set theory and the rough set theory. The existing research on IF rough sets mainly concentrates on the establishment of lower and upper approximation operators using constructive and axiomatic approaches. Less effort has been put on the attribute reduction of databases based on IF rough sets. This paper systematically studies attribute reduction based on IF rough sets. Firstly, attribute reduction with traditional rough sets and some concepts of IF rough sets are reviewed. Then, we introduce some concepts and theorems of attribute reduction with IF rough sets, and completely investigate the structure of attribute reduction. Employing the discernibility matrix approach, an algorithm to find all attribute reductions is also presented. Finally, an example is proposed to illustrate our idea and method. Altogether, these findings lay a solid theoretical foundation for attribute reduction based on IF rough sets.

scholarly journals Topological properties of a pair of relation-based approximation operators

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6175-6183
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Properties ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Basic Concepts

Rough set theory is an important tool for data mining. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough approximation operators are based on equivalence relations and have been extended to relation-based generalized rough approximation operators. This paper presents topological properties of a pair of relation-based generalized rough approximation operators. A topology is induced by the pair of generalized rough approximation operators from an inverse serial relation. Then, connectedness, countability, separation property and Lindel?f property of the topological space are discussed. The results are not only beneficial to obtain more properties of the pair of approximation operators, but also have theoretical and actual significance to general topology.

Rough Set Theory Based Hybrid Method for Network Intrusion Detection

2013 ◽  
Vol 373-375 ◽  
pp. 815-818
Author(s):  
Na Jiao
Keyword(s):  
Intrusion Detection ◽  
Set Theory ◽  
Rough Set ◽  
Hybrid Method ◽  
Rough Set Theory ◽  
Network Intrusion Detection ◽  
Large Network ◽  
Fuzzy C Means ◽  
Network Intrusion ◽  
International Knowledge

In this paper, we propose an intrusion detection method that combines rough set theory and Fuzzy C-Means for network intrusion detection. The first step consists of feature selection which is based on rough set theory. The next phase is clustering by using Fuzzy C-Means. Rough set theory is an efficient tool for further reducing redundancy. Fuzzy C-Means allows objects which are belong to several clusters simultaneously, with different degrees of membership. To evaluate the performance of the introduced approach, we applied them to the international Knowledge Discovery and Data mining intrusion detection dataset. In the experimentations, we compare the performance of the rough set theory based hybrid method for network intrusion detection. Experimental results illustrate that our algorithm is accurate model for handling complex attack patterns in large network. And the method can increase the efficiency and reduce the dataset by looking for overlapping categories.

scholarly journals Rough Set Theory and its Applications: A recent Survey

2020 ◽  
pp. 548-552
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Intelligent Agents ◽  
Rough Set Theory ◽  
Boundary Region ◽  
Process Industry ◽  
Decision Making Process ◽  
Upper Approximation ◽  
Analysis Process ◽  
The Universe

Rough set theory is a mathematical method proposed by Pawlak . Rough set theory has been developed to manage uncertainties in information that presents missing and noises. Rough set theory is an expansion of the conventional set theory that supports approximations in decision making process. Fundamental of assumption of rough set theory is that with every object of the universe has some information associated it. Rough set theory is correlate two crisp sets, called lower and upper approximation. The lower approximation of a set consists of all elements that surely belong to the set, and the upper approximation of the set constitutes of all elements that possibly belong to the set. The boundary region of the set consists of all elements that cannot be classified uniquely as belonging to the set or as belonging to its complement, with respect to the available knowledge Rough sets are applied in several domains, such as, pattern recognition, medicine, finance, intelligent agents, telecommunication, control theory ,vibration analysis, conflict resolution, image analysis, process industry, marketing, banking risk assessment etc. This paper gives detail survey of rough set theory and its properties and various applications of rough set theory.

scholarly journals Idealization of j-approximation spaces

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 287-301
Author(s):  
Mona Hosny
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Current Work ◽  
Core Concept ◽  
Approximation Spaces ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Generalized Rough Set ◽  
The Ideal

The current work concentrates on generating different topologies by using the concept of the ideal. These topologies are used to make more thorough studies on generalized rough set theory. The rough set theory was first proposed by Pawlak in 1982. Its core concept is upper and lower approximations. The principal goal of the rough set theory is reducing the vagueness of a concept to uncertainty areas at their borders by increasing the lower approximation and decreasing the upper approximation. For the mentioned goal, different methods based on ideals are proposed to achieve this aim. These methods are more accurate than the previous methods. Hence it is very interesting in rough set context for removing the vagueness (uncertainty).

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