Int. J. of Granular Computing, Rough Sets and Intelligent Systems   »   2013 Vol.3, No.2

 

 

Title: Condition for covering-based upper approximation operators to be closure operators of matroids

 

Authors: Lirun Su; William Zhu

 

Addresses:
Lab of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China
Lab of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China

 

Abstract: Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. In order to broaden the application and theoretical areas of rough sets and matroids, some authors have combined them from many different viewpoints, such as circuits, rank function and spanning sets. In this paper, we study the relationship between five types of covering-based upper approximation operators and closure operators of matroids. On one hand, comparing those characterisations of five types of covering-based upper approximation operators with the characterisations of closure operators of matroids, we discuss the condition under which five types of covering-based upper approximation operators form closure operators of matroids and get some results. For example, the necessary and sufficient conditions for the second type of covering-based upper approximation operator to satisfy idempotence is obtained. On the other hand, by using the characterisations of unary coverings, close friends, neighbourhoods, indiscernible neighbourhoods and reduct, we present necessary and sufficient conditions for five types of covering-based upper approximation operators to be closure operators of matroids.

 

Keywords: rough sets; upper approximation operators; matroids; closure operators; unary covering; inexact knowledge; uncertain knowledge; vague knowledge; information systems.

 

DOI: 10.1504/IJGCRSIS.2013.057242

 

Int. J. of Granular Computing, Rough Sets and Intelligent Systems, 2013 Vol.3, No.2, pp.144 - 159

 

Available online: 18 Oct 2013

 

 

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