Int. J. of Granular Computing, Rough Sets and Intelligent Systems   »   2014 Vol.3, No.3

 

 

Title: Condition for neighbourhoods induced by a covering to be equal to the covering itself

 

Authors: Hua Yao; William Zhu

 

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

 

Abstract: It is a meaningful issue that under what condition neighbourhoods induced by a covering are equal to the covering itself. In this paper, firstly, through defining some concepts, such as repeat degree and invariable covering, we present a necessary and sufficient condition for this issue. Secondly, we concentrate on the inverse issue of computing neighbourhoods by a covering, namely for a given arbitrary covering, whether or not there exists another covering such that the neighbourhoods induced by it is just the former covering. We present a necessary and sufficient condition for this issue as well. In a word, through the study on the two fundamental issues induced by neighbourhoods, we have gained a deeper understanding of the relationship between neighbourhoods and the covering which induces the neighbourhoods.

 

Keywords: neighbourhoods; reducible elements; repeat degree; core block; invariable covering; granular computing; rough sets; intelligent systems.

 

DOI: 10.1504/IJGCRSIS.2014.060839

 

Int. J. of Granular Computing, Rough Sets and Intelligent Systems, 2014 Vol.3, No.3, pp.195 - 205

 

Available online: 01 May 2014

 

 

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