Relationships among Matroids Induced by Covering-Based Upper Approximation Operators
Received:March 13, 2017  Revised:May 17, 2018
Key Word: covering   matroid   rough set   upper approximation operator   indiscernible neighborhood   neighborhood   close friend  
Fund ProjectL:Supported by the Research Foundation for Middle-aged and Young Scientist of Fujian Province (Grant No.JAT170731).
Author NameAffiliation
Lirun SU Teaching Sector of Chinese and Mathematical Studies,\\ Fuzhou University of International Studies and Trade, Fujian 350202, P. R. China 
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Abstract:
      Covering-based rough sets, as a technique of granular computing, can be a useful tool for dealing with inexact, uncertain or vague knowledge in information systems. Matroids generalize linear independence in vector spaces, graph theory and provide well established platforms for greedy algorithm design. In this paper, we construct three types of matroidal structures of covering-based rough sets. Moreover, through these three types of matroids, we study the relationships among these matroids induced by six types of covering-based upper approximation operators. First, we construct three families of sets by indiscernible neighborhoods, neighborhoods and close friends, respectively. Moreover, we prove that they satisfy independent set axioms of matroids. In this way, three types of matroidal structures of covering-based rough sets are constructed. Secondly, we study some characteristics of the three types of matroid, such as dependent sets, circuits, rank function and closure. Finally, by comparing independent sets, we study relationships among these matroids induced by six types of covering-based upper approximation operators.
Citation:
DOI:10.3770/j.issn:2095-2651.2018.04.003
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