On Certain Rough Inclusion Functions

  • Authors:
  • Anna Gomolińska

  • Affiliations:
  • Department of Mathematics, Białystok University, Białystok, Poland 15267

  • Venue:
  • Transactions on Rough Sets IX
  • Year:
  • 2008

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Abstract

In this article we further explore the idea which led to the standard rough inclusion function. As a result, two more rough inclusion functions (RIFs in short) are obtained, different from the standard one and from each other. With every RIF we associate a mapping which is in some sense complementary to it. Next, these complementary mappings (co-RIFs) are used to define certain metrics. As it turns out, one of these distance functions is an instance of the Marczewski---Steinhaus metric. While the distance functions may directly be used to measure the degree of dissimilarity of sets of objects, their complementary mappings --- also discussed here --- are useful in measuring of the degree of mutual similarity of sets.