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On Certain Rough Inclusion Functions

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Transactions on Rough Sets IX

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5390))

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Białystok University, Akademicka 2, 15267, Białystok, Poland

    Anna Gomolińska

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  1. Anna Gomolińska
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Institute of Computer Science, Warsaw University of Technology, Nowowoiejska 15/19, 00-665, Warsaw, Poland

    Henryk Rybiński

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Gomolińska, A. (2008). On Certain Rough Inclusion Functions. In: Peters, J.F., Skowron, A., Rybiński, H. (eds) Transactions on Rough Sets IX. Lecture Notes in Computer Science, vol 5390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89876-4_3

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  • DOI: https://doi.org/10.1007/978-3-540-89876-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89875-7

  • Online ISBN: 978-3-540-89876-4

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