Developing Complementary Rough Inclusion Functions-Reference-Cited by-同舟云学术

Developing Complementary Rough Inclusion Functions

Published:2020-04-01 Issue:1 Volume:28 Page:105-113
ISSN:1898-9934
Container-title:Formalized Mathematics
language:en
Short-container-title:

Author:

Grabowski Adam¹

Affiliation:

1. Institute of Informatics , University of Białystok , Poland

Abstract

Summary We continue the formal development of rough inclusion functions (RIFs), continuing the research on the formalization of rough sets [15] – a well-known tool of modelling of incomplete or partially unknown information. In this article we give the formal characterization of complementary RIFs, following a paper by Gomolińska [4]. We expand this framework introducing Jaccard index, Steinhaus generate metric, and Marczewski-Steinhaus metric space [1]. This is the continuation of [9]; additionally we implement also parts of [2], [3], and the details of this work can be found in [7].

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics

Link

https://www.sciendo.com/pdf/10.2478/forma-2020-0009

Reference17 articles.

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2. [2] Anna Gomolińska. Rough approximation based on weak q-RIFs. In James F. Peters, Andrzej Skowron, Marcin Wolski, Mihir K. Chakraborty, and Wei-Zhi Wu, editors, Transactions on Rough Sets X, volume 5656 of Lecture Notes in Computer Science, pages 117–135, Berlin, Heidelberg, 2009. Springer. ISBN 978-3-642-03281-3. doi:10.1007/978-3-642-03281-3_4.10.1007/978-3-642-03281-3_4

3. [3] Anna Gomolińska. On three closely related rough inclusion functions. In Marzena Kryszkiewicz, James F. Peters, Henryk Rybiński, and Andrzej Skowron, editors, Rough Sets and Intelligent Systems Paradigms, volume 4585 of Lecture Notes in Computer Science, pages 142–151, Berlin, Heidelberg, 2007. Springer. doi:10.1007/978-3-540-73451-2_16.10.1007/978-3-540-73451-2_16

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5. [5] Adam Grabowski. On the computer-assisted reasoning about rough sets. In B. Dunin-K¸eplicz, A. Jankowski, A. Skowron, and M. Szczuka, editors, International Workshop on Monitoring, Security, and Rescue Techniques in Multiagent Systems Location, volume 28 of Advances in Soft Computing, pages 215–226, Berlin, Heidelberg, 2005. Springer-Verlag. doi:10.1007/3-540-32370-8_15.10.1007/3-540-32370-8_15