<abstract xmlns="http://www.w3.org/1999/xhtml">Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article, continuing the formalization of rough sets [12], we give the formal characterization of three rough inclusion functions (RIFs). We start with the standard one, <italic>κ£</italic>, connected with Łukasiewicz [14], and extend this research for two additional RIFs: <italic>κ</italic>1, and <italic>κ</italic>2, following a paper by Gomolińska [4], [3]. We also define q-RIFs and weak q-RIFs [2]. The paper establishes a formal counterpart of [7] and makes a preliminary step towards rough mereology [16], [17] in Mizar [13].</abstract>

Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article, continuing the formalization of rough sets [12], we give the formal characterization of three rough inclusion functions (RIFs). We start with the standard one, κ£, connected with Łukasiewicz [14], and extend this research for two additional RIFs: κ1, and κ2, following a paper by Gomolińska [4], [3]. We also define q-RIFs and weak q-RIFs [2]. The paper establishes a formal counterpart of [7] and makes a preliminary step towards rough mereology [16], [17] in Mizar [13].

Formal Development of Rough Inclusion Functions

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.

{"article-title":"Formal Development of Rough Inclusion Functions"}

Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article, continuing the...

Formal Development of Rough Inclusion Functions

Published Online: Feb 20, 2020

Page range: 337 - 345

Accepted: Aug 29, 2019

DOI: https://doi.org/10.2478/forma-2019-0028

Keywords
rough set, rough inclusion, approximation space

© 2019 Adam Grabowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.

Formal Development of Rough Inclusion Functions

Published Online: Feb 20, 2020

Page range: 337 - 345

Accepted: Aug 29, 2019

DOI: https://doi.org/10.2478/forma-2019-0028

Keywordsrough set, rough inclusion, approximation space

© 2019 Adam Grabowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.

Keywords
rough set, rough inclusion, approximation space