A Metaphor for Rough Set Theory: Modular Arithmetic
© Springer Nature Switzerland AG 20118. Technically put, a metaphor is a conceptual mapping between two domains, which allows one to better understand the target domain; as Lakoff and Núñes put it, the main function of a metaphor is to allow us to reason about relatively abstract domains using the i...
| Main Authors: | , |
|---|---|
| Format: | Conference Paper |
| Published: |
2018
|
| Online Access: | http://hdl.handle.net/20.500.11937/71542 |
| _version_ | 1848762507593777152 |
|---|---|
| author | Wolski, Marcin Gomolinska, A. |
| author_facet | Wolski, Marcin Gomolinska, A. |
| author_sort | Wolski, Marcin |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © Springer Nature Switzerland AG 20118. Technically put, a metaphor is a conceptual mapping between two domains, which allows one to better understand the target domain; as Lakoff and Núñes put it, the main function of a metaphor is to allow us to reason about relatively abstract domains using the inferential structure of relatively concrete domains. In the paper we would like to apply this idea of framing one domain through conceptual settings of another domain to rough set theory (RST). The main goal is to construe rough sets in terms of the following mathematical metaphor: RST is a modular set-arithmetic. That is, we would like to map/project modular arithmetic onto rough sets, and, as a consequence, to redefine the fundamental concepts/objects of RST. Specifically, we introduce new topological operators (which play a similar role as remainders in modular arithmetic), discuss their formal properties, and finally apply them to the problem of vagueness (which has been intertwined with RST since the 1980’s). |
| first_indexed | 2025-11-14T10:48:40Z |
| format | Conference Paper |
| id | curtin-20.500.11937-71542 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:48:40Z |
| publishDate | 2018 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-715422018-12-14T01:02:40Z A Metaphor for Rough Set Theory: Modular Arithmetic Wolski, Marcin Gomolinska, A. © Springer Nature Switzerland AG 20118. Technically put, a metaphor is a conceptual mapping between two domains, which allows one to better understand the target domain; as Lakoff and Núñes put it, the main function of a metaphor is to allow us to reason about relatively abstract domains using the inferential structure of relatively concrete domains. In the paper we would like to apply this idea of framing one domain through conceptual settings of another domain to rough set theory (RST). The main goal is to construe rough sets in terms of the following mathematical metaphor: RST is a modular set-arithmetic. That is, we would like to map/project modular arithmetic onto rough sets, and, as a consequence, to redefine the fundamental concepts/objects of RST. Specifically, we introduce new topological operators (which play a similar role as remainders in modular arithmetic), discuss their formal properties, and finally apply them to the problem of vagueness (which has been intertwined with RST since the 1980’s). 2018 Conference Paper http://hdl.handle.net/20.500.11937/71542 10.1007/978-3-319-99368-3_9 restricted |
| spellingShingle | Wolski, Marcin Gomolinska, A. A Metaphor for Rough Set Theory: Modular Arithmetic |
| title | A Metaphor for Rough Set Theory: Modular Arithmetic |
| title_full | A Metaphor for Rough Set Theory: Modular Arithmetic |
| title_fullStr | A Metaphor for Rough Set Theory: Modular Arithmetic |
| title_full_unstemmed | A Metaphor for Rough Set Theory: Modular Arithmetic |
| title_short | A Metaphor for Rough Set Theory: Modular Arithmetic |
| title_sort | metaphor for rough set theory: modular arithmetic |
| url | http://hdl.handle.net/20.500.11937/71542 |