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 formalization of rough sets [12], we give the formal characterization of three rough inclusion functions (RIFs). We start with the standard o...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2019-12-01
|
| Series: | Formalized Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/forma-2019-0028 |
| id |
doaj-6da23a9305a5424c9b44756c5deee01e |
|---|---|
| record_format |
Article |
| spelling |
doaj-6da23a9305a5424c9b44756c5deee01e2021-09-05T21:01:04ZengSciendoFormalized Mathematics1426-26301898-99342019-12-0127433734510.2478/forma-2019-0028forma-2019-0028Formal Development of Rough Inclusion FunctionsGrabowski Adam0Institute of Informatics, University of Białystok, PolandRough 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].https://doi.org/10.2478/forma-2019-0028rough setrough inclusionapproximation space03e7068t9903b35 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Grabowski Adam |
| spellingShingle |
Grabowski Adam Formal Development of Rough Inclusion Functions Formalized Mathematics rough set rough inclusion approximation space 03e70 68t99 03b35 |
| author_facet |
Grabowski Adam |
| author_sort |
Grabowski Adam |
| title |
Formal Development of Rough Inclusion Functions |
| title_short |
Formal Development of Rough Inclusion Functions |
| title_full |
Formal Development of Rough Inclusion Functions |
| title_fullStr |
Formal Development of Rough Inclusion Functions |
| title_full_unstemmed |
Formal Development of Rough Inclusion Functions |
| title_sort |
formal development of rough inclusion functions |
| publisher |
Sciendo |
| series |
Formalized Mathematics |
| issn |
1426-2630 1898-9934 |
| publishDate |
2019-12-01 |
| description |
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]. |
| topic |
rough set rough inclusion approximation space 03e70 68t99 03b35 |
| url |
https://doi.org/10.2478/forma-2019-0028 |
| work_keys_str_mv |
AT grabowskiadam formaldevelopmentofroughinclusionfunctions |
| _version_ |
1717781716958969856 |