The Relations between Residuated Frames and Residuated Connections

Yong Chan Kim and Ju-Mok Oh
Additional contact information
Yong Chan Kim: Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo 25457, Korea
Ju-Mok Oh: Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo 25457, Korea

Mathematics, 2020, vol. 8, issue 2, 1-24

Abstract: We introduce the notion of (dual) residuated frames as a viewpoint of relational semantics for a fuzzy logic. We investigate the relations between (dual) residuated frames and (dual) residuated connections as a topological viewpoint of fuzzy rough sets in a complete residuated lattice. As a result, we show that the Alexandrov topology induced by fuzzy posets is a fuzzy complete lattice with residuated connections. From this result, we obtain fuzzy rough sets on the Alexandrov topology. Moreover, as a generalization of the Dedekind–MacNeille completion, we introduce R - R (resp. D R - D R ) embedding maps and R - R (resp. D R - D R ) frame embedding maps.

Keywords: complete residuated lattice; (dual) residuated frames; (dual) residuated connections; R - R (resp. DR - DR ) embedding maps (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/2/295/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/2/295/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:2:p:295-:d:323573

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().