Multilattice as the set of truth values for fuzzy rough sets

Nguepy Dongmo, G.; Koguep Njionou, B. B.; Kwuida, Léonard; Onabid, M. (2024). Multilattice as the set of truth values for fuzzy rough sets Journal of Applied Non-Classical Logics, pp. 1-20. Taylor & Francis 10.1080/11663081.2024.2373016

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Radzikowska and Kerre developed L-fuzzy rough set as a fuzzy generalisation of the notion of rough sets. Specifically, they have taken a residuated lattice L as the underlying set of truth degrees. However, in real life, we may encounter situations where truth degrees are not always linear, or where the existence of the least upper bound of two elements is no longer required. Instead, there may be the possibility of having minimal upper bounds, and dually, maximal lower bounds, multilattices have become a suitable algebraic structure for addressing such cases. Our aim is to extend Radzikowska and Kerre's work by replacing a residuated lattice with a multilattice M, thereby obtaining a more flexible structure. We define M-fuzzy rough sets using operators derived from adjoint pairs within the multilattice M. For a tolerance and an equivalence M-fuzzy relation, we define an appropriate M-fuzzy rough set and investigate its properties.

Item Type:	Journal Article (Original Article)
Division/Institute:	Business School > Institute for Applied Data Science & Finance Business School > Institute for Applied Data Science & Finance > Applied Data Science Business School
Name:	Nguepy Dongmo, G.; Koguep Njionou, B. B.; Kwuida, Léonard0000-0002-9811-0747 and Onabid, M.
ISSN:	1166-3081
Publisher:	Taylor & Francis
Language:	English
Submitter:	Léonard Kwuida
Date Deposited:	21 Aug 2024 13:52
Last Modified:	22 Aug 2024 01:30
Publisher DOI:	10.1080/11663081.2024.2373016
Uncontrolled Keywords:	Fuzzy set; multilattice; adjoint pair; lower approximation; upper approximation
ARBOR DOI:	10.24451/arbor.22210
URI:	https://arbor.bfh.ch/id/eprint/22210