April 2026
Journal papers accepted FSS, INF
14/04/26/10:01 Filed in: Journal paper
R. Belohlavek and M. Ojeda-Hernández. On monotony of fuzzy closure. Fuzzy Sets and Systems 109849, 2026
ABSTRACT Closure operators and systems play a significant role in a variety of areas of fuzzy logic. While the condition of monotony for ordinary closure operators has a straightforward form, two basic conditions of monotony naturally arise from the existing examples in a fuzzy setting. To unify these two conditions, two approaches can be found in the literature, one based on the notion of a filter of truth degrees and the other on the notion of a linguistic hedge. We present results connecting these approaches, explore their variants, and provide a notion of monotony that subsumes both the filter-based and hedge-based approaches. We study properties of this general concept of monotony and discuss open problems along with topics for future research.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero, E. Muñoz-Velasco. Characterising quasi-closed elements via closure systems on complete fuzzy lattices. Informatica, 2026 (to appear)
ABSTRACT The notion of quasi-closed element plays a central role in several branches of mathematics and computer sciences, for instance, in the Duquenne-Guigues basis of attribute implications. This paper deals with the extension of quasi-closed elements to the fuzzy setting by extending the well-known characterisation of quasi-closed elements in the crisp case, which is given in terms of closure systems. Specifically, we provide two distinct definitions, one considering crisp closure systems and another for fuzzy ones. Finally, we obtain a characterisation for each one of these notions..
ABSTRACT Closure operators and systems play a significant role in a variety of areas of fuzzy logic. While the condition of monotony for ordinary closure operators has a straightforward form, two basic conditions of monotony naturally arise from the existing examples in a fuzzy setting. To unify these two conditions, two approaches can be found in the literature, one based on the notion of a filter of truth degrees and the other on the notion of a linguistic hedge. We present results connecting these approaches, explore their variants, and provide a notion of monotony that subsumes both the filter-based and hedge-based approaches. We study properties of this general concept of monotony and discuss open problems along with topics for future research.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero, E. Muñoz-Velasco. Characterising quasi-closed elements via closure systems on complete fuzzy lattices. Informatica, 2026 (to appear)
ABSTRACT The notion of quasi-closed element plays a central role in several branches of mathematics and computer sciences, for instance, in the Duquenne-Guigues basis of attribute implications. This paper deals with the extension of quasi-closed elements to the fuzzy setting by extending the well-known characterisation of quasi-closed elements in the crisp case, which is given in terms of closure systems. Specifically, we provide two distinct definitions, one considering crisp closure systems and another for fuzzy ones. Finally, we obtain a characterisation for each one of these notions..