title: Some new sets of sequences of fuzzy numbers with respect to the partial metric.
abstract: In this paper, we essentially deal with Köthe-Toeplitz duals of fuzzy level sets defined using a partial metric. Since the utilization of Zadeh's extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct some classical notions. In this paper, we present the sets of bounded, convergent, and null series and the set of sequences of bounded variation of fuzzy level sets, based on the partial metric. We examine the relationships between these sets and their classical forms and give some properties including definitions, propositions, and various kinds of partial metric spaces of fuzzy level sets. Furthermore, we study some of their properties like completeness and duality. Finally, we obtain the Köthe-Toeplitz duals of fuzzy level sets with respect to the partial metric based on a partial ordering.
authors.affiliation: Department of Mathematics, Faculty of Sciences, Gazi University, 06500 Ankara, Turkey ; Department of Mathematics, Faculty of Sciences and Arts, Bozok University, 66100 Yozgat, Turkey.
authors.forename: Uğur
authors.identifier: 0000-0001-7095-5257
authors.initials: U
authors.lastname: Kadak
authors.affiliation: Department of Mathematics, Faculty of Sciences, Gazi University, 06500 Ankara, Turkey ; Department of Mathematics, Faculty of Sciences and Arts, Batman University, 72060 Batman, Turkey.
authors.forename: Muharrem
authors.initials: M
authors.lastname: Ozluk