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The Scientific World Journal
Volume 2015, Article ID 735703, 10 pages
Research Article

Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric

1Department of Mathematics, Faculty of Sciences, Gazi University, 06500 Ankara, Turkey
2Department of Mathematics, Faculty of Sciences and Arts, Bozok University, 66100 Yozgat, Turkey
3Department of Mathematics, Faculty of Sciences and Arts, Batman University, 72060 Batman, Turkey

Received 30 May 2014; Revised 25 July 2014; Accepted 7 August 2014

Academic Editor: S. A. Mohiuddine

Copyright © 2015 Uğur Kadak and Muharrem Ozluk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.