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In this paper, we essentially deal withKöthe-Toeplitz duals of fuzzy level sets defined using a partial metric. Since the utilization of Zadeh’sextension principle is quite difficult in practice, we prefer the idea of level sets in order to constructsome classical notions. In this paper, we present the sets of bounded, convergent, and null series and theset of sequences of bounded variation of fuzzy level sets, based on the partial metric. We examine therelationships 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 oftheir properties like completeness and duality. Finally, we obtain the Köthe-Toeplitz duals of fuzzy levelsets with respect to the partial metric based on a partial ordering.

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