Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric
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 pres...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/735703 |
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| author | Uğur Kadak Muharrem Ozluk |
| author_facet | Uğur Kadak Muharrem Ozluk |
| author_sort | Uğur Kadak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4ca9b7565b234ab8934433f65c1dfbef |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-4ca9b7565b234ab8934433f65c1dfbef2025-02-03T01:32:50ZengWileyThe Scientific World Journal2356-61401537-744X2015-01-01201510.1155/2015/735703735703Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial MetricUğur Kadak0Muharrem Ozluk1Department of Mathematics, Faculty of Sciences, Gazi University, 06500 Ankara, TurkeyDepartment of Mathematics, Faculty of Sciences, Gazi University, 06500 Ankara, TurkeyIn 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.http://dx.doi.org/10.1155/2015/735703 |
| spellingShingle | Uğur Kadak Muharrem Ozluk Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric The Scientific World Journal |
| title | Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric |
| title_full | Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric |
| title_fullStr | Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric |
| title_full_unstemmed | Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric |
| title_short | Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric |
| title_sort | some new sets of sequences of fuzzy numbers with respect to the partial metric |
| url | http://dx.doi.org/10.1155/2015/735703 |
| work_keys_str_mv | AT ugurkadak somenewsetsofsequencesoffuzzynumberswithrespecttothepartialmetric AT muharremozluk somenewsetsofsequencesoffuzzynumberswithrespecttothepartialmetric |