Hesitant fuzzy numbers with (α, k)-cuts in compact intervals and applications
•Extension of the fuzzy numbers into hesitant fuzzy numbers.•Introduction a new hesitation fuzzy relationship to compare two HFNs.•Introduction a new binary operation on hesitant fuzzy numbers.•Solving a linear programming with hesitant fuzzy parameters. In this paper, we propose a new definition of...
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| Published in: | Expert systems with applications Vol. 151; p. 113363 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Elsevier Ltd
01.08.2020
Elsevier BV |
| Subjects: | |
| ISSN: | 0957-4174, 1873-6793 |
| Online Access: | Get full text |
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| Summary: | •Extension of the fuzzy numbers into hesitant fuzzy numbers.•Introduction a new hesitation fuzzy relationship to compare two HFNs.•Introduction a new binary operation on hesitant fuzzy numbers.•Solving a linear programming with hesitant fuzzy parameters.
In this paper, we propose a new definition of hesitant fuzzy numbers (HFNs) and study some essential properties of these numbers. We show (α, k)-cuts that were discussed in the recent literature for hesitant fuzzy sets (HFSs), on HFNs have resulted in compact intervals. In the following, we propose a new binary operation on these numbers. It has shown that the outcome of the proposed operation is a HFN. In addition, a new hesitant fuzzy relationship for comparing two HFNs is given. Finally, some applications of these numbers are presented in two examples. For this purpose, we propose a new approach to solve linear programming with hesitant fuzzy parameters. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0957-4174 1873-6793 |
| DOI: | 10.1016/j.eswa.2020.113363 |