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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Bibliographic Details
Published in:Expert systems with applications 2020-08, Vol.151, p.113363, Article 113363
Main Authors: Ranjbar, Mahdi, Miri, Seyed Mohsen, Effati, Sohrab
Format: Article
Language:English
Subjects:
(α, k)-cut
Fuzzy sets
Hesitant fuzzy linear programming
Hesitant fuzzy number
Intervals
Linear programming
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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.
ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2020.113363