2020
DOI: 10.1016/j.eswa.2020.113363
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Hesitant fuzzy numbers with (α, k)-cuts in compact intervals and applications

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Cited by 18 publications
(13 citation statements)
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“…Due to flexibility of HFEs in modeling experimental problems, researchers have defined new extensions of them [ 31 ]. For a fixed set X , , and real numbers , Deli [ 30 ] proposed generalized trapezoidal HFNs (GTHF-numbers) as , where is a set of some values in [0, 1].…”
Section: Some Basic Concepts and Definitionsmentioning
confidence: 99%
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“…Due to flexibility of HFEs in modeling experimental problems, researchers have defined new extensions of them [ 31 ]. For a fixed set X , , and real numbers , Deli [ 30 ] proposed generalized trapezoidal HFNs (GTHF-numbers) as , where is a set of some values in [0, 1].…”
Section: Some Basic Concepts and Definitionsmentioning
confidence: 99%
“…Deli [ 30 ] used a finite set of trapezoidal fuzzy numbers as the elements of HFEs that are called the generalized trapezoidal HFNs (GTHFNs). Ranjbar [ 31 ] assumed that the membership degrees of HFSs were not defined by crisp numbers, but by fuzzy numbers in [0, 1]. This extension is called HFNs, too.…”
Section: Introductionmentioning
confidence: 99%
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“…With the extension of applications of HFSs in the real world on the one hand and variety and complexity of real problems on the other hand, it was cleared that existing kind of HFSs cannot model all situations. For this reason, different types of hesitant fuzzy numbers (HFNs) with reference set R, as the generalization of HFSs, have been proposed [25,43]. Definition 7 (see [25]).…”
Section: Preliminariesmentioning
confidence: 99%
“…From the above investigation, it has been observed that the HFS is a powerful tool to solve the decision-making problems and hence widely used in the literature. Recently, Ranjbar et al [43] presented a new extension of the fuzzy numbers to the hesitant fuzzy numbers (HFNs). Also, they defined the (α, k) cuts of HFNs, binary operations, and a relationship for comparing the two HFNs.…”
Section: Introductionmentioning
confidence: 99%