Hesitant fuzzy numbers with (α, k)-cuts in compact intervals and applications

Archimedean t-Norm and t-Conorm-Based Aggregation Operators of HFNs, with the Approach of Improving Education

“…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].…”

“…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.…”

“…Utilizing such amounts are usually accompanied by some degree of skepticism by decision makers, when the initial conditions and assumptions have changed. In these cases, it does not make sense to use some uncertainty modeling due to the omission of some problem information, i.e., preset values [ 29 , 31 , 38 , 42 ], and others will add to the ambiguity of the problem [ 30 ]. Then, we need another type of HFNs, that include decision makers’ satisfaction scores in addition to the available values [ 43 , 44 ].…”

Multiple-Attribute Decision-Making Problem Using TOPSIS and Choquet Integral with Hesitant Fuzzy Number Information

“…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]).…”

“…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.…”