Frank Aggregation Operators and Their Application to Probabilistic Hesitant Fuzzy Multiple Attribute Decision-Making

Complex q-rung orthopair fuzzy Frank aggregation operators and their application to multi-attribute decision making

“…In recent years, the Frank operator has received increased attention from the scientific community, and it has achieved a lot of researcher results on different fuzzy sets. Some operations on various fuzzy sets have been introduced based on the Frank T-norm and S-norm, such as intuitionistic Frank operations (Xia et al 2012 ; Zhang et al 2015 ), single-valued neutrosophic Frank operations (Garg 2016 ), hesitant Frank operations (Qin et al 2016), dual-hesitant fuzzy Frank operations (Wang et al 2016 ), interval intuitionistic linguistic Frank aggregation operators (Du and Hou 2018 ), Frank prioritized Bonferroni mean operations (Ji et al 2018 ), linguistic intuitionistic fuzzy Frank weighted Heronian mean operator (Peng et al 2018 ), interval-valued probabilistic hesitant fuzzy aggregation operators (Yahya et al 2021 ), triangular interval type-2 fuzzy Frank operations (Qin and Liu 2014 ), interval-valued Pythagorean Frank power operations (Yang et al 2018), picture fuzzy Frank weighted averaging operator (Seikh and Mandal 2021a ). Some researchers also studied various mathematical properties of the Frank t-norms (Liu et al 2018 ; Xing et al 2019 ; Zhou et al 2019 ; Seikh and Mandal 2021b ).…”

Various aggregation operators of the generalized hesitant fuzzy numbers based on Archimedean t-norm and t-conorm functions

“…Due to various practical problems, the conventional model of HFSs did not meet the needs of researchers, and as a result they have been developed to interval-valued HFSs (Yahya et al. 2021 ), generalized trapezoidal hesitant fuzzy numbers (Deli 2020 ), HFNs with two completely different and separate definitions (Ranjbar et al. 2020 ; Keikha 2021 ), type-2 HFSs (Liu et al.…”

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

“…The wide range of applications of HFSs have led to many generalizations, each of which is subject to specific conditions. For example, if the decision maker expresses the degrees of doubt as intervals between 0 and 1, the interval-valued hesitant fuzzy sets (IVHFSs) are defined [ 29 ]. Recently, other generalizations of HFSs called hesitant fuzzy numbers (HFNs) have been introduced and utilized in solving decision-making problems.…”

“…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 ].…”

“…These functions are called t -norm and t -conorm [ 47 ], and different types have been defined so far: Frank, Hamacher, Einstein, algebraic, etc. There are some aggregation operators for HFSs using Frank, Hamacher, Einstein, Dombi, and algebraic t -norms and t -conorms [ 12 , 29 , 48 – 52 ]. It should be noted that, like any other new concept, HFNs have been introduced in response to the need for some real decision situations, which existing methods are unable to solve them.…”