Generalized hesitant fuzzy numbers: Introducing, arithmetic operations, aggregation operators, and an application

Abstract

Uncertainty modeling can be done by different theories, such as probability theory, fuzzy sets theory, vague sets theory, and so forth. Each of them may be appropriate for special cases and circumstances, based on the nature and type of the existing problem. In this

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

“…Keikha ( 2021 ) For the universal set , positive real numbers , and doubtness/membership/satisfaction degrees , the generalized hesitant fuzzy number is defined as As it is seen, a GHFN similar to a HFN contain two parts: a real values part, and a hesitation degrees part. For any two GHFNs, if cardinalities of their real values parts are equal, and simultaneously the cardinalities of their hesitation degrees parts are also the same, they are called adjusted GHFNs (AGHFNs).…”

“…Keikha ( 2021 ) For each GHFNs as , its mean value, score, and variance , displayed by , , and , respectively, can be obtained as follows: …”

“…Keikha ( 2021 ) Let and be two arbitrary GHFNs, with mean values and , respectively. Then, strongly superior ( s .…”

“…For example, fuzzy sets (FSs) theory (Zadeh 1965 ) and some of its generalizations, i.e., type-2 fuzzy sets (Karnik and Mendel 2001 ), intuitionistic fuzzy sets (IFSs) (Atanassov 1983 , 2022 ), Pythagorean fuzzy sets (Wang and Garg 2020 ), Hesitant fuzzy sets (HFSs) (Torra 2010 ), intuitionistic Hesitant fuzzy sets (Mahmood et al. 2021 ), Hesitant fuzzy numbers (HFNs) (Keikha 2021 ), and generalized Hesitant fuzzy numbers (GHFNs) (Keikha 2021 ) are justifiable from this perspective.…”

“…2018 ), interval type-2 HFSs (Hu et al. 2015 ), generalized HFNs (Keikha 2021 ) to solve problems more accurately. Considering that these are in fact kinds of quantification of non-quantitative/uncertain values, it is therefore urgently necessary to invent methods which can be used to carry out arithmetical operations, and aggregation operators (Keikha 2021 ; Liao and Xu 2014b ; Lobillo et al.…”