Negations and aggregation operators based on a new hesitant fuzzy partial ordering

Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~\cite{GaCa:Pohfs}, in this paper a fuzzy disjunction {D} on the set {H} of finite and nonempty subsets of the unit interval and a t-conorm {S} on the set \bar{{B}} of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negations N_n on {H} and \mu_n on \bar{{B}} are proposed. Particularly, their De Morgan's laws are investigated with respect to binary operations {C}  and {D} on {H}, as well as {T}  and {S} on \bar{{B}} respectively, where {C} is a commutative fuzzy conjunction on ({H},\leq_H) and {T} is a t-norm on (\bar{{B}},\leq_B). Finally, the new hesitant fuzzy aggregation operators are presented on {H} and \bar{{B}} and their more general forms are given. Moreover, the validity of the aggregation operations is illustrated by a numerical example on decision making.

Keywords:

Hesitant fuzzy sets , Finite subsets of the unit interval , Partial ordering , t-conorm , Negation , Aggregation operation