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

Document Type : Research Paper

Authors

1 Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

2 College of Science, Southwest Petroleum University, Chengdu 610500, Sichuan, China

Abstract

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