Title of article :
Negations and aggregation operators based on a new hesitant fuzzy partial ordering
Author/Authors :
Ye, M. College of Science - Southwest Petroleum University, Chengdu, Sichuan, China , Jin, J. College of Science - Southwest Petroleum University, Chengdu, Sichuan, China , Feng, Y. College of Science - Southwest Petroleum University, Chengdu, Sichuan, China
Abstract :
Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al. [7], 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 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 Nn on H and n on 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 B
respectively, where C is a commutative fuzzy conjunction
on (H;H) and T is a t-norm on (B
;B). Finally, the new hesitant fuzzy aggregation operators are presented on H
and 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
Journal title :
Iranian Journal of Fuzzy Systems (IJFS)
