Ordering finitely generated sets and finite interval-valued hesitant fuzzy sets

Ordering sets is a long-standing open problem due to its remarkable importance in many areas such as decision making, image processing or human reliability. This work is focused on introducing methods for ordering finitely generated sets as a generalization of those methods previously defined for ordering intervals. In addition, these orders between finitely generated sets are also improved to present orders between finite interval-valued hesitant fuzzy sets. Finally, finite interval-valued hesitant fuzzy preference relations are introduced and used to define a new order between finite interval-valued hesitant fuzzy sets.