Partial orderings for hesitant fuzzy sets

New partial orderings ≤o, ≤p and ≤H are defined, studied and compared on the set H of finite subsets of the unit interval with special emphasis on the last one. Since comparing two sets of the same cardinality is a simple issue, the idea for comparing two sets A and B of different cardinalities n and m respectively using ≤H is repeating their elements in order to obtain two series with the same length. If lcm(n,m) is the least common multiple of n and m we can repeat every element of A lcm(n,m)/m times and every element of B lcm(n,m)/n times to obtain such series and compare them (Definition 2.2).