Note on lexicographical ordering

Farhadinia (2016) developed a lexicographical ordering with respect to hesitant fuzzy elements. In this article,
we will demonstrate that his novel approach fails to satisfy the following three issues: (i) His ranking is
contradicted with previous existing results, (ii) His advantages for repeated items is no longer valid after we
adjust hesitant fuzzy elements with the same length and (iii) His proof for the component-wise ordering being
preserved by his new ranking method is redundant. Our derivations will help researchers realize questionable
results of the novel lexicographical ordering proposed by Farhadinia (2016).