Extension and revisions for Xu's proposed distance measure

摘要

Xu (2017) published a paper in Journal of Intelligent and Fuzzy Systems in which he constructs a new distance measure that not only satisfies the axiom of intuitionistic fuzzy sets, but also fulfills the axiom for traditional distance. However, several questionable results arise in Xu (2017). Thus, the purpose of this paper is threefold. First, his proof is improved. Second, his criticism for two previously published distance measures are amended. Third, it is shown that in his numerical examples, there are several poorly-founded discussions. The refinement will help readers understand Xu (2017) and then apply his new distance measure to pattern recognition problems and medical diagnosis problems.