Affiliations: [a] Department of Tourism, Aletheia University, Zhenli St., Danshui Dist., New Taipei City, Taiwan (R.O.C.) | [b] Department of Hotel Management, Lee-Ming Institute of Technology, Tai-Lin Rd., Taishan Dist., New Taipei City, Taiwan (R.O.C.) | [c] Department of Traffic Science, Central Police University, Shujen Rd., Takang Vil., Kueishan District, Taoyuan City, Taiwan (R.O.C.)
Correspondence:
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Corresponding author. Chun-Hsiao Chu, Department of Tourism, Aletheia University, No.32, Zhenli St., Danshui Dist.,
New Taipei City, Taiwan (R.O.C.). E-mail: [email protected].
Abstract: 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.
