Chordal distance and non-Archimedean chordal distance between Atanassov’s intuitionistic fuzzy set

Article type: Research Article

Authors: Han, Jing^a | Yang, Zhanpeng^{b; *} | Sun, Xian^b | Xu, Guangluan^b

Affiliations: [a] Department of Basic Teaching, Business College of Shanxi University, Taiyuan, PR China | [b] Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing, PR China

Correspondence: [*] Corresponding author. Zhanpeng Yang, Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, PR China. Tel.: +86 010 58887208; E-mail: [email protected].

Abstract: The non-Archimedean normed space theory is an important research object in mathematical physics whose triangle inequality holds in a stronger form. In this note, we propose a generalized chordal distance and a non-Archimedean chordal distance for intuitionistic fuzzy sets. An illustrative example is given to calculate the constructed distances with the different parameters. And some experiments show that the new distances based on chordal distance and non-Archimedean distance are more efficient than the Euclidean-like distances in pattern recognition.

Keywords: Non-Archimedean norm, chordal distance, intuitionistic fuzzy set

DOI: 10.3233/JIFS-17724

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3889-3894, 2017