Affiliations: [a] School of Data Science and Intelligent Engineering, Xiamen Institute of Technology, Xiamen, P.R. China
| [b] Academy of Foundational Education, Neusoft Institute Guangdong, Foshan, P.R. China
| [c] School of Artificial Intelligence, Beijing Normal University, Beijing, P.R. China
| [d] Business School, Sichuan University Chengdu, P.R. China
Correspondence:
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Corresponding authors. Wenyi Zeng and Rong Ma, School of Artificial Intelligence, Beijing Normal University, Beijing 100875, P.R. China. Tel.: +86 10 58805665; Fax: +86 10 58808313; E-mails: zengwy@bnu.edu.cn (Wenyi Zeng); macrosse@163.com (Rong Ma).
Abstract: Pythagorean fuzzy sets, as a generalization of intuitionistic fuzzy sets, have a wide range of applications in many fields including image recognition, data mining, decision making, etc. However, there is little research on clustering algorithms of Pythagorean fuzzy sets. In this paper, a novel clustering idea under Pythagorean fuzzy environment is presented. Firstly, the concept of feature vector of Pythagorean fuzzy number (PFN) is presented by taking into account five parameters of PFN, and some new methods to compute the similarity measure of PFNs by applying the feature vector are proposed. Furthermore, a fuzzy similarity matrix by utilizing similarity measure of PFNs is established. Later, the fuzzy similarity matrix is transformed into a fuzzy equivalent matrix which is utilized to establish a novel Pythagorean fuzzy clustering algorithm. Based on the proposed clustering algorithm, a novel multiple attribute decision making (MADM) method under Pythagorean fuzzy environment is presented. To illustrate the effectiveness and feasibility of the proposed technique, an application example is offered.
