New distance measure for Fermatean fuzzy sets and its application

International Journal of Intelligent SystemsVolume 37, Issue 3 p. 1903-1930 RESEARCH ARTICLE New distance measure for Fermatean fuzzy sets and its application Zhan Deng, Corresponding Author Zhan Deng [email protected] [email protected] orcid.org/0000-0003-0376-2564 School of Automation, Nanjing University of Science and Technology, Nanjing, China Correspondence Zhan Deng, School of Automation, Nanjing University of Science and Technology, 210094 Nanjing, China. Email: [email protected] and [email protected]Search for more papers by this authorJianyu Wang, Jianyu Wang orcid.org/0000-0001-9020-563X School of Automation, Nanjing University of Science and Technology, Nanjing, ChinaSearch for more papers by this author Zhan Deng, Corresponding Author Zhan Deng [email protected] [email protected] orcid.org/0000-0003-0376-2564 School of Automation, Nanjing University of Science and Technology, Nanjing, China Correspondence Zhan Deng, School of Automation, Nanjing University of Science and Technology, 210094 Nanjing, China. Email: [email protected] and [email protected]Search for more papers by this authorJianyu Wang, Jianyu Wang orcid.org/0000-0001-9020-563X School of Automation, Nanjing University of Science and Technology, Nanjing, ChinaSearch for more papers by this author First published: 09 December 2021 https://doi.org/10.1002/int.22760Citations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract As a new extended form of intuitionistic fuzzy sets, Fermatean fuzzy sets are powerful tools for describing vagueness and uncertainty in complex problems. In the method of handling Fermatean fuzzy information, the distance measure is an essential tool to depict the difference between two Fermatean fuzzy sets. However, how to accurately measure the distance between two Fermatean fuzzy sets is still a problem to be solved. In this paper, we devise two novel distance measure methods for Fermatean fuzzy sets. One is the distance measure of Fermatean fuzzy sets based on the Hellinger distance, which is called the FFSH distance. The other is the distance measure of Fermatean fuzzy sets based on the triangular divergence, which is called the FFSTD distance. Then, we prove that the proposed distance measure methods satisfy the axiomatic requirements of the distance function. Afterward, numerical examples are given to reveal that the proposed distance measures are more effective and reasonable than the normalized Euclidean distance measure, which can overcome the counter-intuitive situation. Besides, we utilize the proposed distance measure methods to address the problems of pattern recognition and medical diagnosis under Fermatean fuzzy environment and achieved excellent results. The experimental results illustrate that the proposed distance measure methods can efficiently handle the practical application under Fermatean fuzzy environment, and are more reliable than the normalized Euclidean distance measure. Citing Literature Volume37, Issue3March 2022Pages 1903-1930 RelatedInformation