Fermatean Fuzzy Divergences and Their Applications to Decision-making and Pattern Recognition

Authors

  • Wiyada Kumam Lecturer, Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand https://orcid.org/0000-0001-8773-4821
  • Konrawut Khammahawong Lecturer, Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT) https://orcid.org/0000-0002-7423-8519
  • Muhammad Jabir Khan King Mongkut’s University of Technology Thonburi (KMUTT) https://orcid.org/0000-0002-7983-706X
  • Thanatporn Bantaojai Valaya Alongkorn Rajabhat University under the Royal Patronage https://orcid.org/0000-0001-9259-7462
  • Supak Phiangsungnoen General Education (Mathematics Program), Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin, Samphanthawong https://orcid.org/0000-0003-2227-4304

DOI:

https://doi.org/10.58715/ncao.2023.2.2

Keywords:

Fermatean fuzzy sets, Decision making, Divergence measures, VIKOR method, Fuzzification technique

Abstract

Fermatean fuzzy sets (FFS) generalized the Intuitionistic fuzzy set and Pythagorean fuzzy set in terms of more space available to choose orthopairs. The manuscript provides Chi-square and Canberra divergence measures for FFSs. Divergence measurements’ additional characteristics are looked into to ensure good performance. The entropy and dissimilarity measures from the suggested divergence measures are derived. A technique is developed to transform the real or fuzzy data into Fermatean fuzzy data. An empirically successful VIKOR method is extended for FFSs. The Australasian New Car Assessment Program
(ANCAP) provides the star rankings from a safety point of view for each vehicle. The VIKOR method is employed to draw safety rankings of small cars tested from 2019 to 2021 by ANCAP. The numerical examples are given to clarify each method under discussion.

Author Biographies

Konrawut Khammahawong, Lecturer, Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT)

Assistant Professor in Asst.Prof. at Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110,
Thailand

Muhammad Jabir Khan, King Mongkut’s University of Technology Thonburi (KMUTT)

Researcher, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand

Thanatporn Bantaojai, Valaya Alongkorn Rajabhat University under the Royal Patronage

Mathematics (English Program), Faculty of Education, Valaya Alongkorn Rajabhat University
under the Royal Patronage, Pathum Thani 13160, Thailand

Supak Phiangsungnoen, General Education (Mathematics Program), Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin, Samphanthawong

Assistant Professor in Mathematics at  Rajamangala University of Technology Rattanakosin, Samphanthawong, Bangkok 10100, Thailand 

 

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Published

2023-06-30

How to Cite

Kumam, W., Khammahawong, K., Khan, M. J., Bantaojai, T., & Phiangsungnoen, S. (2023). Fermatean Fuzzy Divergences and Their Applications to Decision-making and Pattern Recognition. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 2(1), 31–53. https://doi.org/10.58715/ncao.2023.2.2

Issue

Vol. 2 No. 1 (2023): January - June, 2023

Section

Articles

License

Copyright (c) 2023 Wiyada Kumam, Konrawut Khammahawong, Muhammad Jabir Khan, Thanatporn Bantaojai, Supak Phiangsungnoen

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