Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure

Reham A Alahmadi; Abdul Haseeb Ganie; Yousef Al-Qudah; Mohammed M Khalaf; Abdul Hamid Ganie

doi:10.1007/s41066-023-00378-x

Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure

Granul Comput. 2023 Apr 3:1-21. doi: 10.1007/s41066-023-00378-x. Online ahead of print.

Authors

Reham A Alahmadi¹, Abdul Haseeb Ganie², Yousef Al-Qudah³, Mohammed M Khalaf⁴, Abdul Hamid Ganie¹

Affiliations

¹ Basic Sciences Department, College of Science and Theoretical Studies, Saudi Electronic University, PO Box 93499, Riyadh, 11673 Kingdom of Saudi Arabia.
² Department of Mathematics, National Institute of Technology, Warangal, Telangana 506004 India.
³ Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953 Jordan.
⁴ Department of Mathematics, Higher Institute of Engineering and Technology, King Marriott, P.O. Box 3135, Egypt, Egypt.

Abstract

To deal with situations involving uncertainty, Fermatean fuzzy sets are more effective than Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. Applications for fuzzy similarity measures can be found in a wide range of fields, including clustering analysis, classification issues, medical diagnosis, etc. The computation of the weights of the criteria in a multi-criteria decision-making problem heavily relies on fuzzy entropy measurements. In this paper, we employ t-conorms to suggest various Fermatean fuzzy similarity measures. We have also discussed all of their interesting characteristics. Using the suggested similarity measurements, we have created some new entropy measures for Fermatean fuzzy sets. By using numerical comparison and linguistic hedging, we have established the superiority of the suggested similarity metrics and entropy measures over the existing measures in the Fermatean fuzzy environment. The usefulness of the proposed Fermatean fuzzy similarity measurements is shown by pattern analysis. Last but not least, a novel multi-attribute decision-making approach is described that tackles a significant flaw in the order preference by similarity to the ideal solution, a conventional approach to decision-making, in a Fermatean fuzzy environment.

Keywords: Entropy measure; Fermatean fuzzy set; Fuzzy set; Multi-attribute decision-making; Similarity measure; t-Conorm.

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