Affiliations: [a] Department of Mathematics, Abdul Wali Khan University, Mardan, KP, Pakistan
| [b] Department of Mathematics, College of Sciences, King Khalid University, Abha, Saudi Arabia
| [c] Center for Combinatorics, Nankai University, Tianjin, China
Correspondence:
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Corresponding author. Asghar Khan, Department of Mathematics, Abdul Wali Khan University, Mardan, KP, Pakistan E-mail: azhar4set@yahoo.com.
Abstract: Many unknowable elements make it difficult to measure cyclone disasters, traditional methods are insufficient to measure these factors. Fuzzy set theory and its expansions are effective ways to measure these uncertainties for these kinds of uncertainty. An evaluation of the cyclone disaster’s spatial vulnerability is necessary in order to build disaster damage reduction methods. In real life, we may come into a hesitant environment when making decisions. To explore such environments, we introduce hesitant fuzzy set (HFS) into Fermatean fuzzy set (FFS) and extend the existing research effort on FFSs in light of the effective tool of HFSs for expressing the hesitant condition. In this study, we develop a comprehensive tropical cyclone disaster assessment by applying Fermatean hesitant fuzzy (FHF) information. In this paper, various unique aggregation strategies for the analysis of decision-making problems are introduced. As a result, Fermatean hesitant fuzzy average (FHFWA), Fermatean hesitant fuzzy ordered weighted average (FHFOWA), Fermatean hesitant fuzzy weighted geometric (FHFWG), and Fermatean hesitant fuzzy ordered weighted geometric (FHFOWG) operators have been developed. We also go over some of the most important features of these operators. Furthermore, we establish an algorithm for addressing a multiple attribute decision-making issue employing Fermatean hesitant fuzzy data by using these operators. and attribute prioritizing. A real-world problem of cyclone disaster damages in several parts of Pakistan is explored to test the applicability of these operators. In the final section, we expand the TOPSIS approach to a Fermatean hesitant fuzzy environment and compare the outcomes of the extended TOPSIS method with operators established in the FHF-environment.
