{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:17:26Z","timestamp":1760059046104,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T00:00:00Z","timestamp":1747612800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study addresses the challenge of effectively modeling uncertainty and hesitation in complex decision-making environments, where traditional fuzzy and vague set models often fall short. To overcome these limitations, we propose the Fermatean neutrosophic vague soft set (FNVSS), an advanced extension that integrates the concepts of neutrosophic sets with Fermatean membership functions into the framework of vague sets. The FNVSS model enhances the representation of truth, indeterminacy, and falsity degrees, providing greater flexibility and resilience in capturing ambiguous and imprecise information. We systematically develop new operations for the FNVSS, including union, intersection, complementation, the Fermatean neutrosophic vague normalized weighted average (FNVNWA) operator, the generalized Fermatean neutrosophic vague normalized weighted average (GFNVNWA) operator, and an adapted Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method. To demonstrate the practicality of the proposed methodology, we apply it to a solar panel selection problem, where managing uncertainty is crucial. Comparative results indicate that the FNVSS significantly outperforms traditional fuzzy and vague set approaches, leading to more reliable and accurate decision outcomes. This work contributes to the advancement of predictive decision-making systems, particularly in fields requiring high precision, adaptability, and robust uncertainty modeling.<\/jats:p>","DOI":"10.3390\/axioms14050381","type":"journal-article","created":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T07:34:03Z","timestamp":1747640043000},"page":"381","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution"],"prefix":"10.3390","volume":"14","author":[{"given":"Najla","family":"Althuniyan","sequence":"first","affiliation":[{"name":"Department of Computer Sciences, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-9898-0880","authenticated-orcid":false,"given":"Abedallah","family":"Al-shboul","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-2035-0880","authenticated-orcid":false,"given":"Sarah","family":"Aljohani","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3554-322X","authenticated-orcid":false,"given":"Kah Lun","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia"}]},{"given":"Kok Bin","family":"Wong","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9139-3150","authenticated-orcid":false,"given":"Khaleed","family":"Alhazaymeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid 21110, Jordan"},{"name":"Jadara Research Center, Jadara University, Irbid 21110, Jordan"}]},{"given":"Suhad Subhi","family":"Aiady","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. 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