Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution
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 exten...
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/5/381 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850257920960233472 |
|---|---|
| author | Najla Althuniyan Abedallah Al-shboul Sarah Aljohani Kah Lun Wang Kok Bin Wong Khaleed Alhazaymeh Suhad Subhi Aiady |
| author_facet | Najla Althuniyan Abedallah Al-shboul Sarah Aljohani Kah Lun Wang Kok Bin Wong Khaleed Alhazaymeh Suhad Subhi Aiady |
| author_sort | Najla Althuniyan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d7d0ba44711c478d8dc36bcfc8a3fdc8 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-d7d0ba44711c478d8dc36bcfc8a3fdc82025-08-20T01:56:17ZengMDPI AGAxioms2075-16802025-05-0114538110.3390/axioms14050381Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal SolutionNajla Althuniyan0Abedallah Al-shboul1Sarah Aljohani2Kah Lun Wang3Kok Bin Wong4Khaleed Alhazaymeh5Suhad Subhi Aiady6Department of Computer Sciences, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaInstitute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, MalaysiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaInstitute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, MalaysiaInstitute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, MalaysiaDepartment of Mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid 21110, JordanDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaThis 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.https://www.mdpi.com/2075-1680/14/5/381Fermatean neutrosophic vague soft setdecision-makingTOPSISFNVNWAGFNVNWA |
| spellingShingle | Najla Althuniyan Abedallah Al-shboul Sarah Aljohani Kah Lun Wang Kok Bin Wong Khaleed Alhazaymeh Suhad Subhi Aiady Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution Axioms Fermatean neutrosophic vague soft set decision-making TOPSIS FNVNWA GFNVNWA |
| title | Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution |
| title_full | Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution |
| title_fullStr | Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution |
| title_full_unstemmed | Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution |
| title_short | Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution |
| title_sort | decision making with fermatean neutrosophic vague soft sets using a technique for order of preference by similarity to ideal solution |
| topic | Fermatean neutrosophic vague soft set decision-making TOPSIS FNVNWA GFNVNWA |
| url | https://www.mdpi.com/2075-1680/14/5/381 |
| work_keys_str_mv | AT najlaalthuniyan decisionmakingwithfermateanneutrosophicvaguesoftsetsusingatechniquefororderofpreferencebysimilaritytoidealsolution AT abedallahalshboul decisionmakingwithfermateanneutrosophicvaguesoftsetsusingatechniquefororderofpreferencebysimilaritytoidealsolution AT sarahaljohani decisionmakingwithfermateanneutrosophicvaguesoftsetsusingatechniquefororderofpreferencebysimilaritytoidealsolution AT kahlunwang decisionmakingwithfermateanneutrosophicvaguesoftsetsusingatechniquefororderofpreferencebysimilaritytoidealsolution AT kokbinwong decisionmakingwithfermateanneutrosophicvaguesoftsetsusingatechniquefororderofpreferencebysimilaritytoidealsolution AT khaleedalhazaymeh decisionmakingwithfermateanneutrosophicvaguesoftsetsusingatechniquefororderofpreferencebysimilaritytoidealsolution AT suhadsubhiaiady decisionmakingwithfermateanneutrosophicvaguesoftsetsusingatechniquefororderofpreferencebysimilaritytoidealsolution |