An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator
The single valued neutrosophic probabilistic hesitant fuzzy rough Einstein aggregation operator (SV-NPHFRE-AO) is an extension of the neutrosophic probabilistic hesitant fuzzy rough set theory. It is a powerful decision-making tool that combines the concepts of neutrosophic logic, probability theory...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-06-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231051?viewType=HTML |
| _version_ | 1797784202378215424 |
|---|---|
| author | Jia-Bao Liu Rashad Ismail Muhammad Kamran Esmail Hassan Abdullatif Al-Sabri Shahzaib Ashraf Ismail Naci Cangul |
| author_facet | Jia-Bao Liu Rashad Ismail Muhammad Kamran Esmail Hassan Abdullatif Al-Sabri Shahzaib Ashraf Ismail Naci Cangul |
| author_sort | Jia-Bao Liu |
| collection | DOAJ |
| description | The single valued neutrosophic probabilistic hesitant fuzzy rough Einstein aggregation operator (SV-NPHFRE-AO) is an extension of the neutrosophic probabilistic hesitant fuzzy rough set theory. It is a powerful decision-making tool that combines the concepts of neutrosophic logic, probability theory, hesitant fuzzy sets, rough sets, and Einstein aggregation operators. SV-NPHFRE-AO can be applied in many fields, including livestock decision making. Making judgments about a wide range of issues, including feed formulation, breeding program design, disease diagnostics, and market analysis, is part of the process of managing livestock. By combining data from many sources, SV-NPHFRE-AO can assist decision-makers in livestock management in integrating and evaluating diverse criteria, which can result in more informed choices. It also provides a more accurate and comprehensive representation of decision-making problems by considering the multiple criteria involved and the relationships between them. The single valued neutrosophic set (SV-NS) aggregation operators (AOs) based on Einstein properties using hesitant fuzzy sets (HFSs) and probabilistic hesitant fuzzy sets (PHFSs) with rough sets (RSs) are proposed in this study and can handle a large volume of data, making them suitable for complex and large-scale livestock decision-making problems. We first defined SV-neutrosophic probabilistic hesitant fuzzy rough weighted averaging (SV-NPHFRWA), SV-neutrosophic probabilistic hesitant fuzzy rough weighted geometric (SV-NPHFRWG), SV-neutrosophic probabilistic hesitant fuzzy rough ordered weighted averaging (SV-NPHFROWA) and SV-neutrosophic probabilistic hesitant fuzzy rough hybrid weighted averaging (SV-NPHFRHWA) AOs. Then, based on Einstein properties, we extended these operators and developed the single-valued neutrosophic probabilistic hesitant fuzzy rough Einstein weighted averaging (SV-NPHFREWA) operator. Additionally, an illustrative scenario to show the applicability of the suggested decision-making approach is provided, along with a sensitivity analysis and comparison analysis, which demonstrate that its outcomes are realistic and reliable. We also provide another relation between criteria and alternatives of decision-making using neutrosophic information with quaternion context. By using such type of operators, livestock managers can make more informed decisions, leading to better animal health, higher productivity, and increased profitability. |
| first_indexed | 2024-03-13T00:36:36Z |
| format | Article |
| id | doaj.art-3d251180b07a48f097adcd7194422f20 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T00:36:36Z |
| publishDate | 2023-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3d251180b07a48f097adcd7194422f202023-07-10T01:24:24ZengAIMS PressAIMS Mathematics2473-69882023-06-019206122065310.3934/math.20231051An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operatorJia-Bao Liu0Rashad Ismail 1Muhammad Kamran2Esmail Hassan Abdullatif Al-Sabri 3Shahzaib Ashraf 4Ismail Naci Cangul51. School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China2. Department of Mathematics, Faculty of Science and Arts, King Khalid University, Muhayl Assir 61913, Saudi Arabia 3. Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb 70270, Yemen4. Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan2. Department of Mathematics, Faculty of Science and Arts, King Khalid University, Muhayl Assir 61913, Saudi Arabia4. Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan5. Department of Mathematics, Bursa Uluda University, Gorukle 16059, TurkeyThe single valued neutrosophic probabilistic hesitant fuzzy rough Einstein aggregation operator (SV-NPHFRE-AO) is an extension of the neutrosophic probabilistic hesitant fuzzy rough set theory. It is a powerful decision-making tool that combines the concepts of neutrosophic logic, probability theory, hesitant fuzzy sets, rough sets, and Einstein aggregation operators. SV-NPHFRE-AO can be applied in many fields, including livestock decision making. Making judgments about a wide range of issues, including feed formulation, breeding program design, disease diagnostics, and market analysis, is part of the process of managing livestock. By combining data from many sources, SV-NPHFRE-AO can assist decision-makers in livestock management in integrating and evaluating diverse criteria, which can result in more informed choices. It also provides a more accurate and comprehensive representation of decision-making problems by considering the multiple criteria involved and the relationships between them. The single valued neutrosophic set (SV-NS) aggregation operators (AOs) based on Einstein properties using hesitant fuzzy sets (HFSs) and probabilistic hesitant fuzzy sets (PHFSs) with rough sets (RSs) are proposed in this study and can handle a large volume of data, making them suitable for complex and large-scale livestock decision-making problems. We first defined SV-neutrosophic probabilistic hesitant fuzzy rough weighted averaging (SV-NPHFRWA), SV-neutrosophic probabilistic hesitant fuzzy rough weighted geometric (SV-NPHFRWG), SV-neutrosophic probabilistic hesitant fuzzy rough ordered weighted averaging (SV-NPHFROWA) and SV-neutrosophic probabilistic hesitant fuzzy rough hybrid weighted averaging (SV-NPHFRHWA) AOs. Then, based on Einstein properties, we extended these operators and developed the single-valued neutrosophic probabilistic hesitant fuzzy rough Einstein weighted averaging (SV-NPHFREWA) operator. Additionally, an illustrative scenario to show the applicability of the suggested decision-making approach is provided, along with a sensitivity analysis and comparison analysis, which demonstrate that its outcomes are realistic and reliable. We also provide another relation between criteria and alternatives of decision-making using neutrosophic information with quaternion context. By using such type of operators, livestock managers can make more informed decisions, leading to better animal health, higher productivity, and increased profitability.https://www.aimspress.com/article/doi/10.3934/math.20231051?viewType=HTMLneutrosophic informationeinstein aggregation operatorsprobabilistic hesitant informationrough setsmulti-criteria decision-making |
| spellingShingle | Jia-Bao Liu Rashad Ismail Muhammad Kamran Esmail Hassan Abdullatif Al-Sabri Shahzaib Ashraf Ismail Naci Cangul An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator AIMS Mathematics neutrosophic information einstein aggregation operators probabilistic hesitant information rough sets multi-criteria decision-making |
| title | An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator |
| title_full | An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator |
| title_fullStr | An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator |
| title_full_unstemmed | An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator |
| title_short | An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator |
| title_sort | optimization strategy with sv neutrosophic quaternion information and probabilistic hesitant fuzzy rough einstein aggregation operator |
| topic | neutrosophic information einstein aggregation operators probabilistic hesitant information rough sets multi-criteria decision-making |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231051?viewType=HTML |
| work_keys_str_mv | AT jiabaoliu anoptimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT rashadismail anoptimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT muhammadkamran anoptimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT esmailhassanabdullatifalsabri anoptimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT shahzaibashraf anoptimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT ismailnacicangul anoptimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT jiabaoliu optimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT rashadismail optimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT muhammadkamran optimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT esmailhassanabdullatifalsabri optimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT shahzaibashraf optimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator AT ismailnacicangul optimizationstrategywithsvneutrosophicquaternioninformationandprobabilistichesitantfuzzyrougheinsteinaggregationoperator |