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.
Citation: 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[J]. AIMS Mathematics, 2023, 8(9): 20612-20653. doi: 10.3934/math.20231051
[1] | Muhammad Kamran, Shahzaib Ashraf, Nadeem Salamat, Muhammad Naeem, Thongchai Botmart . Cyber security control selection based decision support algorithm under single valued neutrosophic hesitant fuzzy Einstein aggregation information. AIMS Mathematics, 2023, 8(3): 5551-5573. doi: 10.3934/math.2023280 |
[2] | Muhammad Kamran, Rashad Ismail, Shahzaib Ashraf, Nadeem Salamat, Seyma Ozon Yildirim, Ismail Naci Cangul . Decision support algorithm under SV-neutrosophic hesitant fuzzy rough information with confidence level aggregation operators. AIMS Mathematics, 2023, 8(5): 11973-12008. doi: 10.3934/math.2023605 |
[3] | Misbah Rasheed, ElSayed Tag-Eldin, Nivin A. Ghamry, Muntazim Abbas Hashmi, Muhammad Kamran, Umber Rana . Decision-making algorithm based on Pythagorean fuzzy environment with probabilistic hesitant fuzzy set and Choquet integral. AIMS Mathematics, 2023, 8(5): 12422-12455. doi: 10.3934/math.2023624 |
[4] | Attaullah, Shahzaib Ashraf, Noor Rehman, Asghar Khan, Muhammad Naeem, Choonkil Park . Improved VIKOR methodology based on q-rung orthopair hesitant fuzzy rough aggregation information: application in multi expert decision making. AIMS Mathematics, 2022, 7(5): 9524-9548. doi: 10.3934/math.2022530 |
[5] | Shougi S. Abosuliman, Abbas Qadir, Saleem Abdullah . Multi criteria group decision (MCGDM) for selecting third-party logistics provider (3PL) under Pythagorean fuzzy rough Einstein aggregators and entropy measures. AIMS Mathematics, 2023, 8(8): 18040-18065. doi: 10.3934/math.2023917 |
[6] | Attaullah, Shahzaib Ashraf, Noor Rehman, Asghar Khan, Choonkil Park . A decision making algorithm for wind power plant based on q-rung orthopair hesitant fuzzy rough aggregation information and TOPSIS. AIMS Mathematics, 2022, 7(4): 5241-5274. doi: 10.3934/math.2022292 |
[7] | Attaullah, Asghar Khan, Noor Rehman, Fuad S. Al-Duais, Afrah Al-Bossly, Laila A. Al-Essa, Elsayed M Tag-eldin . A novel decision model with Einstein aggregation approach for garbage disposal plant site selection under q-rung orthopair hesitant fuzzy rough information. AIMS Mathematics, 2023, 8(10): 22830-22874. doi: 10.3934/math.20231163 |
[8] | D. Jeni Seles Martina, G. Deepa . Some algebraic properties on rough neutrosophic matrix and its application to multi-criteria decision-making. AIMS Mathematics, 2023, 8(10): 24132-24152. doi: 10.3934/math.20231230 |
[9] | Esmail Hassan Abdullatif Al-Sabri, Muhammad Rahim, Fazli Amin, Rashad Ismail, Salma Khan, Agaeb Mahal Alanzi, Hamiden Abd El-Wahed Khalifa . Multi-criteria decision-making based on Pythagorean cubic fuzzy Einstein aggregation operators for investment management. AIMS Mathematics, 2023, 8(7): 16961-16988. doi: 10.3934/math.2023866 |
[10] | Muhammad Naeem, Aziz Khan, Shahzaib Ashraf, Saleem Abdullah, Muhammad Ayaz, Nejib Ghanmi . A novel decision making technique based on spherical hesitant fuzzy Yager aggregation information: application to treat Parkinson's disease. AIMS Mathematics, 2022, 7(2): 1678-1706. doi: 10.3934/math.2022097 |
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.
The recent emergence of big data in chemistry and biology demands special methodologies to analyze these complex datasets. The volume, speed at which the data is created, and diversity of big data combined with the recent advancements in data storage and computer processing has facilitated the training of powerful Artificial Intelligence (AI) models to perform a wide variety of classification and prediction tasks.
AI has the potential to address global health and environmental challenges. It is increasingly used in clinical decision-making to inform precision medicine with the potential to revolutionize medical practice. However, there is a gap between published AI manuscripts and clinical deployment of them. Thus, the significance and utility of big data and AI research needs to be carefully examined. The scientific community should continue to work toward developing and refining both novel and existing methods using AI and data science to make the tools applicable in real-world scenarios.
The first challenge is to understand the fairness of AI algorithms. If the connection between the input data and the model output is indecipherable (the so-called ‘black box’ problem), under inappropriate management, it could lead to unexpected and unjustified decisions that can be particularly problematic in the field of medicine where lives would be on the line. We need to think critically how important it is to understand the way AI works depending on the context, and provide transparent and interpretable models that can better understand underlying mechanisms where appropriate. Moreover, we need to be aware of the extent to which AI can reliably identify causal links in data and exploit their potential to advance our knowledge and determine effective strategies. It should be also noted that AI is an umbrella term for a set of related tools and approaches, and successful outcomes in one field does not imply equivalent success in others.
The second challenge relates to the collection and preprocessing of the input data which might cause bias in the model development. Developing strategies and tools to handle the biological heterogeneity and tease out important biological signals from technical noise such as artificial batch effects will improve our understanding and predictions of biological systems. Importantly, there is an urgent need for benchmark and quality control assessment of the current and future approaches to make reproducible and standardized pipelines.
The third challenge is to develop tools to reduce the dimensionality of the data in a contextually meaningful manner. These tools should also take into consideration the data generating process of the state of the art techniques so that assumptions embedded in these techniques are met. In addition, the availability of high volume of data, for instance in Electronic Health Records (EHRs), single-cell and/or other ‘omics’ fields, offers opportunities for data driven research while requiring caution for data dredging, bias, or confounding.
Importantly, caution must be exercised before deploying such algorithms for decision support, as there may be underlying societal biases and health privacy issues. AI and big data offer opportunities and challenges to support minorities' health, address the importance of consent and patient governance in data collection. Systematic biases in AI models have been a problem in other fields such as the judicial system, which showed racial biases. Instead of making the court fairer, sometimes AI introduces further bias to decision-making to the court. Similarly, in the medical field it is crucial to understand the underlying data and models and identify factors that may lead to biases when designing algorithms.
The aim of this special issue is to come up with models to process, analyze and understand the data to support and improve the performance of current tasks as well as improving our understanding of complex systems involved in biological processes. Future benefits of deploying AI models to support and enhance research will only be possible by means of interdisciplinary working teams and critical thinking. With this issue we hope to elaborate on these challenges and invite scientists to pave the ground for integrating AI to process and understand complex biological data.
[1] |
A. Mardani, R. E. Hooker, S. Ozkul, S. Yifan, M. Nilashi, H. Z. Sabzi, et al., Application of decision making and fuzzy sets theory to evaluate the healthcare and medical problems: A review of three decades of research with recent developments, Expert Syst. Appl., 137 (2019), 202–231. https://doi.org/10.1016/j.eswa.2019.07.002 doi: 10.1016/j.eswa.2019.07.002
![]() |
[2] |
Z. Bashir, A. Wahab, T. Rashid, Three-way decision with conflict analysis approach in the framework of fuzzy set theory, Soft Comput., 26 (2022), 309–326. https://doi.org/10.1007/s00500-021-06509-3 doi: 10.1007/s00500-021-06509-3
![]() |
[3] |
X. Gou, Z. Xu, H. Liao, Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queuing method for multiple criteria decision making, Inform. Sci., 388 (2017), 225–246. https://doi.org/10.1016/j.ins.2017.01.033 doi: 10.1016/j.ins.2017.01.033
![]() |
[4] |
X. Fu, Y. Zhang, Y. G. Zhang, Y. L. Yin, S. C. Yan, Y. Z. Zhao, et al., Research and application of a new multilevel fuzzy comprehensive evaluation method for cold stress in dairy cows, J. Dairy Sci., 105 (2022), 9137–9161. https://doi.org/10.3168/jds.2022-21828 doi: 10.3168/jds.2022-21828
![]() |
[5] |
L. P. Maziero, M. G. M. Chacur, C. P. Cremasco, F. F. Putti, L. R. A. G. Filho, Fuzzy system for assessing bovine fertility according to semen characteristics, Livest. Sci., 256 (2022), 104821. https://doi.org/10.1016/j.livsci.2022.104821 doi: 10.1016/j.livsci.2022.104821
![]() |
[6] |
R. Zhang, Z. Xu, X. Gou, ELECTRE II method based on the cosine similarity to evaluate the performance of financial logistics enterprises under double hierarchy hesitant fuzzy linguistic environment, Fuzzy Optim. Decis. Ma., 22 (2023), 23–49. https://doi.org/10.1007/s10700-022-09382-3 doi: 10.1007/s10700-022-09382-3
![]() |
[7] |
R. Bosma, U. Kaymak, J. V. Berg, H. Udo, J. Verreth, Using fuzzy logic modelling to simulate farmers' decision-making on diversification and integration in the Mekong Delta, Vietnam, Soft Comput., 15 (2011), 295–310. https://doi.org/10.1007/s00500-010-0618-7 doi: 10.1007/s00500-010-0618-7
![]() |
[8] | L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X |
[9] | D. J. Dubois, Fuzzy sets and systems: Theory and applications, Academic press, 144 (1980). |
[10] | K. T. Atanassov, Intuitionistic fuzzy sets, in Intuitionistic fuzzy sets, Physica, Heidelberg, 1999, 1–137. https://doi.org/10.1007/978-3-7908-1870-3_1 |
[11] | H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single valued neutrosophic sets, Infin. Study, 2010. |
[12] |
J. Ye, Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment, Int. J. Gen. Syst., 42 (2013), 386–394. https://doi.org/10.1080/03081079.2012.761609 doi: 10.1080/03081079.2012.761609
![]() |
[13] | R. Şahin, Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic, Comput. Sci., 2014. https://doi.org/10.5281/zenodo.22994 |
[14] | Y. Jin, M. Kamran, N. Salamat, S. Zeng, R. H. Khan, Novel distance measures for single-valued neutrosophic fuzzy sets and their applications to multicriteria group decision-making problem, J. Func. Space., 2022. |
[15] |
M. Riaz, M. R. Hashmi, D. Pamucar, Y. M. Chu, Spherical linear Diophantine fuzzy sets with modeling uncertainties in MCDM, Comput. Model. Eng. Sci., 126 (2021), 1125–1164. https://doi.org/10.32604/cmes.2021.013699 doi: 10.32604/cmes.2021.013699
![]() |
[16] | S. Broumi, F. Smarandache, M. Dhar, Rough neutrosophic sets, Infin. Study, 2014. https://doi.org/10.5281/zenodo.30310 |
[17] | R. Krishankumaar, A. R. Mishra, X. Gou, K. S. Ravichandran, New ranking model with evidence theory under probabilistic hesitant fuzzy context and unknown weights, Neural Comput. Appl., 2022, 1–15. https://doi.org/10.1007/s00521-021-06653-9 |
[18] |
Z. Hao, Z. Xu, H. Zhao, Z. Su, Probabilistic dual hesitant fuzzy set and its application in risk evaluation, Knowl.-Based Syst., 127 (2017), 16–28. https://doi.org/10.1016/j.knosys.2017.02.033 doi: 10.1016/j.knosys.2017.02.033
![]() |
[19] |
W. Zhou, Z. Xu, Group consistency and group decision making under uncertain probabilistic hesitant fuzzy preference environment, Inform. Sci., 414 (2017), 276–288. https://doi.org/10.1016/j.ins.2017.06.004 doi: 10.1016/j.ins.2017.06.004
![]() |
[20] |
X. Gou, Z. Xu, H. Liao, F. Herrera, Probabilistic double hierarchy linguistic term set and its use in designing an improved VIKOR method: The application in smart healthcare, J. Oper. Res. Soc., 72 (2021), 2611–2630. https://doi.org/10.1080/01605682.2020.1806741 doi: 10.1080/01605682.2020.1806741
![]() |
[21] |
M. Rasheed, E. Tag-Eldin, N. A. Ghamry, M. A. Hashmi, M. Kamran, U. Rana, Decision-making algorithm based on Pythagorean fuzzy environment with probabilistic hesitant fuzzy set and Choquet integral, AIMS Math., 8 (2023), 12422–12455. https://doi.org/10.3934/math.2023624 doi: 10.3934/math.2023624
![]() |
[22] |
H. Garg, A novel trigonometric operation-based q-rung orthopair fuzzy aggregation operator and its fundamental properties, Neural Comput. Appl., 32 (2020), 15077–15099. https://doi.org/10.1007/s00521-020-04859-x doi: 10.1007/s00521-020-04859-x
![]() |
[23] |
K. Ullah, T. Mahmood, H. Garg, Evaluation of the performance of search and rescue robots using T-spherical fuzzy Hamacher aggregation operators, Int. J. Fuzzy Syst., 22 (2020), 570–582. https://doi.org/10.1007/s40815-020-00803-2 doi: 10.1007/s40815-020-00803-2
![]() |
[24] | C. Carlsson, R. Fullér, Fuzzy reasoning in decision making and optimization, Springer Science & Business Media, 82 (2001). |
[25] |
N. Gonul Bilgin, D. Pamučar, M. Riaz, Fermatean neutrosophic topological spaces and an spplication of neutrosophic Kano method, Symmetry, 14 (2022), 2442. https://doi.org/10.3390/sym14112442 doi: 10.3390/sym14112442
![]() |
[26] |
Z. Xu, W. Zhou, Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment, Fuzzy Optim. Deci. Ma., 16 (2017), 481–503. https://doi.org/10.1007/s10700-016-9257-5 doi: 10.1007/s10700-016-9257-5
![]() |
[27] |
S. Shao, X. Zhang, Y. Li, C. Bo, Probabilistic single-valued (interval) neutrosophic hesitant fuzzy set and its application in multi-attribute decision making, Symmetry, 10 (2018), 419. https://doi.org/10.3390/sym10090419 doi: 10.3390/sym10090419
![]() |
[28] | R. M. Zulqarnain, A. Iampan, I. Siddique, H. Abd, E. W. Khalifa, Some fundamental operations for multi-polar interval-valued neutrosophic soft set and a decision-making approach to solve MCDM problem, Neutrosophic Sets Sy., 51 (2022), 205–220. |
[29] |
R. M. Zulqarnain, X. L. Xin, M. Saqlain, M. Saeed, F. Smarandache, M. I. Ahamad, Some fundamental operations on interval valued neutrosophic hypersoft set with their properties, Neutrosophic Sets Sy., 40 (2021), 134–148. https://doi.org/10.5281/zenodo.4549352 doi: 10.5281/zenodo.4549352
![]() |
[30] | M. Kamran, S. Ashraf, M. Naeem, A promising approach for decision modeling with single-valued neutrosophic probabilistic hesitant fuzzy Dombi operators, Yugoslav J. Oper. Res., 2023. http://dx.doi.org/10.2298/YJOR230115007S |
[31] |
R. Sahin, F. Altun, Decision making with MABAC method under probabilistic single-valued neutrosophic hesitant fuzzy environment, J. Amb. Intel. Hum. Comp., 11 (2020), 4195–4212. https://doi.org/10.1007/s12652-020-01699-4 doi: 10.1007/s12652-020-01699-4
![]() |
[32] |
M. Riaz, Y. Almalki, S. Batool, S. Tanveer, Topological structure of single-valued neutrosophic hesitant fuzzy sets and data analysis for uncertain supply chains, Symmetry, 14 (2022), 1382. https://doi.org/10.3390/sym14071382 doi: 10.3390/sym14071382
![]() |
[33] |
C. F. Liu, Y. S. Luo, New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making, Pattern Anal. Appl., 22 (2019), 417–427. https://doi.org/10.1007/s10044-017-0635-6 doi: 10.1007/s10044-017-0635-6
![]() |
[34] | M. Kamran, S. Ashraf, M. Naeem, A promising approach for decision modeling with single-valued neutrosophic probabilistic hesitant fuzzy Dombi operators, Jugoslav J. Oper. Res., 2023. |
[35] | G. Kaur, H. Garg, A novel algorithm for autonomous parking vehicles using adjustable probabilistic neutrosophic hesitant fuzzy set features, Expert Syst. Appl., 2023, 120101. https://doi.org/10.1016/j.eswa.2023.120101 |
[36] |
M. Kamran, R. Ismail, E. H. A. Al-Sabri, N. Salamat, M. Farman, S. Ashraf, An optimization strategy for MADM framework with confidence level aggregation operators under probabilistic neutrosophic hesitant fuzzy rough environment, Symmetry, 15 (2023), 578. https://doi.org/10.3390/sym15030578 doi: 10.3390/sym15030578
![]() |