Single – Valued Neutrosophic Yager Power Aggregation Operators and Its Application to MCDM
Abstract
The notion of Single-valued neutrosophic sets (SVNSs) being a generalization of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets enhances implications of these methods in various interdisciplinary problems. Aggregation operator is a prevalent tool for unifying the data from various sources and applied to solve the problems of decision-making. In this article, the Yager's operations and power averaging operator are utilized to formulate and investigate some single-valued neutrosophic Yager power operators, i.e., single-valued neutrosophic Yager power weighted averaging (SVNYPWA) operators, single-valued neutrosophic Yager power order weighted averaging (SVNYPOWA) operator, single-valued neutrosophic Yager power weighted geometric averaging (SVNYPWGA) operator, and single-valued neutrosophic Yager power ordered weighted geometric averaging (SVNYPOWGA). Some important properties of the suggested operators are discussed. Furthermore, SVNYPWA and SVNYPWGA operators in the SVN environment are applied to solve the multi-criteria decision-making (MCDM) problem for selecting a suitable road construction company. Also, the proposed method has been verified using the multi-attributive border approximation area comparison (MABAC) method. Finally, a comparative analysis has been done, to establish the advantage of the proposed approach over the existing methods.
References
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C. Jana, M. Pal, and J. Q. Wang, "Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making," Soft Computing, vol. 24, pp. 3631–3646, 2020.
P. D. Liu, and Y. Wang, "Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean," Neural Computing and Applications, vol. 25, pp. 2001–2010, 2014.
Z. Lu, and J. Ye, "Single-valued neutrosophic hybrid arithmetic and geometric aggregation operators and their decision-making method," Information, vol. 8, no. 3, pp. 84, 2017.
P.D. Liu, and X. Liu, "Multiattribute group decision-making methods based on linguistic intuitionistic fuzzy power Bonferroni mean operators," Complexity, vol. 2017, no. 1, 3571459, 2017.
Z. S. Xu, and R. R. Yager, "Some geometric aggregation operators based on intuitionistic fuzzy sets," International Journal of General Systems, vol. 35, no. 4, pp. 417–433, 2006.
D.J. Yu, "Group decision-making based on the generalized intuitionistic fuzzy prioritized geometric operator," International Journal of Intelligent Systems, vol. 27, no. 7, pp. 635–661, 2012.
R. R. Yager, and J. Kacprzyk, The ordered weighted averaging operators: theory and applications, Springer Science and Bussiness Media, 2012.
J. Ye, "A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets," Journal of Intelligent and Fuzzy Systems, vol. 26, no. 5, pp. 2459–2466, 2014.
C. Fan, J. Ye, K. Hu, E. Fan, "Bonferroni mean operators of linguistic neutrosophic numbers and their multiple attribute group decision-making methods," Information, vol. 8, no. 3, 107, 2017.
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R. R. Yager, "Aggregation operators and fuzzy systems modeling," Fuzzy Sets and Systems, vol. 67, no. 2, pp. 129–145, 1994.
M. Akram, G. Shahzadi, "A hybrid decision-making model under q-rung ortho-pair fuzzy Yager aggregation operators," Granular Computing, vol. 6, pp. 763-777, 2020.
M. Akram, X. Peng, and A. Sattar, "Multi-criteria decision-making model using complex pythagorean fuzzy yager aggregation operators," Arabian Journal for Science and Engineering, vol. 46, pp. 1691-1717, 2020.
H. Garg, G. Shahzadi, M. Akram, "Decision-making analysis based on fermatean fuzzy yager aggregation operators with application in COVID-19 testing facility," Mathematical Problems in Engineering, vol. 2020, no. 1, 7279027, 2020.
S. Khan, S. Abdullah, S. Ashraf, R. Chinram, and S. Baupradist, "Decision support technique based on neutrosophic Yager aggregation operators: Application in solar power plant locations—Case study of Bahawalpur, Pakistan," Mathematical Problems in Engineering, vol. 2020, no. 1, 6677676, 2020.
M. Liaqat, S. Yin, M. Akram, and S. Ijaz, "Aczel-Alsina Aggregation Operators Based on Interval-valued Complex Single-valued Neutrosophic Information and Their Application in Decision-Making Problems," Journal of Innovative Research in Mathematical and Computational Sciences, vol. 1, no. 2, pp. 40-66, 2022.
S. Zhao, D. Wang, C. Liang, Y. Leng, and J. Xu, "Some single-valued neutrosophic power Heronian aggregation operators and their application to multi-attribute group decision making," Symmetry, vol. 11, no. 653, pp. 1-26, 2019.
C. Jana and M. Pal, "Multi-criteria decision-making process based on some single-valued neutrosophic Dombi power aggregation operators," Soft Computing, vol. 25, pp. 5055-5072, 2021.
S. Broumi and F. Smarandache, "Correlation coefficient of interval neutrosophic set," Applied Mechanics and Material, vol. 436, pp. 511–517, 2013.
K. T. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 20, pp. 87-96, 1986.
F. Smarandache, "Neutrosophic Set- A Generalization of the Intuitionistic Fuzzy Set," International Journal of Pure and Applied Mathematics, vol. 24, pp. 287-297, 2005.
H. Wang, F. Smarandache, Y. Zhang, and R. Sunderraman, "Single valued neutrosophic sets," Infinite Study, vol. 4, 410–413, 2010.
R. R. Yager, "The power average operator," IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, vol. 31, no. 6, pp. 724 –731, 2001.
Z. S. Xu, and R. R. Yager, "Power-geometric operators and their use in group decision making," IEEE Trans. on Fuzzy Systems, vol. 18, no. 1, pp. 94-105, 2010.
L. G. Zhou, H. Y. Chen, and J. P. Liu, "Generalized power aggregation operators and their applications in group decision making," Computers and Industrial Engineering, vol. 62, no. 4, pp. 989-999, 2012.
H. Y. Zhang, J. Q. Wang, and X. H. Chen, "Interval neutrosophic sets and their application in multicriteria decision making problems," Scientific World Journal, vol. 1, pp. 1-15, 2014.
X. Zhang, P. Liu, and Y. Wang, "Multiple attribute group decision-making methods based on intuitionistic fuzzy frank power aggregation operators," Journal of Intelligent and Fuzzy Systems, vol. 29, no. 5, pp. 2235-2246, 2015.
D. Rani, and H. Garg, "Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision‐making," Expert Systems, vol. 35, no. 6, 2018.
L. Yang, and B. Li, "A multi-criteria decision-making method using power aggregation operators for single-valued neutrosophic sets," Infinite Study, 2016.
I. Deli, and Y. Subas, "Single Valued Neutrosophic Numbers and Their Applications to Multicriteria Decision Making Problem," Neutrosophic Sets and Systems, vol. 2, no. 1, pp. 1-13, 2018.
J. Ye, "Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment," Journal of Intelligent and Fuzzy Systems, vol. 24, no. 1, pp. 23–36, 2015.
L. Han, and C. Wei, "Group decision-making method based on single valued neutrosophic Choquet integral operator," Operational Research Transactions, 21, pp. 111–118, 2017.
S. Sharma, and S. Singh, "A complementary dual of single-valued neutrosophic entropy with application to MAGDM," Mathematics, vol. 10, no. 20, pp. 3726, 2022.
S. Singh, and S. Sharma, "Divergence measures and aggregation operators for single-valued neutrosophic sets with applications in decision-making problems," Neutrosophic Systems with Applications, vol. 20, pp. 27-44, 2024.
G. Beliakov, A. Pradera, and T. Calvo, Aggregation functions: a guide for practitioners, Heidelberg, Springer, 2007.
T. Mahmood, J. Ahmmad, U. Rehman, and M. Aslam, "Assessment of neural networks in different sectors by employing the notion of bipolar fuzzy Schweizer-sklar aggregation operators," Ain Shams Engineering Journal, vol. 15, no., 102852, 2024.
G. Deschrijver, C. Cornelis, and E. E. Kerre, "On the representation of intuitionistic fuzzy tnorms and t-conorms," IEEE Trans. Fuzzy Syst., vol. 12, no. 1, pp. 45–61, 2004.
Y. D. He, H. Y. Chen, and L. G. Zhou, "Generalized interval-valued Atanassov intuitionistic fuzzy power operators and their application to group decision making," International Journal of Fuzzy Systems, vol. 15, no. 4, 2013.
C. Jana, M. Pal, and J. Q. Wang, "Bipolar fuzzy Dombi aggregation operators and its application in multiple attribute decision-making process," Journal of Ambient Intelligence and Humanized Computing, vol. 10, no. 9, pp. 3533–3549, 2019.
C. Jana, T. Senapati, M. Pal, and R. R. Yager, "Picture fuzzy Dombi aggregation operators: application to MADM process," Applied Soft Computing, vol. 74, no. 1, pp. 99–109, 2019.
K. Ullah, M. Naeem, A. Hussain, M. Waqas, and I. Haleemzai, "Evaluation of Electric Motor Cars Based Frank Power Aggregation Operators Under Picture Fuzzy Information and a MultiAttribute Group Decision-Making Process," IEEE Access, vol. 11, pp. 67201-67219, 2023.
A. Jaleel, "WASPAS Technique Utilized for Agricultural Robotics System based on Dombi Aggregation Operators under Bipolar Complex Fuzzy Soft Information," Journal of Innovative Research in Mathematical and Computational Sciences, vol. 1, no. 2, pp. 67-95, 2022.
K. Jabeen, K. Ullah, M. Akram, and I. Haleemzai, "Interval Valued Picture Fuzzy AczelAlsina Aggregation Operators and Their Application by Using the Multi-attribute Decision Making Problem," Journal of Mathematics, pp. 1-23, 1707867, 2023.
C. Jana, T. Senapati, and M. Pal, "Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision making," International Journal of Intelligent Systems, vol. 34, no. 9, pp. 2019–2038, 2019.
C. Jana, M. Pal, F. Karaaslan, and J. Q. Wang, "Trapezoidal neutrosophic aggregation operators and its application in multiple attribute decision-making process," Scientia Iranica, vol. 27, no. 3, pp. 1655–1673, 2020.
C. Jana, M. Pal, and J. Q. Wang, "Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making," Soft Computing, vol. 24, pp. 3631–3646, 2020.
P. D. Liu, and Y. Wang, "Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean," Neural Computing and Applications, vol. 25, pp. 2001–2010, 2014.
Z. Lu, and J. Ye, "Single-valued neutrosophic hybrid arithmetic and geometric aggregation operators and their decision-making method," Information, vol. 8, no. 3, pp. 84, 2017.
P.D. Liu, and X. Liu, "Multiattribute group decision-making methods based on linguistic intuitionistic fuzzy power Bonferroni mean operators," Complexity, vol. 2017, no. 1, 3571459, 2017.
Z. S. Xu, and R. R. Yager, "Some geometric aggregation operators based on intuitionistic fuzzy sets," International Journal of General Systems, vol. 35, no. 4, pp. 417–433, 2006.
D.J. Yu, "Group decision-making based on the generalized intuitionistic fuzzy prioritized geometric operator," International Journal of Intelligent Systems, vol. 27, no. 7, pp. 635–661, 2012.
R. R. Yager, and J. Kacprzyk, The ordered weighted averaging operators: theory and applications, Springer Science and Bussiness Media, 2012.
J. Ye, "A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets," Journal of Intelligent and Fuzzy Systems, vol. 26, no. 5, pp. 2459–2466, 2014.
C. Fan, J. Ye, K. Hu, E. Fan, "Bonferroni mean operators of linguistic neutrosophic numbers and their multiple attribute group decision-making methods," Information, vol. 8, no. 3, 107, 2017.
P. D. Liu, "The aggregation operators based on Archimedean t-conorm and t-norm for singlevalued neutrosophic numbers and their application to decision making," International Jornal of Fuzzy Syst, vol. 18, pp. 849–863, 2016.
R. R. Yager, "Aggregation operators and fuzzy systems modeling," Fuzzy Sets and Systems, vol. 67, no. 2, pp. 129–145, 1994.
M. Akram, G. Shahzadi, "A hybrid decision-making model under q-rung ortho-pair fuzzy Yager aggregation operators," Granular Computing, vol. 6, pp. 763-777, 2020.
M. Akram, X. Peng, and A. Sattar, "Multi-criteria decision-making model using complex pythagorean fuzzy yager aggregation operators," Arabian Journal for Science and Engineering, vol. 46, pp. 1691-1717, 2020.
H. Garg, G. Shahzadi, M. Akram, "Decision-making analysis based on fermatean fuzzy yager aggregation operators with application in COVID-19 testing facility," Mathematical Problems in Engineering, vol. 2020, no. 1, 7279027, 2020.
S. Khan, S. Abdullah, S. Ashraf, R. Chinram, and S. Baupradist, "Decision support technique based on neutrosophic Yager aggregation operators: Application in solar power plant locations—Case study of Bahawalpur, Pakistan," Mathematical Problems in Engineering, vol. 2020, no. 1, 6677676, 2020.
M. Liaqat, S. Yin, M. Akram, and S. Ijaz, "Aczel-Alsina Aggregation Operators Based on Interval-valued Complex Single-valued Neutrosophic Information and Their Application in Decision-Making Problems," Journal of Innovative Research in Mathematical and Computational Sciences, vol. 1, no. 2, pp. 40-66, 2022.
S. Zhao, D. Wang, C. Liang, Y. Leng, and J. Xu, "Some single-valued neutrosophic power Heronian aggregation operators and their application to multi-attribute group decision making," Symmetry, vol. 11, no. 653, pp. 1-26, 2019.
C. Jana and M. Pal, "Multi-criteria decision-making process based on some single-valued neutrosophic Dombi power aggregation operators," Soft Computing, vol. 25, pp. 5055-5072, 2021.
S. Broumi and F. Smarandache, "Correlation coefficient of interval neutrosophic set," Applied Mechanics and Material, vol. 436, pp. 511–517, 2013.
Published
2025-02-20
How to Cite
SHARMA, Sonam; SINGH, Surender.
Single – Valued Neutrosophic Yager Power Aggregation Operators and Its Application to MCDM.
Yugoslav Journal of Operations Research, [S.l.], feb. 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1326>. Date accessed: 22 feb. 2025.
doi: https://doi.org/10.2298/YJOR240715004S.
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Section
Research Articles
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