Volume 26 , Issue 1 , PP: 159-170, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
R. Radha 1 , R. Rajalakshmi 2 , B. Indhumathi 3 , R. Poornima 4 , M. Karthika 5 , M. Mary Victoria Florence 6
Doi: https://doi.org/10.54216/IJNS.260114
This paper introduces the concept of Pentapartitioned Neutrosophic Numbers (PNNs) and proposes score and accuracy functions to effectively rank PNNs based on their score values. Utilizing the adaptability of Dombi operators to accommodate various parameters, the study applies these operators to address complex Multicriteria Attribute Group Decision Making (MAGDM) problems. To achieve precise aggregation under neutrosophic conditions, Dombi T-norm and T-conorm operations for two PNNs are defined. Building upon these Dombi operations, the paper presents two weighted aggregation operators—PNDWAA (Pentapartitioned Neutrosophic Dombi Weighted Arithmetic Average) and PNDWGA (Pentapartitioned Neutrosophic Dombi Weighted Geometric Average)—and investigates their properties within the pentapartitioned neutrosophic environment. Furthermore, the study explores a Multicriteria Attribute Decision Making (MADM) approach that utilizes either the PNDWAA or PNDWGA operators for decision-making.An illustrative example is provided to demonstrate the proposed method, offering a detailed step-by-step process that highlights the effectiveness of the approach in determining the optimal alternative based on ranking order.
Pentapartitioned Neutrosophic Set , Score and Accuracy functions , Dombi Weighted Aggregation Operators
[1] K. Atanasov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, pp. 87–96, 1986.
[2] M. Abdel-Basset, M. Ali, and A. Atef, “Uncertainty assessments of linear time-cost tradeoffs using neutrosophic set,” Computers and Industrial Engineering, vol. 141, p. 106286, 2020.
[3] M. Abdel-Basset, et al., “Solving the supply chain problem using the best-worst method based on a novel Plithogenic model,” Optimization Theory Based on Neutrosophic and Plithogenic Sets, Academic Press, pp. 1–19, 2020.
[4] M. Abdel-Basset and R. Mohamed, “A novel plithogenic TOPSIS-CRITIC model for sustainable supply chain risk management,” Journal of Cleaner Production, vol. 247, p. 119586, 2020.
[5] M. Abdel-Basset, M. Ali, and A. Atef, “Resource levelling problem in construction projects under neutrosophic environment,” The Journal of Supercomputing, pp. 1–25, 2019.
[6] M. Abdel-Basset, M. Mohamed, M. Elhoseny, F. Chiclana, and A. E. N. H. Zaied, “Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases,” Artificial Intelligence in Medicine, vol. 101, p. 101735, 2019.
[7] J. Chen and J. Ye, “Some single-valued neutrosophic Dombi weighted aggregation operators for multiple attribute decision-making,” Symmetry, vol. 9, no. 6, p. 82, 2017.
[8] D. A. Chiang and N. P. Lin, “Correlation of fuzzy sets,” Fuzzy Sets and Systems, vol. 102, pp. 221–226, 1999.
[9] J. Dombi, “A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators,” Fuzzy Sets and Systems, vol. 8, pp. 149–163, 1982.
[10] D. H. Hong, “Fuzzy measures for a correlation coefficient of fuzzy numbers under Tw (the weakest t-norm)-based fuzzy arithmetic operations,” Information Sciences, vol. 176, pp. 150–160, 2006.
[11] P. D. Liu and Y. M. 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.
[12] P. D. Liu, Y. C. Chu, Y. W. Li, and Y. B. Chen, “Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making,” Journal of Intelligent and Fuzzy Systems, vol. 16, pp. 242–255, 2014.
[13] P. D. Liu and Y. M. Wang, “Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making,” Journal of Systems Science and Complexity, vol. 29, pp. 681–697, 2016.
[14] K. Mohana and M. Mohanasundari, “On some similarity measures of single valued neutrosophic rough sets,” Neutrosophic Sets and Systems, vol. 24, pp. 10–22, 2019.
[15] K. Mohana and M. Mohanasundari, “Quadripartitioned single valued neutrosophic rough sets,” Nirmala Annual Research Congress (NARC-2018), ISBN-978-93-5321-859-1, vol. 3, pp. 165, 2018.
[16] Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, vol. 11, no. 5, pp. 341–356, 1982.
[17] R. Chatterjee, P. Majumdar, and S. K. Samanta, “On some similarity measures and entropy on quadripartitioned single valued neutrosophic sets,” Journal of Intelligent and Fuzzy Systems, vol. 30, pp. 2475–2485, 2016.
[18] R. Mallick and S. Pramanik, “Pentapartitioned neutrosophic set and its properties,” Neutrosophic Sets and Systems, vol. 36, pp. 184–192, 2020.
[19] F. Smarandache, A Unifying Field in Logics: Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth, 1999.
[20] H. X. Sun, H. X. Yang, J. Z. Wu, and O. Y. Yao, “Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making,” Journal of Intelligent and Fuzzy Systems, vol. 28, pp. 2443–2455, 2015.
[21] H. Wang, F. Smarandache, Y. Q. Zhang, and R. Sunderraman, “Single valued neutrosophic sets,” Multispace and Multistructure, vol. 4, pp. 410–413, 2010.
[22] X. H. Wu, J. Q. Wang, J. J. Peng, and X. H. Chen, “Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision-making problems,” Journal of Intelligent and Fuzzy Systems, vol. 18, pp. 1104–1116, 2016.
[23] H. L. Yang, “A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model,” Soft Computing, vol. 21, pp. 6253–6267, 2017.
[24] J. Ye, “Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval valued intuitionistic fuzzy sets,” Applied Mathematical Modelling, vol. 34, pp. 3864–3870, 2010.
[25] J. Ye, “Another form of correlation coefficient between single valued neutrosophic sets and its multiple attribute decision making method,” Neutrosophic Sets and Systems, vol. 1, pp. 8–12, 2013.
[26] J. Ye, “Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment,” International Journal of General Systems, vol. 42, no. 4, pp. 386–394, 2013.
[27] J. Ye, “Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making,” Applied Mathematical Modelling, vol. 38, pp. 659–666, 2014.
[28] J. Ye, “A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets,” Journal of Intelligent and Fuzzy Systems, vol. 26, pp. 2459–2466, 2014.
[29] J. Ye, “Improved correlation coefficients of single valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making,” Journal of Intelligent and Fuzzy Systems, vol. 27, pp. 2453–2462, 2014.
[30] J. Ye, “Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods,” SpringerPlus, vol. 5, p. 1488, 2016.
[31] L. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 87–96, 1965.
[32] 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. 2014, p. 645953.
[33] A. W. Zhao, J. G. Du, and H. J. Guan, “Interval valued neutrosophic sets and multi-attribute decision-making,” Journal of Intelligent and Fuzzy Systems, vol. 29, pp. 2697–2706, 2015.
