A Robust Algorithmic Framework for the Evaluation of World Happiness Ranking Based on Q Rung Orthopair Triangular Fuzzy Neutrosophic Set With Possibility Setting (PQ-RTFNS)
Abstract
This paper presents a robust algorithmic framework for evaluating and ranking world happiness using a novel model based on q-rung orthopair triangular fuzzy neutrosophic sets (PQ-RTFNs) in a possibility setting. Traditional methods of ranking countries by happiness often face challenges in handling the complexity and uncertainty of the various social, economic, and environmental factors that influence well-being. To address this, the authors integrate the flexible and powerful PQ-RTFN model, which allows for better representation of indeterminate and inconsistent data. This approach enhances decision-making accuracy by effectively managing the fuzziness and ambiguity inherent in world happiness metrics. Through a comprehensive evaluation, the proposed framework demonstrates improved performance in ranking nations compared to existing models, offering a more reliable tool for policymakers and researchers to assess global happiness indices.
References
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L. A. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965.
M. Black, “Vagueness: An exercise in logical analysis,” Philosophy of science, vol. 4, no. 4, pp. 427–455, 1937.
M. Saeed, U. Ali, J. Ali, and F. Dayan, “Fuzzy soft relative method and its application in decision making problem: Fuzzy soft relative method and its application in decision making problem,” Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, vol. 57, no. 1, pp. 21–30, 2020.
T.Senapati, A. Sarkar, and G. Chen, “Enhancing healthcare supply chain management through artificial intelligence-driven group decision-making with sugeno–weber triangular norms in a dual hesitant q-rung orthopair fuzzy context,” Engineering Applications of Artificial Intelligence, vol. 135, p. 108794, 2024.
T. Senapati, G. Chen, I. Ullah, M. S. A. Khan, and F. Hussain, “A novel approach towards multiattribute decision making using q-rung orthopair fuzzy dombi–archimedean aggregation operators,” Heliyon, vol. 10, no. 6, 2024.
S.Petchimuthu, B. Palpandi, T. Senapati, et al., “Exploring pharmacological therapies through complex q-rung picture fuzzy aczel–alsina prioritized ordered operators in adverse drug reaction analysis,” Engineering Applications of Artificial Intelligence, vol. 133, p. 107996, 2024.
S. Petchimuthu, H. Kamacı, T. Senapati, et al., “Evaluation of artificial intelligence-based solid waste segregation technologies through multi-criteria decision-making and complex qrung picture fuzzy frank aggregation operators,” Engineering Applications of Artificial Intelligence, vol. 133, p. 108154, 2024.
A. Zeb, W. Ahmad, M. Asif, T. Senapati, V. Simic, and M. Hou, “A decision analytics approach for sustainable urbanisation using q-rung orthopair fuzzy soft set-based aczel-alsina aggregation operators,” Socio-Economic Planning Sciences, p. 101949, 2024.
A. Hussain and K. Ullah, “An intelligent decision support system for spherical fuzzy sugenoweber aggregation operators and real-life applications,” Spectrum of Mechanical Engineering and Operational Research, vol. 1, no. 1, pp. 177–188, 2024.
J. Kannan, V. Jayakumar, and M. Pethaperumal, “Advanced fuzzy-based decision-making: the linear diophantine fuzzy codas method for logistic specialist selection,” Spectrum of Operational Research, vol. 2, no. 1, pp. 41–60, 2025.
M.Akram, A.Bashir, and S. Edalatpanah, “A hybrid decision-making analysis under complex q-rung picture fuzzy einstein averaging operators. comput appl math 40: 305,” 2021.
F. Smarandache, The dynamic interplay of opposites in zoroastrianism. Infinite Study, 2024.
M. Ghaforiyan, A. Sorourkhah, and S. A. Edalatpanah, “Identifying and prioritizing antifragile tourism strategies in a neutrosophic environment,” Journal of Fuzzy Extension and Applications, vol. 5, no. 3, pp. 374–394, 2024.
A. Nafei, S. P. Azizi, S. A. Edalatpanah, and C.-Y. Huang, “Smart topsis: a neural networkdriven topsis with neutrosophic triplets for green supplier selection in sustainable manufacturing,” Expert systems with applications, vol. 255, p. 124744, 2024.
M. Ihsan, M. Saeed, and A. Rahman, “Optimizing hard disk selection via a fuzzy parameterized single-valued neutrosophic soft set approach,” Journal of operational and strategic analytics, vol. 1, no. 2, pp. 62–69, 2023.
W. Abdullah, “A study of neutrosophic sets and deep learning models for breast cancer classification,” Multicriteria Algorithms with Applications, vol. 3, pp. 50–59, 2024.
H. Zare Ahmadabadi, A. Saffari Darberazi, F. Zamzam, M. S. Babakhanifard, M. Kiani, and E. Mofatehzadeh, “A model of the factors affecting supply chain resilience: an integrative approach incorporating hesitant fuzzy topsis and meta-synthesis,” Journal of Applied Research on Industrial Engineering, vol. 11, no. 2, pp. 195–211, 2024.
S. Jana, A. Patel, and J. Mahanta, “Decomposition of a pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects,” Journal of Fuzzy Extension and Applications, vol. 5, no. 2, pp. 251–274, 2024.
P. Mahalakshmi, J. Vimala, K. Jeevitha, and S. Nithya Sri, “Advancing cybersecurity strategies for multinational corporations: Novel distance measures in q-rung orthopair multi-fuzzy systems,” J. Oper. Strateg Anal, vol. 2, no. 1, pp. 49–55, 2024.
M. Pethaperumal, V. Jayakumar, S. A. Edalatpanah, A. B. K. Mohideen, and S. Annamalai, “An enhanced madm with l q* q-rung orthopair multi-fuzzy soft set in healthcare supplier selection,” Journal of Intelligent & Fuzzy Systems, no. Preprint, pp. 1–12, 2024.
N. N. Mostafa, A. K. Kumar, and Y. Ali, “A comparative study on x-ray image enhancement based on neutrosophic set,” Sustainable Machine Intelligence Journal, vol. 7, pp. 2–1, 2024.
M. Mohamed, A. Salam, and J. Ye, “Selection of sustainable material for the construction of drone aerodynamic wing using neutrosophic rawec,” Systems Assessment and Engineering Management, vol. 1, pp. 54–72, 2024.
M. Saeed and M. I. Harl, “Fundamentals of picture fuzzy hypersoft set with application,” Neutrosophic Sets and Systems, vol. 53, no. 1, p. 24, 2023.
M. Saeed, M. Ahsan, M. H. Saeed, A. Mehmood, and S. El-Morsy, “Assessment of solid waste management strategies using an efficient complex fuzzy hypersoft set algorithm based on entropy and similarity measures,” IEEE Access, vol. 9, pp. 150700–150714, 2021.
J. A. Goguen, “L-fuzzy sets,” Journal of mathematical analysis and applications, vol. 18, no. 1, pp. 145–174, 1967.
Y. Gentilhomme, “Les ensembles flous en linguistique,” Cahiers de linguistique th´eorique et appliqu´ee, vol. 5, pp. 47–63, 1968.
D. Dubois and H. Prade, “Twofold fuzzy sets and rough sets—some issues in knowledge representation,” Fuzzy sets and Systems, vol. 23, no. 1, pp. 3–18, 1987.
M. Saeed, M. El-Ghoneimy, and H. Kamal, “An enhanced fuzzy logic optimization technique based on user mobility for lte handover,” in 2017 34th national radio science conference (NRSC), pp. 230–237, IEEE, 2017.
J. A. Goguen, “L-fuzzy sets,” Journal of mathematical analysis and applications, vol. 18, no. 1, pp. 145–174, 1967.
K. Atanassov, “Review and new results on intuitionistic fuzzy sets,” preprint IM-MFAIS-1-88, sofia, vol. 5, no. 1, 1988.
K. T. Atanassov and K. T. Atanassov, “Interval valued intuitionistic fuzzy sets,” Intuitionistic fuzzy sets: Theory and applications, pp. 139–177, 1999.
G.-J. Wang and Y.-Y. He, “Intuitionistic fuzzy sets and l-fuzzy sets,” Fuzzy Sets and Systems, vol. 110, no. 2, pp. 271–274, 2000.
E. Kerre, “A first view on the alternatives of fuzzy set theory,” in Computational intelligence in Theory and Practice, pp. 55–71, Springer, 2001.
G. Deschrijver and E. E. Kerre, “On the relationship between some extensions of fuzzy set theory,” Fuzzy sets and systems, vol. 133, no. 2, pp. 227–235, 2003.
D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, and H. Prade, “Terminological difficulties in fuzzy set theory—the case of “intuitionistic fuzzy sets”,” Fuzzy sets and systems, vol. 156, no. 3, pp. 485–491, 2005.
G. Takeuti and S. Titani, “Intuitionistic fuzzy logic and intuitionistic fuzzy set theory,” The journal of symbolic logic, vol. 49, no. 3, pp. 851–866, 1984.
F. Smarandache, “Neutrosophic set-a generalization of the intuitionistic fuzzy set.,” International journal of pure and applied mathematics, vol. 24, no. 3, p. 287, 2005.
K. Georgiev, “A simplification of the neutrosophic sets. neutrosophic logic and intuitionistic fuzzy sets,” Notes on Intuitionistic Fuzzy Sets, vol. 11, no. 2, pp. 28–31, 2005.
M. Saeed, A. Mehmood, and M. Arslan, “Multipolar interval-valued fuzzy set with application of similarity measures and multi-person topsis technique,” Punjab University Journal of Mathematics, vol. 53, no. 10, 2021.
M. Saeed, M. Ahsan, M. H. Saeed, A. U. Rahman, A. Mehmood, M. A. Mohammed, M. M. Jaber, and R. Damaˇ seviˇ cius, “An optimized decision support model for covid-19 diagnostics based on complex fuzzy hypersoft mapping,” Mathematics, vol. 10, no. 14, p. 2472, 2022.
M. Saeed, M. Ahsan, A. Ur Rahman, M. H. Saeed, and A. Mehmood, “An application of neutrosophic hypersoft mapping to diagnose brain tumor and propose appropriate treatment,” Journal of Intelligent & Fuzzy Systems, vol. 41, no. 1, pp. 1677–1699, 2021.
H. Wang, F. Smarandache, Y. Zhang, and R. Sunderraman, “Single valued neutrosophic sets,” Infinite study, vol. 12, p. 20110, 2010.
M. Saeed, M. Saqlain, A. Mehmood, and S. Yaqoob, “Multi-polar neutrosophic soft sets with application in medical diagnosis anddecision-making,” Neutrosophic Sets and Systems, vol. 33, pp. 183–207, 2020.
J. Ye, “A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets,” Journal of Intelligent & Fuzzy Systems, vol. 26, no. 5, pp. 2459–2466, 2014.
J.-j. Peng, J.-q. Wang, J. Wang, H.-y. Zhang, and X.-h. Chen, “Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems,” International journal of systems science, vol. 47, no. 10, pp. 2342–2358, 2016.
P. 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.
X.ZhangandP.Liu, “Methodforaggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making,” Technological and economic development of economy, vol. 16, no. 2, pp. 280–290, 2010.
L. A. Zadeh, G. J. Klir, and B. Yuan, Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers, vol. 6. World scientific, 1996.
L. A. Zadeh, “Fuzzy sets and information granularity,” Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers, pp. 433–448, 1979.
M. Mizumoto and K. Tanaka, “Some properties of fuzzy sets of type 2,” Information and control, vol. 31, no. 4, pp. 312–340, 1976.
M. I. Ali, “Another view on q-rung orthopair fuzzy sets,” International Journal of Intelligent Systems, vol. 33, no. 11, pp. 2139–2153, 2018.
H. Oh, H. Kim, H. Kim, and C. Kim, “A method for improving the multiplicative inconsistency based on indeterminacy of an intuitionistic fuzzy preference relation,” Information Sciences, vol. 602, pp. 1–12, 2022.
S. Alblowi, A. Salama, and M. Eisa, New concepts of neutrosophic sets. Infinite Study, 2014.
R. Mallick and S. Pramanik, Pentapartitioned neutrosophic set and its properties, vol. 36. Infinite Study, 2020.
A. M. Khalil, D. Cao, A. Azzam, F. Smarandache, and W. R. Alharbi, “Combination of the single-valued neutrosophic fuzzy set and the soft set with applications in decision-making,” Symmetry, vol. 12, no. 8, p. 1361, 2020.
F. Smarandache, “Neutrosophic set is a generalization of intuitionistic fuzzy set, inconsistent intuitionistic fuzzy set (picture fuzzy set, ternary fuzzy set), pythagorean fuzzy set, spherical fuzzy set, and q-rung orthopair fuzzy set, while neutrosophication is a generalization of regret theory, grey system theory, and three-ways decision (revisited),” Journal of New Theory, no. 29, pp. 1–31, 2019.
J. P. Kleijnen and R. Y. Rubinstein, “Optimization and sensitivity analysis of computer simulation models by the score function method,” European Journal of Operational Research, vol. 88, no. 3, pp. 413–427, 1996.
R. Kliegl, U. Maayr, and R. T. Krampe, “Time-accuracy functions for determining process and person differences: An application to cognitive aging,” Cognitive Psychology, vol. 26, no. 2, pp. 134–164, 1994.
M. Kokoc¸ and S. Ers¨ oz, “New score and accuracy function for ivif sets and their applications to ahp for mcgdm,” Cybernetics and Systems, vol. 53, no. 3, pp. 257–281, 2022.
J. Ali, M. Naeem, and W. Mahmood, “Generalized q-rung picture linguistic aggregation operators and their application in decision making,” Journal of Intelligent & Fuzzy Systems, no. Preprint, pp. 1–25.
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Published
2025-07-08
How to Cite
SAEED, Muhammad et al.
A Robust Algorithmic Framework for the Evaluation of World Happiness Ranking Based on Q Rung Orthopair Triangular Fuzzy Neutrosophic Set With Possibility Setting (PQ-RTFNS).
Yugoslav Journal of Operations Research, [S.l.], july 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1349>. Date accessed: 09 july 2025.
doi: https://doi.org/10.2298/YJOR240718017S.
Issue
Section
Research Articles
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
