Volume 27 , Issue 2 , PP: 413-436, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
F. Smarandache 1 , B. Kalins 2 , D. Anandakumar 3 , N. Selvanayaki 4 , S. Krishnaprakash 5 *
Doi: https://doi.org/10.54216/IJNS.270234
This study addresses the inherent challenges of uncertainty, vagueness, and imprecision in real-world decision-making, particularly focusing on the problem small-scale farmer’s face in optimally selecting short-term crops across diverse planting seasons. The central challenge is the absence of a systematic framework to evaluate multiple, often conflicting, criteria such as initial investment, expected yield, market demand, water and soil requirements, specific fertilizer needs, and pest susceptibility. To overcome this, a robust Multi-Criteria Decision-Making (MCDM) framework is introduced, integrating Cubic Spherical Neutrosophic Sets (CSNS) with Neutrosophic Hyper Soft Sets (NHSS). The research proposes the cubic spherical neutrosophic Bonferroni mean operator as a novel geometric representation for aggregating neutrosophic sets, which enables a more refined modeling of uncertainty and indeterminacy in complex environments. Cubic Spherical Neutrosophic Sets embed neutrosophic information within a spherical structure using interval-based (Truth, Indeterminacy, Falsity) triplets and a radius, offering robust aggregation and ranking capabilities. Neutrosophic hypersoft sets further enhance logical expressiveness by associating each multi-parameter tuple with a neutrosophic triplet, effectively managing complex multi-attribute decision-making tasks with deep interdependencies. The applicability and effectiveness of this approach are demonstrated through a practical case study involving the selection of the most suitable crop for different climatic zones (Pattams) in Tamil Nadu, considering agricultural, environmental, and economic factors. Expert linguistic assessments are converted into neutrosophic values and aligned with seasonal cropping patterns. A subsequent sensitivity analysis confirms the robustness of the model, revealing a perfect correlation between the outcomes of different decision-making methods and thereby validating the consistency and reliability of the proposed approach. This context-aware, data-driven tool aims to enhance decision-making, improve resource utilization, reduce risks, and promote agricultural sustainability and improved farmer livelihoods.
Soft sets , Hypersoft sets, Neutrosophic Soft sets , Neutrosophic Hypersoft sets
[1] Abbas, M., Murtaza, G., and Smarandache, F., "Basic operations on hypersoft sets and hypersoft point," Neutrosophic Sets and Systems, vol. 35, no. 1, pp. 1–8, 2020.
[2] Ahmed, A., Badawy, M., and Gubarah, G. F., "Modelling of Green Human Resource Management using Pythagorean Neutrosophic Bonferroni Mean Approach," International Journal of Neutrosophic Science, vol. 24, no. 2, 2024.
[3] Azam, M., and Jadoon, A. M., "Neutrosophic Cubic Fuzzy Bonferroni Arithematic Mean Operator and Its Application in Group Decision Making Problems," 2024.
[4] M. S. Bin Mohammad Kamari, Z. B. M. Rodzi, R. H. Al-Obaidi, F. Al-Sharq, and A. Al-Quran, "Deciphering the geometric Bonferroni mean operator in Pythagorean neutrosophic sets framework," Neutrosophic Sets and Systems, vol. 75, pp. 139-161, 2025.
[5] Badawood, D., "Pythagorean Neutrosophic Bonferroni Mean Based Machine Learning Model for Data Analytics and Sentiment Classification of Product Reviews," International Journal of Neutrosophic Science, vol. 25, no. 3, 2025.
[6] Bonferroni, C. E., "Sulle medie multiple di potenze," Bollettino della Unione Matematica Italiana, vol. 5, pp. 267–270, 1950.
[7] Darvesh, A., Naeem, K., and Shah, S. B. H., "Scrutiny of Neutrosophic Cubic Fuzzy Data with Different Parametric Values using Bonferroni Weighted Mean: A Robust MCDM Approach," Decision Making Advances, vol. 3, no. 1, pp. 245-265, 2025.
[8] Fan, Z., and Song, W., "Sustainable Cost Management and Risk Evaluation in Prefabricated Infrastructure Projects under the Neutrosophic Bonferroni Mean Operator," Neutrosophic Sets and Systems, vol. 83, pp. 910-926, 2025.
[9] Gomathi, S., Krishnaprakash, S., Karpagadevi, M., and Broumi, S., "Cubic Spherical Neutrosophic Sets," International Journal of Neutrosophic Science, pp. 172-180, 2023.
[10] Hema, R., Sudharani, R., and Kavitha, M., "A novel approach on plithogenic interval valued neutrosophic hypersoft sets and its application in decision making," Indian Journal of Science and Technology, 2023.
[11] Kanchana, A., Nagarajan, D., and Broumi, S., "Multi-attribute group decision-making based on the Neutrosophic Bonferroni mean operator," Neutrosophic Sets and Systems, vol. 57, p. 139, 2024.
[12] Kara, K., Yalcin, G. C., Gurol, P., Simic, V., and Pamucar, D., "Enhancing decision support system for finished vehicle logistics service provider selection through a single-valued neutrosophic Dombi Bonferroni-based model," Engineering Applications of Artificial Intelligence, vol. 138, p. 109441, 2024.
[13] Khan, M., Gulistan, M., Alhussein, M., Aurangzeb, K., and Khurshid, A., "Navigating ambiguity: A novel neutrosophic cubic shapley normalized weighted Bonferroni Mean aggregation operator with application in the investment environment," Heliyon, vol. 10, no. 17, 2024.
[14] Krishnaprakash, S., R. Mariappan, and Said Broumi, "Cubic Spherical Neutrosophic Sets and Selection of Electric Truck Using Cosine Similarity Measure," Neutrosophic Sets and Systems, vol. 67, no. 1, 2024.
[15] Matyakubov, U., Sharofutdinova, R., Ilyin, A., Shichiyakh, R., Shankar, K., and Lydia, E. L., "An Intelligent Decision Support Systems for Financial Fraud Detection Using Pythagorean Neutrosophic Bonferroni Mean Approach with Machine Learning Models," International Journal of Neutrosophic Science, vol. 25, no. 4, 2025.
[16] Molodtsov, D., "Soft set theory—First results," Computers & Mathematics with Applications, vol. 37, no. 4–5, pp. 19–31, 1999.
[17] Noorraha, A. R., "Enhancing Digital Social Innovation Ecosystems: A Pythagorean Neutrosophic Bonferroni Mean (PNBM)-DEMATEL Analysis of Barriers Factors for Young Entrepreneurs," International Journal of Neutrosophic Science, vol. 23, no. 4, pp. 170-180, 2024.
[18] Önden, A., Kara, K., Önden, İ., Yalçın, G. C., Simic, V., and Pamucar, D., "Exploring the adoption of the metaverse and chat generative pre-trained transformer: A single-valued neutrosophic Dombi Bonferroni-based method for the selection of software development strategies," Engineering Applications of Artificial Intelligence, vol. 133, p. 108378, 2024.
[19] R. M. Zulqarnain, I. Siddique, R. Ali, F. Jarad, A. Samad, and T. Abdeljawad, "Neutrosophic Hypersoft Matrices with Application to Solve Multiattributive Decision‐Making Problems," Complexity, vol. 2021, no. 1, p. 5589874, 2021.
[20] A. Saleh and M. M. Ali, "Plithogenic Hypersoft Sets and Their Application in Multi-Attribute Decision Making," IEEE Access, vol. 8, pp. 123456-123467, 2024.
[21] Revathy, A., Inthumathi, V., Krishnaprakash, S., Gomathi, S., and Akiladevi, N., "MCDM Using Normalized Weighted Bonferroni Mean Operator in Fermatean Neutrosophic Environment," in Neutrosophic and Plithogenic Inventory Models for Applied Mathematics, pp. 387-410, IGI Global, 2025.
[22] X. Peng and J. Dai, "A Novel Dombi Bonferroni Mean Operator under Pythagorean Neutrosophic Environment for Renewable Energy Source Selection," International Journal of Intelligent Systems, vol. 35, no. 10, pp. 2345-2367, 2023.
[23] Rodzi, Z., N. A. Binti Shafie, N. B. Abdul Razak, F. Al-Sharqi, A. Al-Quran, and A. Bany Awad, "Enhancing Digital Social Innovation Ecosystems: A Pythagorean Neutrosophic Bonferroni Mean (PNBM)-DEMATEL Analysis of Barriers Factors for Young Entrepreneurs," International Journal of Neutrosophic Science, vol. 23, no. 4, 2024.
[24] Saeed, M., Ahsan, M., Siddique, M., and Ahmad, M., "A study of the fundamentals of hypersoft set theory," International Journal of Science and Engineering Research, pp. 1–10, 2020.
[25] Smarandache, F., A unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic. American Research Press, 1999.
[26] Smarandache, F., "Foundation of the super hypersoft set and the fuzzy extension super hypersoft set: A new vision," Neutrosophic Systems with Applications, vol. 11, pp. 48–51, 2023.