A Similarity Measures-Based TOPSIS Method for Neutrosophic Hypersoft Set with Application in Crop Production

Authors

  • Vijay Govindarajan Distribution and Supply Technology, Expedia Group, Seattle, WA 98119, USA https://orcid.org/0009-0004-1915-1519
  • Amr Yousef Electrical Engineering Department, University of Business and Technology, Jeddah, 21432, Saudi Arabia | Engineering Mathematics Department, Alexandria University, Alexandria, 21544, Egypt https://orcid.org/0000-0003-0875-6462
  • Aleen Ijaz Chaudhary Department of Mathematics, University of Management and Technology, Lahore, Pakistan | Department of Mathematics, Faculty of Basic Sciences, Lahore Garrison University, DHA Phase 6, 54000, Lahore, Pakistan
  • Adil Ahmad Department of Computer Science and Information Technology, Virtual University of Pakistan, Pakistan
  • Zaffar Ahmed Shaikh Department of Computer Science and Information Technology, Benazir Bhutto Shaheed University Lyari, Karachi, 75660, Pakistan | School of Engineering, Ecole Polytechnique Federale de Lausanne, 1015, Lausanne, Switzerland https://orcid.org/0000-0003-0323-2061
Volume: 16 | Issue: 1 | Pages: 31863-31873 | February 2026 | https://doi.org/10.48084/etasr.15496

Abstract

Neutrosophic sets and hypersoft sets are both fuzzy set extensions that deal with various aspects of uncertainty and missing data. Combining these two frameworks within Multi-Criteria Decision-Making (MCDM) allows choosing an optimal solution from a wide range of scenarios and alternatives. TOPSIS is a significant practical method for evaluating and selecting numerous possibilities, which ranks preferences according to how closely they resemble the ideal solution. This study used similarity and distance measures for NHSS and aggregate NHSS decision matrices by employing aggregation operators. The proposed NHSS-TOPSIS technique was used to assess the fertility of the soil for the production of specific crops. Multiple criteria were considered to make decisions regarding crop production based on soil conditions and other factors. This work can be further broadened to various existing hybrids of hypersoft sets, such as Intuitionistic Fuzzy Hypersoft Sets (IFHSS), Pythagorean Fuzzy Hypersoft Sets (PFHSS), Bipolar fuzzy hypersoft sets, Pythagorean Fuzzy Hypersoft Matrices (PFHSM), and neutrosophic hybrids.

Keywords:

Multi-Criteria Decision-Making (MCDM), distance, similarity, Neutrosophic Hypersoft Set (NHSS), Neutrosophic Hypersoft Matrices (NHSM), TOPSIS

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References

L. A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, no. 3, pp. 338–353, June 1965. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X

K. T. Atanassov, "Intuitionistic Fuzzy Sets," in Intuitionistic Fuzzy Sets: Theory and Applications, K. T. Atanassov, Ed. Physica-Verlag HD, 1999, pp. 1–137. DOI: https://doi.org/10.1007/978-3-7908-1870-3_1

J. M. Mendel and R. I. B. John, "Type-2 fuzzy sets made simple," IEEE Transactions on Fuzzy Systems, vol. 10, no. 2, pp. 117–127, Apr. 2002. DOI: https://doi.org/10.1109/91.995115

R. R. Yager and A. M. Abbasov, "Pythagorean Membership Grades, Complex Numbers, and Decision Making," International Journal of Intelligent Systems, vol. 28, no. 5, pp. 436–452, 2013. DOI: https://doi.org/10.1002/int.21584

F. Smarandache, Neutrosophy: Neutrosophic Probability, Set, and Logic : Analytic Synthesis & Synthetic Analysis. American Research Press, 1998.

H. Wang, F. Smarandache, Y. Zhang, and R. Sunderraman, "Single Valued Neutrosophic Sets," in Multispace & Multistructure. Neutrosophic Transdisciplinarity, North European Scientific Publishers, 2010.

D. Molodtsov, "Soft set theory—First results," Computers & Mathematics with Applications, vol. 37, no. 4, pp. 19–31, Feb. 1999. DOI: https://doi.org/10.1016/S0898-1221(99)00056-5

P. K. Maji, R. Biswas, and A. R. Roy, "Soft set theory," Computers & Mathematics with Applications, vol. 45, no. 4, pp. 555–562, Feb. 2003. DOI: https://doi.org/10.1016/S0898-1221(03)00016-6

A. R. Roy and P. K. Maji, "A fuzzy soft set theoretic approach to decision making problems," Journal of Computational and Applied Mathematics, vol. 203, no. 2, pp. 412–418, June 2007. DOI: https://doi.org/10.1016/j.cam.2006.04.008

H. Wang, F. Smarandache, R. Sunderraman, and Y. Q. Zhang, "Interval Neutrosophic Sets," in Interval Neutrosophic Sets and Logic: Theory and Applications in Computing: Theory and Applications in Computing, ProQueast Information & Learning, 2005.

J. Peng, J. Wang, J. Wang, H. Zhang, and X. 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, July 2016. DOI: https://doi.org/10.1080/00207721.2014.994050

P. K. Maji, "Neutrosophic soft set," Annals of Fuzzy Mathematics and Informatics, vol. 5, no. 1, pp. 157–1668, Jan. 2013.

J. Ye, "An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers," Journal of Intelligent & Fuzzy Systems, vol. 28, no. 1, pp. 247–255, Jan. 2015. DOI: https://doi.org/10.3233/IFS-141295

Z. Tian, J. Wang, H. Zhang, X. Chen, and J. Wang, "Simplified Neutrosophic Linguistic Normalized Weighted Bonferroni Mean Operator and Its Application to Multi-Criteria Decision-Making Problems," Filomat, vol. 30, no. 12, pp. 3339–3360, 2016. DOI: https://doi.org/10.2298/FIL1612339T

J. Q. Wang and X. E. Li, "TODIM method with multi-valued neutrosophic sets," Control Decision, vol. 30, no. 6, pp. 1139–1142, 2015.

S. Broumi, F. Smarandache, and M. Dhar, "Rough Neutrosophic Sets," in Collected Papers On Neutrosophics, Plithogenics, Hypersoft Set, Hypergraphs, and other topics, vol. X, Global Knowledge, 2022.

M. Riaz, M. A. Khokhar, D. Pamucar, and M. Aslam, "Cubic M-polar Fuzzy Hybrid Aggregation Operators with Dombi’s T-norm and T-conorm with Application," Symmetry, vol. 13, no. 4, Apr. 2021, Art. no. 646. DOI: https://doi.org/10.3390/sym13040646

S. Broumi and F. Smarandache, "Several Similarity Measures of Neutrosophic Sets," in Collected Papers On Neutrosophics Theory and Applications, vol. XII, Global Knowledge, 2022.

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, May 2013. DOI: https://doi.org/10.1080/03081079.2012.761609

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, May 2014. DOI: https://doi.org/10.3233/IFS-130916

J. Ye, "Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making," International Journal of Fuzzy Systems, vol. 16, no. 2, Jun. 2014.

P. Majumdar and S. K. Samanta, "On similarity and entropy of neutrosophic sets," Journal of Intelligent & Fuzzy Systems, vol. 26, no. 3, pp. 1245–1252, Mar. 2014. DOI: https://doi.org/10.3233/IFS-130810

J. Ye, "Clustering Methods Using Distance-Based Similarity Measures of Single-Valued Neutrosophic Sets," Journal of Intelligent Systems, vol. 23, no. 4, pp. 379–389, Dec. 2014. DOI: https://doi.org/10.1515/jisys-2013-0091

J. S. Chai et al., "New similarity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems," Complex & Intelligent Systems, vol. 7, no. 2, pp. 703–723, Apr. 2021. DOI: https://doi.org/10.1007/s40747-020-00220-w

K. Mondal and S. Pramanik, "Neutrosophic tangent similarity measure and its application to multiple attribute decision making," Neutrosophic Sets and Systems, vol. 9, pp. 80–88, Sept. 2015.

C. Liu, "New similarity measures of simplified neutrosophic sets and their applications," Journal of Information Processing Systems, vol. 14, no. 3, pp. 790–800, Jun. 2018.

M. Naveed, A. Farooq, K. Javed, and N. Nawaz, "Similarity Measures of Tangent, Cotangent and Cosines in Neutrosophic Environment and their Application in Selection of Academic Programs," International Journal of Computer Applications, vol. 177, no. 46, pp. 17–24, Mar. 2020. DOI: https://doi.org/10.5120/ijca2020919980

M. Akram, F. Ilyas, and H. Garg, "Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information," Soft Computing, vol. 24, no. 5, pp. 3425–3453, Mar. 2020. DOI: https://doi.org/10.1007/s00500-019-04105-0

H. Garg, Nancy, H. Garg, and Nancy, "Some New Biparametric Distance Measures on Single-Valued Neutrosophic Sets with Applications to Pattern Recognition and Medical Diagnosis," Information, vol. 8, no. 4, Dec. 2017. DOI: https://doi.org/10.3390/info8040162

M. S. Yang and D. C. Lin, "On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering," Computers & Mathematics with Applications, vol. 57, no. 6, pp. 896–907, Mar. 2009. DOI: https://doi.org/10.1016/j.camwa.2008.10.028

W. L. Hung and M. S. Yang, "Similarity measures between type-2 fuzzy sets," International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 12, no. 06, pp. 827–841, Dec. 2004. DOI: https://doi.org/10.1142/S0218488504003235

D. D. Trung, "Development of data normalization methods for multi-criteria decision making: applying for MARCOS method," Manufacturing Review, vol. 9, 2022, Art. no. 22. DOI: https://doi.org/10.1051/mfreview/2022019

D. D. Trung, N. X. Truong, D. V. Duc, and N. C. Bao, "Data normalization in RAWEC method: Limitations and remedies," Yugoslav Journal of Operations Research, vol. 35, no. 3, pp. 467–482, 2025. DOI: https://doi.org/10.2298/YJOR240315020T

D. D. Trung, B. Dudic, N. T. Nguyen, and A. Ašonja, "Data Normalization for Root Assessment Methodology," International Journal of Industrial Engineering and Management, vol. 15, no. 2, pp. 156–168, June 2024. DOI: https://doi.org/10.24867/IJIEM-2024-2-354

D. D. Trung, N. Ersoy, T. V. Dua, and H. X. Thinh, "A comparative evaluation of data normalization techniques using different metrics: practical application to a MCDM method," Manufacturing Review, vol. 12, 2025, Art. no. 19. DOI: https://doi.org/10.1051/mfreview/2025013

M. Shams and S. Abdullah, "Selection of best industrial waste management technique under complex non-linear Diophantine fuzzy Dombi aggregation operators," Applied Soft Computing, vol. 148, Nov. 2023, Art. no. 110855. DOI: https://doi.org/10.1016/j.asoc.2023.110855

M. N. Kordkandy, A. Arash, and M. N. Kordkandy, "Hydrogen Gas Production in a Stand-Alone Wind Farm," Engineering, Technology & Applied Science Research, vol. 7, no. 2, pp. 1444–1449, Apr. 2017. DOI: https://doi.org/10.48084/etasr.991

W. M. A. W. Ahmad, R. A. A. Rohim, Y. Norhayati, N. A. Aleng, and Z. Ali, "Developing A New Dimension of an Applied Exponential Model: Application in Biological Sciences," Engineering, Technology & Applied Science Research, vol. 8, no. 4, pp. 3130–3134, Aug. 2018. DOI: https://doi.org/10.48084/etasr.2124

F. Smarandache, "Extension of Soft Set to Hypersoft Set, and Then to Plithogenic Hypersoft Set," Neutrosophic Sets and Systems, vol. 22, no. 1, pp. 168–170, 2018.

M. N. Jafar and M. Saeed, "Aggregation Operators of Fuzzy Hypersoft Sets," Turkish Journal of Fuzzy Systems, vol. 11, no. 1, 2021.

M. Saeed, M. Ahsan, and T. Abdeljawad, "A Development of Complex Multi-Fuzzy Hypersoft Set With Application in MCDM Based on Entropy and Similarity Measure," IEEE Access, vol. 9, pp. 60026–60042, 2021. DOI: https://doi.org/10.1109/ACCESS.2021.3073206

M. Saqlain, S. Moin, M. N. Jafar, M. Saeed, and F. Smarandache, "Aggregate Operators of Neutrosophic Hypersoft Set," Neutrosophic Sets and Systems, vol. 32, pp. 294–306, 2020.

M. Saeed, M. Ahsan, M. H. Saeed, A. Mehmood, and T. Abdeljawad, "An Application of Neutrosophic Hypersoft Mapping to Diagnose Hepatitis and Propose Appropriate Treatment," IEEE Access, vol. 9, pp. 70455–70471, 2021. DOI: https://doi.org/10.1109/ACCESS.2021.3077867

M. Saeed, M. Ahsan, A. Mehmood, M. H. Saeed, and J. Asad, "Infectious Diseases Diagnosis and Treatment Suggestions Using Complex Neutrosophic Hypersoft Mapping," IEEE Access, vol. 9, pp. 146730–146744, 2021. DOI: https://doi.org/10.1109/ACCESS.2021.3123659

A. U. Rahman, M. Saeed, and A. Dhital, "Decision Making Application Based on Neutrosophic Parameterized Hypersoft Set Theory," Neutrosophic Sets and Systems, vol. 41, pp. 1–14, Mar. 2021.

M. N. Jafar, M. Saeed, K. M. Khan, F. S. Alamri, and H. A. E. W. Khalifa, "Distance and Similarity Measures Using Max-Min Operators of Neutrosophic Hypersoft Sets With Application in Site Selection for Solid Waste Management Systems," IEEE Access, vol. 10, pp. 11220–11235, 2022. DOI: https://doi.org/10.1109/ACCESS.2022.3144306

M. N. Jafar, M. Saeed, M. Saqlain, and M. S. Yang, "Trigonometric Similarity Measures for Neutrosophic Hypersoft Sets With Application to Renewable Energy Source Selection," IEEE Access, vol. 9, pp. 129178–129187, 2021. DOI: https://doi.org/10.1109/ACCESS.2021.3112721

M. N. Jafar, M. Saeed, A. Saeed, A. Ijaz, M. Ashraf, and F. Jarad, "Cosine and cotangent similarity measures for intuitionistic fuzzy hypersoft sets with application in MADM problem," Heliyon, vol. 10, no. 7, Apr. 2024. DOI: https://doi.org/10.1016/j.heliyon.2024.e27886

S. Opricovic and G. H. Tzeng, "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, vol. 156, no. 2, pp. 445–455, July 2004. DOI: https://doi.org/10.1016/S0377-2217(03)00020-1

J. P. Brans, Ph. Vincke, and B. Mareschal, "How to select and how to rank projects: The Promethee method," European Journal of Operational Research, vol. 24, no. 2, pp. 228–238, Feb. 1986. DOI: https://doi.org/10.1016/0377-2217(86)90044-5

X. Zhang and Z. Xu, "Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets," International Journal of Intelligent Systems, vol. 29, no. 12, pp. 1061–1078, 2014. DOI: https://doi.org/10.1002/int.21676

C. L. Hwang and K. Yoon, Multiple Attribute Decision Making, vol. 186. Springer, 1981. DOI: https://doi.org/10.1007/978-3-642-48318-9

M. Behzadian, S. Khanmohammadi Otaghsara, M. Yazdani, and J. Ignatius, "A state-of the-art survey of TOPSIS applications," Expert Systems with Applications, vol. 39, no. 17, pp. 13051–13069, Dec. 2012. DOI: https://doi.org/10.1016/j.eswa.2012.05.056

M. Saqlain, M. Riaz, M. A. Saleem, and M. S. Yang, "Distance and Similarity Measures for Neutrosophic HyperSoft Set (NHSS) With Construction of NHSS-TOPSIS and Applications," IEEE Access, vol. 9, pp. 30803–30816, 2021. DOI: https://doi.org/10.1109/ACCESS.2021.3059712

H. Meinke et al., "Increasing profits and reducing risks in crop production using participatory systems simulation approaches," Agricultural Systems, vol. 70, no. 2, pp. 493–513, Nov. 2001. DOI: https://doi.org/10.1016/S0308-521X(01)00057-9

S. Kousar and N. Kausar, "Multi-Criteria Decision-Making for Sustainable Agritourism: An Integrated Fuzzy-Rough Approach," Spectrum of Operational Research, vol. 2, no. 1, pp. 134–150, Jan. 2025. DOI: https://doi.org/10.31181/sor21202515

S. Biswas, S. Bhattacharjee, B. Biswas, K. Mitra, and N. Khawas, "An Expert Opinion-Based Soft Computing Framework for Comparing Nanotechnologies used in Agriculture," Spectrum of Operational Research, pp. 1–39, 2027. DOI: https://doi.org/10.31181/sor4156

T. Fujita, "The Hyperfuzzy VIKOR and Hyperfuzzy DEMATEL Methods for Multi-Criteria Decision-Making," Spectrum of Decision Making and Applications, vol. 3, no. 1, pp. 292–315, 2026. DOI: https://doi.org/10.31181/sdmap31202654

T. Basuri, K. H. Gazi, P. Bhaduri, S. G. Das, and S. P. Mondal, "Decision-analytics-based Sustainable Location Problem - Neutrosophic CRITIC-COPRAS Assessment Model," Management Science Advances, vol. 2, no. 1, pp. 19–58, Feb. 2025. DOI: https://doi.org/10.31181/msa2120257

S. Eraslan and F. Karaaslan, "A Group Decision Making Method Based on TOPSIS Under Fuzzy Soft Environment," Journal of New Theory, no. 3, pp. 30–40, Apr. 2015.

X. Peng and J. Dai, "Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function," Neural Computing and Applications, vol. 29, no. 10, pp. 939–954, May 2018. DOI: https://doi.org/10.1007/s00521-016-2607-y

K. Naeem, M. Riaz, and D. Afzal, "Pythagorean m-polar fuzzy sets and TOPSIS method for the selection of advertisement mode," Journal of Intelligent & Fuzzy Systems, vol. 37, no. 6, pp. 8441–8458, Dec. 2019. DOI: https://doi.org/10.3233/JIFS-191087

H. Garg and K. Kumar, "A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory," Artificial Intelligence Review, vol. 53, no. 1, pp. 595–624, Jan. 2020. DOI: https://doi.org/10.1007/s10462-018-9668-5

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V. Govindarajan, A. Yousef, A. I. Chaudhary, A. Ahmad, and Z. A. Shaikh, “A Similarity Measures-Based TOPSIS Method for Neutrosophic Hypersoft Set with Application in Crop Production”, Eng. Technol. Appl. Sci. Res., vol. 16, no. 1, pp. 31863–31873, Feb. 2026.

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