The Hyperfuzzy VIKOR and Hyperfuzzy DEMATEL Methods for Multi-Criteria Decision-Making

Takaaki Fujita

doi:10.31181/sdmap31202654

Authors

Takaaki Fujita Independent Researcher, Shinjuku, Tokyo, Japan Author https://orcid.org/0000-0002-9380-386X

DOI:

https://doi.org/10.31181/sdmap31202654

Keywords:

Hyperfuzzy set, Fuzzy set, SuperHyperfuzzy Set, VIKOR, DEMATEL, Fuzzy VIKOR, Fuzzy DEMATEL

Abstract

Handling uncertainty in information systems remains an active area of research, with foundational frameworks such as fuzzy sets, rough sets, intuitionistic fuzzy sets, neutrosophic sets, hyperneutrosophic sets, and plithogenic sets, among others. In particular, Hyperfuzzy Sets and SuperHyperfuzzy Sets offer a powerful means to capture multi-layered uncertainty. At the same time, fuzzy set–based decision-making techniques—such as the Analytic Hierarchy Process (AHP), DEMATEL, VIKOR, TOPSIS, and other MCDM methods—have proven highly effective in practice. In this paper, we introduce novel formulations of Hyperfuzzy VIKOR and Hyperfuzzy DEMATEL that extend the classical Fuzzy VIKOR and Fuzzy DEMATEL methods. We further develop corresponding extensions built upon the SuperHyperfuzzy Set paradigm, laying the groundwork for richer, hierarchically structured decision-making models.

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References

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X

Zadeh, L. A. (1969). Biological application of the theory of fuzzy sets and systems. Proceedings of an International Symposium on Biocybernetics of the Central Nervous System, 199–206.

Fujita, T., & Smarandache, F. (2025a). Exploring concepts of HyperFuzzy, HyperNeutrosophic, and HyperPlithogenic sets (I). Infinite Study.

Fujita, T., & Singh, P. K. (2025). Hyperfuzzy graph and hyperfuzzy hypergraph. Journal of Neutrosophic and Fuzzy Systems, 10(1), 1–13. DOI: https://doi.org/10.54216/JNFS.100101

Song, S.-Z., Kim, S. J., & Jun, Y. B. (2017). Hyperfuzzy ideals in BCK/BCI-algebras. Mathematics, 5(4), 81. DOI: https://doi.org/10.3390/math5040081

Fujita, T., & Smarandache, F. (2025b). Examples of fuzzy sets, hyperfuzzy sets, and superhyperfuzzy sets in climate change and the proposal of several new concepts. Climate Change Reports, 2, 1–18. DOI: https://doi.org/10.61356/j.ccr.2025.2485

Smarandache, F. (2017). Hyperuncertain, superuncertain, and superhyperuncertain sets/logics/probabilities/statistics. Infinite Study.

Smarandache, F. (2024). Foundation of SuperHyperStructure & Neutrosophic SuperHyperStructure. Neutrosophic Sets and Systems, 63(1), 21.

Fujita, T. (2025a). A theoretical exploration of hyperconcepts: Hyperfunctions, hyperrandomness, hyperdecision-making, and beyond (including a survey of hyperstructures). Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond, 344(498), 111.

Zadeh, L. A. (1996). Fuzzy logic, neural networks, and soft computing. In Fuzzy sets, fuzzy logic, and fuzzy systems: Selected papers by Lotfi A. Zadeh (pp. 775–782). World Scientific. DOI: https://doi.org/10.1142/9789814261302_0040

Jun, Y. B., Hur, K., & Lee, K. J. (2017). Hyperfuzzy subalgebras of BCK/BCI-algebras. Annals of Fuzzy Mathematics and Informatics. DOI: https://doi.org/10.3390/math6010011

Nazari, Z., & Mosapour, B. (2018). The entropy of hyperfuzzy sets. Journal of Dynamical Systems and Geometric Theories, 16(2), 173–185. DOI: https://doi.org/10.1080/1726037X.2018.1436270

Bordbar, H., Bordbar, M. R., Borzooei, R. A., & Jun, Y. B. (2021). N-subalgebras of BCK/BCI-algebras which are induced from hyperfuzzy structures. Iranian Journal of Mathematical Sciences and Informatics, 16(2), 179–195. DOI: https://doi.org/10.52547/ijmsi.16.2.163

Fujita, T. (2025b). Advancing uncertain combinatorics through graphization, hyperization, and uncertainization: Fuzzy, neutrosophic, soft, rough, and beyond. Biblio Publishing.

Ishak, A., Ginting, R., & Wanli, W. (2021). Evaluation of e-commerce services quality using fuzzy AHP and TOPSIS. IOP Conference Series: Materials Science and Engineering, 1041. DOI: https://doi.org/10.1088/1757-899X/1041/1/012042

Sun, C.-C. (2010). A performance evaluation model by integrating fuzzy AHP and fuzzy TOPSIS methods. Expert Systems with Applications, 37(12), 7745–7754. DOI: https://doi.org/10.1016/j.eswa.2010.04.066

Varmazyar, M., & Movahhed Nouri, B. (2014). A fuzzy AHP approach for employee recruitment. Decision Science Letters, 3, 27–36. DOI: https://doi.org/10.5267/j.dsl.2013.08.006

Kukreja, V. (2022). Fuzzy AHP-TOPSIS approaches to prioritize teaching solutions for intellect errors. Journal of Engineering Education Transformations, 35(4), 50–58. DOI: https://doi.org/10.16920/jeet/2022/v35i4/22104

Kutlu Gündoğdu, F., & Kahraman, C. (2019). Spherical fuzzy sets and spherical fuzzy TOPSIS method. Journal of Intelligent & Fuzzy Systems, 36(1), 337–352. DOI: https://doi.org/10.3233/JIFS-181401

Gündoğdu, F. K., & Kahraman, C. (2019). A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets. Engineering Applications of Artificial Intelligence, 85, 307–323. DOI: https://doi.org/10.1016/j.engappai.2019.06.003

Beg, I., & Rashid, T. (2013). TOPSIS for hesitant fuzzy linguistic term sets. International Journal of Intelligent Systems, 28(12), 1162–1171. DOI: https://doi.org/10.1002/int.21623

Kahraman, C., Cebi, S., Oztaysi, B., & Onar, S. C. (2023). Decomposed fuzzy sets and their usage in multi-attribute decision making: A novel decomposed fuzzy TOPSIS method. DOI: https://doi.org/10.20944/preprints202306.1398.v1

Kizielewicz, B., & Baczkiewicz, A. (2021). Comparison of fuzzy TOPSIS, fuzzy VIKOR, fuzzy WASPAS and fuzzy MMOORA methods in the housing selection problem. Procedia Computer Science, 192, 4578–4591. DOI: https://doi.org/10.1016/j.procs.2021.09.236

Fujita, T. (2025c). Some types of hyperdecision-making and superhyperdecision-making. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond, 221. DOI: https://doi.org/10.31224/4324

Abdel-Basset, M., Zhou, Y., Mohamed, M., & Chang, V. (2018). A group decision making framework based on neutrosophic VIKOR approach for e-government website evaluation. Journal of Intelligent & Fuzzy Systems, 34(6), 4213–4224. DOI: https://doi.org/10.3233/JIFS-171952

Eroğlu, H., & Şahin, R. (2020). A neutrosophic VIKOR method-based decision-making with an improved distance measure and score function: Case study of selection for renewable energy alternatives. Cognitive Computation, 12(6), 1338–1355. DOI: https://doi.org/10.1007/s12559-020-09765-x

Kilic, H. S., & Yalcin, A. S. (2020). Comparison of municipalities considering environmental sustainability via neutrosophic DEMATEL based TOPSIS. Socio-Economic Planning Sciences, 100827. DOI: https://doi.org/10.1016/j.seps.2020.100827

Mamites, I., Almerino Jr, P., Sitoy, R., Atibing, N. M., Almerino, J. G., Cebe, D., Ybañez, R., Tandag, J., Villaganas, M. A., Lumayag, C., et al. (2022). Factors influencing teaching quality in universities: Analyzing causal relationships based on neutrosophic DEMATEL. Education Research International, 2022(1), 9475254. DOI: https://doi.org/10.1155/2022/9475254

Abdullah, L., Ong, Z., & Mohd Mahali, S. (2021). Single-valued neutrosophic DEMATEL for segregating types of criteria: A case of subcontractors’ selection. Journal of Mathematics, 2021(1), 6636029. DOI: https://doi.org/10.1155/2021/6636029

Abdel-Basset, M., Mohamed, M., & Smarandache, F. (2018). An extension of neutrosophic AHP–SWOT analysis for strategic planning and decision-making. Symmetry, 10(4), 116. DOI: https://doi.org/10.3390/sym10040116

Bolturk, E., & Kahraman, C. (2018). A novel interval-valued neutrosophic AHP with cosine similarity measure. Soft Computing, 22, 4941–4958. DOI: https://doi.org/10.1007/s00500-018-3140-y

Senapati, T., & Chen, G. (2022). Picture fuzzy WASPAS technique and its application in multi-criteria decision-making. Soft Computing, 26(9), 4413–4421. DOI: https://doi.org/10.1007/s00500-022-06835-0

Turskis, Z., Zavadskas, E. K., Antucheviciene, J., & Kosareva, N. (2015). A hybrid model based on fuzzy AHP and fuzzy WASPAS for construction site selection. Proceedings of the International Conference on Modern Building Materials, Structures and Techniques. DOI: https://doi.org/10.15837/ijccc.2015.6.2078

Hemmati, N., Rahiminezhad Galankashi, M., Imani, D. M., & Farughi, H. (2018). Maintenance policy selection: A fuzzy-ANP approach. Journal of Manufacturing Technology Management, 29(7), 1253–1268. DOI: https://doi.org/10.1108/JMTM-06-2017-0109

Dargi, A., Anjomshoae, A., Galankashi, M. R., Memari, A., & Tap, M. B. M. (2014). Supplier selection: A fuzzy-ANP approach. Procedia Computer Science, 31, 691–700. DOI: https://doi.org/10.1016/j.procs.2014.05.317

Xia, H.-C., Li, D.-F., Zhou, J.-Y., & Wang, J.-M. (2006). Fuzzy LINMAP method for multiattribute decision making under fuzzy environments. Journal of Computer and System Sciences, 72(4), 741–759. DOI: https://doi.org/10.1016/j.jcss.2005.11.001

Wan, S.-P., & Li, D.-F. (2013). Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees. Omega, 41(6), 925–940. DOI: https://doi.org/10.1016/j.omega.2012.12.002

Xue, W., Xu, Z., Zhang, X., & Tian, X. (2018). Pythagorean fuzzy LINMAP method based on the entropy theory for railway project investment decision making. International Journal of Intelligent Systems, 33(1), 93–125. DOI: https://doi.org/10.1002/int.21941

Li, D.-F., & Sun, T. (2007). Fuzzy LINMAP method for multiattribute group decision making with linguistic variables and incomplete information. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 15(2), 153–173. DOI: https://doi.org/10.1142/S0218488507004509

Xu, Z., & Liao, H. (2013). Intuitionistic fuzzy analytic hierarchy process. IEEE Transactions on Fuzzy Systems, 22(4), 749–761. DOI: https://doi.org/10.1109/TFUZZ.2013.2272585

Sadiq, R., & Tesfamariam, S. (2009). Environmental decision-making under uncertainty using intuitionistic fuzzy analytic hierarchy process (IF-AHP). Stochastic Environmental Research and Risk Assessment, 23(1), 75–91. DOI: https://doi.org/10.1007/s00477-007-0197-z

Bastos, T. R., Longaray, A. A., Machado, C. M. S., Ensslin, L., Ensslin, S. R., & Dutra, A. (2024). Applying a genetic algorithm to implement the fuzzy-MACBETH method in decision-making processes. International Journal of Computational Intelligence Systems, 17, 48. DOI: https://doi.org/10.1007/s44196-024-00433-8

Bastos, T. R., Longaray, A. A., Machado, C. M. S., Ensslin, L., Ensslin, S. R., & Dutra, A. (2023). Fuzzy-MACBETH hybrid method: Mathematical treatment of a qualitative scale using the fuzzy theory. International Journal of Computational Intelligence Systems, 16. DOI: https://doi.org/10.1007/s44196-023-00195-9

Turgay, S., & Yilmaz, R. (2024). Enhancing organizational effectiveness through job evaluation in manufacturing: A scoring method with fuzzy ARAS approach. Engineering World. DOI: https://doi.org/10.37394/232025.2024.6.9

Jovanovic, S., Zavadskas, E. K., Stevic, Ž., Marinkovic, M., Alrasheedi, A. F., & Badi, I. (2023). An intelligent fuzzy MCDM model based on D and Z numbers for paver selection: IMF D-SWARA - Fuzzy ARAS-Z model. Axioms, 12, 573. DOI: https://doi.org/10.3390/axioms12060573

Abdel-Basset, M., Manogaran, G., Gamal, A., & Smarandache, F. (2019). A group decision making framework based on neutrosophic TOPSIS approach for smart medical device selection. Journal of Medical Systems, 43, 1–13. DOI: https://doi.org/10.1007/s10916-019-1156-1

Biswas, P., Pramanik, S., & Giri, B. C. (2019). Neutrosophic TOPSIS with group decision making. In Fuzzy multi-criteria decision-making using neutrosophic sets (pp. 543–585). Springer. DOI: https://doi.org/10.1007/978-3-030-00045-5_21

Berge, C. (1984). Hypergraphs: Combinatorics of finite sets (Vol. 45). Elsevier.

Bretto, A. (2013). Hypergraph theory: An introduction. Springer. DOI: https://doi.org/10.1007/978-3-319-00080-0

Feng, Y., You, H., Zhang, Z., Ji, R., & Gao, Y. (2019). Hypergraph neural networks. Proceedings of the AAAI Conference on Artificial Intelligence, 33(1), 3558–3565. DOI: https://doi.org/10.1609/aaai.v33i01.33013558

Hamidi, M., Smarandache, F., & Davneshvar, E. (2022). Spectrum of superhypergraphs via flows. Journal of Mathematics, 2022(1), 9158912. DOI: https://doi.org/10.1155/2022/9158912

Smarandache, F. (2022). Introduction to the n-SuperHyperGraph—the most general form of graph today. Infinite Study.

Alqahtani, M. (2025). Intuitionistic fuzzy quasi-supergraph integration for social network decision making. International Journal of Analysis and Applications, 23, 137. DOI: https://doi.org/10.28924/2291-8639-23-2025-137

Fujita, T., & Smarandache, F. (2024). A concise study of some SuperHyperGraph classes. Neutrosophic Sets and Systems, 77, 548–593.

Fujita, T., & Smarandache, F. (2025c). Considerations of HyperNeutrosophic Set and Forest-Neutrosophic Set in livestock applications and proposal of new neutrosophic sets. Precision Livestock, 2, 11–22. DOI: https://doi.org/10.61356/j.pl.2025.2484

Fujita, T., & Smarandache, F. (2025d). Hyperneutrosophic Set and Forest HyperNeutrosophic Set with practical applications in agriculture. Optimization in Agriculture, 2, 10–21. DOI: https://doi.org/10.61356/j.oia.2025.2478

Fujita, T., & Smarandache, F. (2025e). A concise introduction to hyperfuzzy, hyperneutrosophic, hyperplithogenic, hypersoft, and hyperrough sets with practical examples. Neutrosophic Sets and Systems, 80, 609–631.

Fujita, T. (2025d). Hyperplithogenic Cubic Set and SuperHyperPlithogenic Cubic Set. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond, 79. DOI: https://doi.org/10.31224/4317