Integrating Cognitive Decision-Making and Production Workflowswith HyperFuzzy Trace and HyperFuzzy Front-End

Authors

https://doi.org/10.48314/ceti.vi.59

Abstract

Fuzzy sets model vagueness by assigning each element a membership degree in the interval [0, 1]. Hyperfuzzy sets generalize this notion by mapping each element to a nonempty subset of [0, 1], thereby accommodating both uncertainty and variability in membership degrees. An (m, n)-superhyperfuzzy set further extends these frameworks by assigning to each nonempty member of the m-th and n-th iterated powersets a nonempty family of subsets of [0, 1], enabling hierarchical and nested imprecision. These generalized fuzzy models have found applications in decision-making and many other domains. Meanwhile, the theories of Fuzzy Trace—retaining both verbatim and gist representations of information—and Fuzzy Front-Ends—using graded membership functions to evaluate and aggregate multiple criteria for soft go/no-go decisions—play a crucial role in information processing and innovation screening. However, corresponding concepts built upon hyperfuzzy and superhyperfuzzy structures have not yet been explored. To bridge this gap, we introduce extensions of Fuzzy Trace and Fuzzy Front-Ends based on hyperfuzzy and (m, n)-superhyperfuzzy sets. We present their formal definitions, examine basic properties, and illustrate them with examples. By doing so, we open the door to applying Fuzzy Trace and Fuzzy Front-End methodologies in contexts characterized by hierarchical uncertainty.

Keywords:

Fuzzy set, Fuzzy trace, Hyperfuzzy trace, Hyperfuzzy front-end, Fuzzy front-end

References

  1. [1] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  2. [2] Akram, M. (2011). Bipolar fuzzy graphs. Information sciences, 181(24), 5548-5564. https://doi.org/10.1016/j.ins.2011.07.037
  3. [3] Atanassov, K. T. (2020). Circular intuitionistic fuzzy sets. Journal of intelligent & fuzzy systems, 39(5), 5981-5986.
  4. [4] https://doi.org/10.3233/JIFS-189072
  5. [5] Broumi, S., Talea, M., Bakali, A., & Smarandache, F. (2016). Single valued Neutrosophic graphs. Journal of new theory, (10), 86
  6. [6] -101. https://izlik.org/JA44RD85ED
  7. [7] Xu, Z. (2014). Hesitant fuzzy sets theory. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-04711-9
  8. [8] Radha, R., Mary, A. S. A., & Smarandache, F. (2021). Quadripartitioned Neutrosophic pythagorean soft set. International
  9. [9] jounal of Neutrosophic science (IJNS), 14(1), 9- 23. https://doi.org/10.5281/zenodo.4678763
  10. [10] Chatterjee, T., & Pramanik, S. (2024). Triangular fuzzy quadripartitioned Neutrosophic set and its properties. Neutrosophic
  11. [11] sets and systems, 75(1), 2. https://digitalrepository.unm.edu/nss_journal/vol75/iss1/2
  12. [12] Akram, M., Saleem, D., & Al-Hawary, T. (2020). Spherical fuzzy graphs with application to decision-making. Mathematical
  13. [13] and computational applications, 25(1), 8. https://doi.org/10.3390/mca25010008
  14. [14] Smarandache, F. (2018). Plithogenic set, an extension of crisp, fuzzy, intuitionistic fuzzy, and Neutrosophic sets-revisited.
  15. [15] Neu-trosophic sets and systems, 21(1), 153–166. https://fs.unm.edu/nss8/index.php/111/article/view/316
  16. [16] Sultana, F., Gulistan, M., Ali, M., Yaqoob, N., Khan, M., Rashid, T., & Ahmed, T. (2022). A study of plithogenic graphs:
  17. [17] Ap-plications in spreading coronavirus disease (Covid-19) globally. Journal of ambient intelligence and humanized computing, 14 (10), 13139 -13159. https://doi.org/10.1007/s12652-022-03772-6
  18. [18] Jun, Y. B., Hur, K., & Lee, K. J. (2017). Hyperfuzzy subalgebras of Bck/Bci-algebras. Annals of fuzzy mathematics and infor-matics, 15
  19. [19] (1),17-28. https://doi.org/10.30948/afmi.2018.15.1.17
  20. [20] Song, S. Z., Kim, S. J., & Jun, Y. B. (2017). Hyperfuzzy ideals in Bck/Bci-algebras. Mathematics, 5(4), 81. https://doi.org/10.3390/math5040081
  21. [21] Fujita, T., & Smarandache, F. (2025). Hierarchical uncertainty modeling via (m, n)-superhyperuncertainand (h, k)-ary (m, n)- superhyperuncertain
  22. [22] sets: Unified extensions of fuzzy, Neutrosophic, soft, rough, and plithogenic set theories. European journal of pure and applied
  23. [23] mathematics, 18(4), 6834-6834. https://doi.org/10.29020/nybg.ejpam.v18i4.6834
  24. [24] Fujita, T. (2025). Advancing uncertain combinatorics through graphization, hyperization, and uncertainization: Fuzzy, Neutro-
  25. [25] sophic, soft, rough, and beyond. Biblio Publishing.
  26. [26] Hjorth, G. (2005). T. Jech. Set theory. The third millennium edition, revised and expanded. Springer-Verlag, Berlin, 2003, viii+769 pp. Bul-
  27. [27] letin of symbolic logic, 11(2), 243-245. https://doi.org/10.1017/S1079898600003358
  28. [28] Smarandache, F. (2024). Foundation of superhyperstructure & Neutrosophic superhyperstructure. Neutrosophic sets and systems, 63(2024),
  29. [29] -381. https://doi.org/10.5281/zenodo.10535374
  30. [30] Nazari, Z., & Mosapour, B. (2018). The entropy of hyperfuzzy sets. Journal of dynamical systems and geometric theories, 16
  31. [31] (2), 173-185. https://doi.org/10.1080/1726037X.2018.1436270
  32. [32] Smarandache, F. (2017). HyperUncertain, superuncertain, and superhyperuncertain sets/logics/probabilities/statistics. Critical
  33. [33] Review, 14, 10–19. https://fs.unm.edu/CR/HyperUncertain-SuperUncertain-SuperHyperUncertain.pdf
  34. [34] Reyna, V. F., & Brainerd, C. J. (1998). Fuzzy-trace theory and false memory: New frontiers. Journal of experimental childpsy-
  35. [35] chology, 71(2), 194-209. https://doi.org/10.1006/jecp.1998.2472
  36. [36] Blalock, S. J., & Reyna, V. F. (2016). Using fuzzy-trace theory to understand and improve health judgments, decisions, and
  37. [37] behaviors: A literature review. Health psychology, 35(8), 781. https://psycnet.apa.org/doi/10.1037/hea0000384
  38. [38] Reyna, V. F., & Brainerd, C. J. (1995). Fuzzy-trace theory: An interim synthesis. Learning and individual differences, 7(1), 1-75.
  39. [39] https://doi.org/10.1016/1041-6080(95)90031-4
  40. [40] Brainerd, C. J., & Reyna, V. F. (1998). Fuzzy-trace theory and children's false memories. Journal of experimental child psychol-
  41. [41] ogy, 71(2), 81-129. https://doi.org/10.1006/jecp.1998.2464
  42. [42] Brainerd, C. J., Bialer, D. M., & Chang, M. (2022). Fuzzy-trace theory and false memory: Meta-analysis of conjoint recognition.
  43. [43] Journal of experimental psychology: Learning, memory, and cognition, 48(11), 1680. https://psycnet.apa.org/doi/10.1037/xlm0001040
  44. [44] Morrow, D., Azevedo, R. F. L., Garcia-Retamero, R., Hasegawa-Johnson, M., Huang, T., Schuh, W., ... & Zhang, Y. (2019).
  45. [45] Contextualizing numeric clinical test results for gist comprehension: Implications for EHR patient portals. Journal of experimental
  46. [46] psychology: Applied, 25(1), 41. https://psycnet.apa.org/doi/10.1037/xap0000203
  47. [47] Koen, P. A., Ajamian, G. M., Boyce, S., Clamen, A., Fisher, E., Fountoulakis, S., Puri, P., & Seibert, R. (2002). Fuzzy front
  48. [48] end: Effective methods, tools, and techniques. In The PDMA toolbook for new product development (pp. 5–35). John Wiley & Sons.
  49. [49] https://www.wi-ley.com/en-us/The+PDMA+ToolBook+for+New+Product+Development-p-9780471236628
  50. [50] Khurana, A., & Rosenthal, S. R. (1997). Integrating the fuzzy front end of new product development. IEEE engineering manage-
  51. [51] ment review, 25(4), 35-49. https://sloanreview.mit.edu/article/integrating-the-fuzzy-front-end-of-new-product-development/
  52. [52] Kim, J., & Wilemon, D. (2002). Focusing the fuzzy front–end in new product development. R&d management, 32(4), 269-279.
  53. [53] https://doi.org/10.1111/1467-9310.00259
  54. [54] Gassmann, O., & Schweitzer, F. (2014). Management of the fuzzy front end of innovation. Springer Cham.
  55. [55] https://doi.org/10.1007/978-3-319-01056-4
  56. [56] Herstatt, C., & Verworn, B. (2004). The ‘fuzzy front end’of innovation. In Bringing technology and innovation into the board-
  57. [57] room: Strategy, innovation and competences for business value (pp. 347-372). London: Palgrave Macmillan UK. https://doi.org/10.1057/9780230512771_16
  58. [58] Gassmann, O., & Schweitzer, F. (2013). Managing the unmanageable: The fuzzy front end of innovation. In Management of
  59. [59] the fuzzy front end of innovation (pp. 3-14). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-01056-4_1
  60. [60] Berrezueta, R. A., Aldaz, E. M., López, B. C. E., & Aguirre, J. A. A. (2023). Neutrosophic assessment of personality traits.
  61. [61] Neu-trosophic sets and systems, 62(1), 17. https://digitalrepository.unm.edu/nss_journal/vol62/iss1/17/
  62. [62] Zhang, H. (2025). Neutrosophic approaches for analyzing the interaction between the sports industry and community health: A
  63. [63] multi-attribute decision-making perspective. Neutrosophic sets and systems, 77(1), 20–40. https://digitalrepository.unm.edu/nss_journal/vol77/iss1/2
  64. [64] Alhasan, Y. A., & Abdulfatah, R. A. (2023). Division of refined Neutrosophic numbers. Neutrosophic sets and systems, 60, 1–5.
  65. [65] https://doi.org/10.5281/zenodo.10224078
  66. [66] Smarandache, F. (2013). n-Valued refined Neutrosophic logic and its applications to physics. Progress in physics, 4, 143-146.
  67. [67] https://doi.org/10.5281/zenodo.30245
  68. [68] Fujita, T., & Smarandache, F. (2025). A unified framework for U-structures and functorial structure: Managing super, hyper, su-
  69. [69] perhyper, tree, and forest uncertain over/under/off models. Neutrosophic sets and systems, 91, 337–380. https://doi.org/10.5281/zenodo.16754933 [36] Fujita, T., & Smarandache, F. (2025). A dynamic survey of fuzzy, intuitionistic fuzzy, Neutrosophic, plithogenic, and exten-
  70. [70] sional.SetsNeutrosophic Science International Association. https://pdfhost.io/v/HaB6hdkPHH_A_Dynamic_Survey_of_Fuzzy__Intu-itionistic_Fuzzy__Neutrosophic__Plithogenic__and_Extensional_Sets
  71. [71] Ramos, E. L. H., Ayala, L. R. A., & Macas, K. A. S. (2025). Study of factors that influence a victim’s refusal to testify for sexual
  72. [72] reasons due to external influence using plithogenic n-superhypergraphs. Operational research journal, 46(2), 328–337. https://rev-inv-
  73. [73] ope.pantheonsor-bonne.fr/sites/default/files/inline-files/4602-19STUDY%20OF%20FACTORS%20THAT%20INFLUENCE%20A %20VICTIM%27S %20RE-FUSAL%20TO %20TESTIFY%20FOR%20SEXUAL%20REASONS%20DUE%20TO%20EX-TERNAL %20INFLUENCE%20USING %20PLYTHOGENIC%20N-SUPERHYPERGRAPHS_0.pdf
  74. [74] Smarandache¹, F. (2018). Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic sets and
  75. [75] systems: An international book series in information science and engineering, 22/2018(22), 168-170. https://fs.unm.edu/NSS/Exten-
  76. [76] sionOfSoftSetToHypersoftSet.pdf
  77. [77] Smarandache, F. (2020). Extension of hypergraph to n-superhypergraph and to Plithogenic n-superhypergraph, and exten-
  78. [78] sion of hyperalgebra to n-ary (classical-/neutro-/anti-) hyperalgebra. Neutrosophic sets and systems, 33, 290–296. https://doi.org/10.5281/zenodo.3783103

Published

2025-06-24

Issue

Vol. 2 No. 2 (2025): Computational Engineering and Technology Innovations

Section

Articles

How to Cite

Fujita, T. (2025). Integrating Cognitive Decision-Making and Production Workflowswith HyperFuzzy Trace and HyperFuzzy Front-End. Computational Engineering and Technology Innovations, 2(2), 151-171. https://doi.org/10.48314/ceti.vi.59

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