Fuzzy thinking, neutrosophic thinking, and related thinking in business management

Takaaki Fujita

Fuzzy thinking, neutrosophic thinking, and related thinking in business management

Abstract

This paper examines several reasoning styles for business decision-making under uncertainty, including zero–one thinking, fuzzy thinking, neutrosophic thinking, Upside-Down Thinking, intuitive thinking, anti-intuitive thinking, fuzzy intuitive thinking, and neutrosophic critical thinking. For each reasoning style, we provide a precise logical definition, establish formal relationships showing how more expressive paradigms generalize simpler ones, and present concrete business examples, including credit scoring, inventory management, strategic project approval, supplier evaluation, pricing, and hiring.

Keywords

Supporting Institution

This study was conducted without any financial support from external organizations or grant

Ethical Statement

As this study does not involve experiments with human participants or animals, no ethical approval was required.

Thanks

We would like to express our sincere gratitude to everyone who provided valuable insights, support, and encouragement throughout this research. We also extend our thanks to the readers for their interest and to the authors of the referenced works, whose scholarly contributions have greatly influenced this study. Lastly, we are deeply grateful to the publishers and reviewers who facilitated the dissemination of this work.

References

[1] Jech, T. (2003). Set theory: The third millennium edition, revised and expanded. Springer.
[2] Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
[3] Atanassov, K. T. (2012). On intuitionistic fuzzy sets theory. Springer.
[4] Broumi, S., Talea, M., Bakali, A., & Smarandache, F. (2016). Single valued neutrosophic graphs. Journal of New Theory, 10, 86–101.
[5] Radha, R., Mary, A. S. A., & Smarandache, F. (2021). Quadripartitioned neutrosophic pythagorean soft set. International Journal of Neutrosophic Science, 14 (1), 9-23. https://doi.org/10.54216/IJNS.140101
[6] Smarandache, F. (2018). Plithogenic set, an extension of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets–revisited. Neutrosophic Sets and Systems, 21, 153–166. https://doi.org/10.5281/zenodo.1408740
[7] Feng, F., Liu, X., Leoreanu-Fotea, V., & Jun, Y. B. (2011). Soft sets and soft rough sets. Information Sciences, 181(6), 1125–1137. https://doi.org/10.1016/j.ins.2010.11.004
[8] Molodtsov, D. (1999). Soft set theory–First results. Computers & Mathematics with Applications, 37(4-5), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5

[9] Smarandache, F. (1999). A unifying field in logics: Neutrosophic logic. In Philosophy, American Research Press.
[10] Fujita, T., & Smarandache, F. (2026). A dynamic survey of fuzzy, intuitionistic fuzzy, neutrosophic, plithogenic, and extensional sets. Neutrosophic Science International Association (NSIA). https://doi.org/ 10.5281/zenodo.18973238
[11] Smarandache, F. (2015). Neutrosophic social structures specificities. Social Sciences and Education Research Review, 2(1), 3–10.
[12] Rodríguez, R. C., Sánchez, J. M. D., & Salcedo, V. L. (2022). Evaluation of social projects using neutrosophic AHP. International Journal of Neutrosophic Science (IJNS), 19(1), 280–289. https://doi.org/10.54216/IJNS. 190124
[13] Jarrín, A. A. A., Tamayo, D. S. P., Giler, S. A. M., Zambrano, J. C. A., & Macazana, D. M. (2021). Neutrosophic statistics applied in social science. Neutrosophic Sets and Systems, 44(1), 1–9. https://doi.org/10. 5281/zenodo.5162418
[14] Zadeh, L. A. (1996). Fuzzy logic, neural networks, and soft computing. Advances in Fuzzy Systems — Applications and Theory, 6, 775–782. https://doi.org/10.1142/2895
[15] Wang, H., Smarandache, F., Sunderraman, R., & Zhang, Y.-Q. (2005). Interval neutrosophic sets and logic: theory and applications in computing: Theory and applications in computing. Infinite Study.
[16] Chinoy, S., Nunn, N., Sequeira, S., & Stantcheva, S. (2026). Zero-sum thinking and the roots of US political differences. American Economic Review, 116(3), 1052-1096. https://doi.org/10.1257/aer.20240692
[17] Matsunaga, L. H., Petersen, J., Aoki, T., & Faiad, C. (2025). The science of zero-sum thinking: a scoping review of 10 years of empirical research. Dynamics of Asymmetric Conflict, 18(3), 1–21. https://doi.org/10. 1080/17467586.2024.2441504
[18] Carvalho, J.-P., Bergeron, A., Henrich, J., Nunn, N., & Weigel, J. (2023). Zero-sum thinking, the evolution of effort-suppressing beliefs, and economic development. National Bureau of Economic Research, Article 31663.
[19] Oshio, A. (2012). An all-or-nothing thinking turns into darkness: Relations between dichotomous thinking and personality disorders 1. Japanese Psychological Research, 54(4), 424–429. https://doi.org/10.1111/j. 1468-5884.2012.00515.x
[20] Oshio, A., Mieda, T., & Taku, K. (2016). Younger people, and stronger effects of all-or-nothing thoughts on aggression: Moderating effects of age on the relationships between dichotomous thinking and aggression. Fujita / Düzce Math. Res. (2026) 2:1 56 Cogent Psychology, 3(1), Article 1244874. https://doi.org/10.1080/23311908.2016.1244874
[21] Gebhardt, C., Alliger-Horn, C., Mitte, K., & Glaesmer, H. (2017). All-or-nothing thinking: the processing of emotional expressions in traumatized post-deployment soldiers. Journal of Anxiety Disorders, 47, 69–74. https://doi.org/10.1016/j.janxdis.2016.12.004
[22] Altman, N. (2000). Black and white thinking: A psychoanalyst reconsiders race. Psychoanalytic Dialogues, 10(4), 589–605. https://doi.org/10.1080/10481881009348569
[23] Zarkadi, T., & Schnall, S. (2013). “Black and White” thinking: Visual contrast polarizes moral judgment. Journal of Experimental Social Psychology, 49(3), 355–359. https://doi.org/10.1016/j.jesp.2012.11.012
[24] Kosko, B., & Toms, M. (1994). Fuzzy thinking: The new science of fuzzy logic, London:Flamingo.
[25] Seeger, A. (1989). Dualism: fuzzy thinking or fuzzy sets. The Attraction of Opposites: Thought and Society in the Dualistic Mode, 191–208.
[26] Downey, J. (2020). Comparative media studies in the digital age| comparative communication research: Why we really need some more fuzzy thinking. International Journal of Communication, 14, 5787–5798.
[27] Li, Q., & Kong, X. (2025). A mathematical neutrosophic offset framework with upside down logics for quality evaluation of multi-sensor intelligent vehicle environment perception systems. Neutrosophic Sets and Systems, 87, 1014–1023. https://doi.org/10.5281/zenodo.15758624
[28] Lou, J., Zhang, D., & Mo, Y. (2025). Upside-down neutrosophic multi-fuzzy ideals for it-enhanced college dance teaching quality assessment. Neutrosophic Sets and Systems, 93, 370–380. https://doi.org/10.5281/ zenodo.16934695
[29] Bu, Y. (2025). An upside-down logic-based neutrosophic methodology: Assessment of online marketing effectiveness in e-commerce enterprises. Neutrosophic Sets and Systems, 85, 801–813. https://doi.org/10. 5281/zenodo.15380951
[30] Fujita, T., & Smarandache, F. (2024). Introduction to upside-down logic: Its deep relation to neutrosophic logic and applications. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization:Fuzzy, Neutrosophic, Soft, Rough, and Beyond, 3, 9-50.
[31] Smarandache, F. (2024). Upside-down logics: Falsification of the truth and truthification of the false. Systems Assessment and Engineering Management, 1, 1–7. https://doi.org/10.61356/j.saem.2024.1248
[32] Berrezueta, R. A., Aldaz, E. M., López, B. C. E., & Aguirre, J. A. A. (2023). Neutrosophic assessment of personality traits. Neutrosophic Sets and Systems, 62, 137–145. https://doi.org/10.5281/zenodo.10436855
[33] Gafour, O. W. A., & Gafour, W. A. (2020). Creative thinking skills—A review article. Journal of Education and e-Learning, 4(1), 44–58.
[34] McFadzean, E. (1998). Enhancing creative thinking within organisations. Management Decision, 36(5), 309–315. https://doi.org/10.1108/00251749810220513
[35] Brown, T. (2008). Design thinking. Harvard Business Review, 86(6), 84.
[36] Martin, R. L. (2009). The design of business: Why design thinking is the next competitive advantage. Harvard Business Press.
[37] Liedtka, J. (2018). Why design thinking works. Harvard Business Review, 96(5), 72–79.
[38] You, X. (2022). Applying design thinking for business model innovation. Journal of Innovation and Entrepreneurship, 11(1), Article 59. https://doi.org/10.1186/s13731-022-00251-2
[39] Bono, E. D., & Zimbalist, E. (1970). Lateral thinking. Penguin London.
[40] Bono, E. D. (2009). Lateral thinking: A textbook of creativity. Penguin UK.
[41] Butler, S. A. (2010). Solving business problems using a lateral thinking approach. Management Decision, 48(1), 58–64. https://doi.org/10.1108/00251741011014454
[42] Sloane, P. (2017). The leader’s guide to lateral thinking skills: Unlock the creativity and innovation in you and your team. Kogan Page Publishers.
[43] Azeem, M., Rashid, H., Jamil, M. K., Gütmen, S., & Tirkolaee, E. B. (2024). Plithogenic fuzzy graph: A study of fundamental properties and potential applications. Journal of Dynamics and Games. 12(3), 196–214. https://doi.org/10.3934/jdg.2024023
[44] Priyadharshini, S. P., & Irudayam, F. N. (2021). A new approach of multi-dimensional single valued plithogenic neutrosophic set in multi criteria decision making. Neutrosophic Sets and Systems, 45, 151-161. https://doi.org/10.5281/zenodo.5486033
[45] Chen, R., Liu, Q., Zhang, Y., & Weng, W. (2025). A probabilistic plithogenic neutrosophic rough set for uncertainty–aware food safety analysis. Neutrosophic Sets and Systems, 90, 888–904. https://doi.org/10.5281/ zenodo.16658838

Details

Primary Language

English

Subjects

Pure Mathematics (Other), Applied Mathematics (Other)

Journal Section

Research Article

Authors

Takaaki Fujita ^*
0009-0007-1509-2728
Japan

Publication Date

June 5, 2026

Submission Date

December 8, 2025

Acceptance Date

March 5, 2026

Published in Issue

Year 2026 Volume: 2 Number: 1

IZ

https://izlik.org/JA48YU82WB

Cite

RIS / Bibtex

APA

Fujita, T. (2026). Fuzzy thinking, neutrosophic thinking, and related thinking in business management. Düzce Mathematical Research, 2(1), 20-57. https://izlik.org/JA48YU82WB

AMA

1.Fujita T. Fuzzy thinking, neutrosophic thinking, and related thinking in business management. Düzce Mathematical Research. 2026;2(1):20-57. https://izlik.org/JA48YU82WB

Chicago

Fujita, Takaaki. 2026. “Fuzzy Thinking, Neutrosophic Thinking, and Related Thinking in Business Management”. Düzce Mathematical Research 2 (1): 20-57. https://izlik.org/JA48YU82WB.

EndNote

Fujita T (June 1, 2026) Fuzzy thinking, neutrosophic thinking, and related thinking in business management. Düzce Mathematical Research 2 1 20–57.

IEEE

[1]T. Fujita, “Fuzzy thinking, neutrosophic thinking, and related thinking in business management”, Düzce Mathematical Research, vol. 2, no. 1, pp. 20–57, June 2026, [Online]. Available: https://izlik.org/JA48YU82WB

ISNAD

Fujita, Takaaki. “Fuzzy Thinking, Neutrosophic Thinking, and Related Thinking in Business Management”. Düzce Mathematical Research 2/1 (June 1, 2026): 20-57. https://izlik.org/JA48YU82WB.

JAMA

1.Fujita T. Fuzzy thinking, neutrosophic thinking, and related thinking in business management. Düzce Mathematical Research. 2026;2:20–57.

MLA

Fujita, Takaaki. “Fuzzy Thinking, Neutrosophic Thinking, and Related Thinking in Business Management”. Düzce Mathematical Research, vol. 2, no. 1, June 2026, pp. 20-57, https://izlik.org/JA48YU82WB.

Vancouver

1.Takaaki Fujita. Fuzzy thinking, neutrosophic thinking, and related thinking in business management. Düzce Mathematical Research [Internet]. 2026 Jun. 1;2(1):20-57. Available from: https://izlik.org/JA48YU82WB