Abstract
Environmental uncertainty poses a significant barrier to collaborative innovation in platform-driven manufacturing enterprises. However, existing studies often overlook the platform’s dynamic coordination role, and the quantification of uncertainty. This paper investigates the collaborative interaction processes and key influencing factors within the internal innovation ecosystem of platform-based manufacturing enterprises under environmental uncertainty using a triangular fuzzy evolutionary game model. Subsequently, we conducted numerical examples and case validation of the model results, which demonstrated that: (1) External environmental uncertainty primarily affects organizational collaborative stability through three pathways: punitive fluctuations, cognitive divergence, and information arbitrage. (2) The difference between collaborative and non-collaborative benefits drives strategic choices.The risk of free-riding and unilateral revenue growth can significantly weaken the willingness to cooperate. (3) Platform resource integration mitigates the impact of uncertainty through a dual mechanism: On one hand, it reduces collaboration costs by leveraging global resources, reusing technologies, and digitizing processes; on the other hand, it enhances incentives through additional benefits such as two-way collaboration compensation, effectively expanding the feasible probability range of the collaboration strategy. (4) The double-edged sword effect of fines is reflected in two aspects: on the one hand, they compel employees to engage in cooperation through coercive constraints; on the other, they diminish the dynamism of innovative groups.This paper for the first time constructs a triangular fuzzy game model involving ‘platform-innovation group-employees’, integrates platform governance variables and realizes the quantification of uncertainty, providing strategic guidance for collaborative innovation within platform-based manufacturing enterprises, thereby fostering the development of their internal innovation ecosystems, and it aligns with the trend of sustainable and people-oriented manufacturing transformation. Furthermore, this study identified specific ways model results improve operational performance, offering practical insights for manufacturing enterprises.
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References
Li, Y. et al. Research on value co-creation mechanism of platform enterprises in digital innovation ecosystem: A case study on Haier HOPE platform in China. Front. Psychol. 13, 1055932 (2022).
Hu, K. & Tu, M. E. Research Progress on Synergic Innovation Theory - A Literature Review. Int. J. Econ. Manag Sci. 5, 307 (2015).
Xie, X., Mu, X., Tao, N. & Yin, S. The coupling mechanism of the digital innovation ecosystem and value co-creation. Adv. Environ. Eng. Res. 4 (1), 013 (2023).
Yu, F. & Chen, J. The impact of industrial internet platform on green innovation: evidence from a quasi-natural experiment. J. Clean. Prod. 414, 13 (2023).
Zadeh, L. A. Fuzzy sets. Inf. Control. 8, 338–353 (1965).
Dubois, D. & Prade, H. Fuzzy sets and probability: Misunderstandings, bridges and gaps.Second IEEE International Conference on Fuzzy Systems, San Francisco, CA, USA, pp. 1059–1068. (1993). https://doi.org/10.1109/FUZZY.1993.327367
Zavadskas, E. K., Turskis, Z. & Kildienė, S. State of art surveys of overviews on MCDM/MADM methods. Technol. Econ. Dev. Eco. 20, 165–179 (2014).
Kilincci, O. & Onal, S. A. Fuzzy AHP approach for supplier selection in a washing machine company. Expert Syst. Appl. 38, 9656–9664 (2011).
Van Laarhoven, P. J. M. & Pedrycz, W. A fuzzy extension of Saaty’s priority theory. Fuzzy Set Syst. 11, 229–241 (1983).
Mardani, A., Jusoh, A. & Zavadskas, E. K. Fuzzy multiple criteria decision-making techniques and applications-Two decades review from 1994 to 2014. Expert Syst. Appl. 42, 4126–4148 (2015).
Yen-Chun, L. & Chou, C. Technology evaluation and selection of 3dic integration using a three-stage fuzzy mcdm. Sustainability 8, 114 (2016).
Zavadskas, E. K., Antucheviciene, J., Hajiagha, S. H. R. & Hashemi, S. S. Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF). Appl. Soft Comput. 24, 1013–1021 (2014).
Leng, J. et al. Federated learning-empowered smart manufacturing and product lifecycle management: a review. Adv. Eng. Inf. 65, 103179 (2025).
Chesbrough, H. W. The era of open innovation. MIT Sloan Manage. Rev. 44, 35–41 (2003).
Ghobadi, S. N. & Esmaeili, M. A game theory model for pricing and supplier selection in a closed-loop supply chain. Int. J. Procure. Manage. 11, 472 (2018).
Govindan, K., Rajendran, S., Sarkis, J. & Murugesan, P. Multi criteria decision making approaches for green supplier evaluation and selection: a literature review. J. Clean. Prod. 98, 66–83 (2015).
Nambisan, S., Wright, M. & Feldman, M. The digital transformation of innovation and entrepreneurship: Progress, challenges and key themes. Res. Policy. 48, 103773 (2019).
Tversky, A. & Kahneman, D. Judgment under Uncertainty: Heuristics and Biases. Science 185, 1124–1131 (1974).
Hendijani, R. Behavioral operations management: a review of the field. J. Psychol. Res. 1, 1–30 (2019).
Liu, Y., Zhang, Y., Xie, X. & Mei, S. Affording digital transformation: the role of industrial internet platform in traditional manufacturing enterprises digital transformation. Heliyon 10, e28772 (2024).
Kuratko, D. F., Hornsby, J. S. & Hayton, J. Corporate entrepreneurship: the innovative challenge for a new global economic reality. Small Bus. Econ. 45, 245–253 (2015).
Tiwana, A., Konsynski, B. & Bush, A. A. Research Commentary—Platform evolution: Coevolution of platform architecture, governance, and environmental dynamics. Inf. Syst. Res. 21, 675–687 (2010).
Gawer, A. & Cusumano, M. A. Industry platforms and ecosystem innovation. J. Prod. Innovat Manag. 31, 417–433 (2014).
Eisenmann, T., Parker, G. & Van Alstyne, M. Platform envelopment. Strategic Manage. J. 32, 1270–1285 (2011).
Parker, G. G. & Van Alstyne, M. W. Two-sided network effects: A theory of information product design. Manage. Sci. 51, 1494–1504 (2005).
Jacobides, M. G., Cennamo, C. & Gawer, A. Towards a theory of ecosystems. Strategic Manage. J. 39, 2255–2276 (2018).
Yoo, Y., Henfridsson, O. & Lyytinen, K. Research commentary -the new organizing logic of digital innovation: An agenda for information systems research. Inf. Syst. Res. 21, 724–735 (2010).
George, F. J., Mol, M. J. & Kamel, M. Management innovation made in China: Haier’s Rendanheyi. Calif. Manage. Rev. 1, 71–93 (2019).
Malone, T. W. & Crowston, K. The interdisciplinary study of coordination. ACM Comput. Surv. 26, 87–119 (1994).
Rao, R. & Leibler, S. Evolutionary dynamics, evolutionary forces, and robustness: a nonequilibrium statistical mechanics perspective. Proc. Natl. Acad. Sci. USA. 119 e2112083119 (2022).
Yongseol, L., Insu, Cho, H. & Park The effect of collaboration quality on collaboration performance: empirical evidence from manufacturing smes in the republic of korea. Total Qual. Manag Bus. 26, 986–1001 (2015).
Nguyen, H. A., Nguyen, H., Nguyen, H. T., Phan, A. C. & Matsui, Y. Empirical study on the role of collaboration in new product development in manufacturing companies. Int. J. Qual. Res. 12, 363–384 (2018).
Dubois, D. & Prade, H. Fuzzy sets and probability: misunderstandings, bridges and gaps. Second IEEE Int. Conf. Fuzzy Syst. 2, 1059–1068 (1993).
Lodwick, W. A. Fuzzy, possibility, probability, and generalized uncertainty theory in mathematical analysis. J. Mahani Math. Res. Cent. 10, 49–70 (2021).
Kilincci, O. & Onal, S. A. Fuzzy AHP approach for supplier selection in a washing machine company. Expert Syst. Appl. 38, 9656–9664 (2011).
Sugapriya, C., Saranyaa, P., Nagarajan, D. & Pamucar, D. Triangular intuitionistic fuzzy number based backorder and lost sale in production, remanufacturing and inspection process. Expert Syst. Appl. 240, 122479 (2024).
Ikram, M. & Sadki, J. E. Resilient and sustainable green technology strategies: a study of Morocco’s path toward sustainable development. Sustain. Futur. 8, 100327 (2024).
Siwiec, D., Gawlik, R. & Pacana, A. Triangular fuzzy numbers for satisfactory quality-environmental decisions in product development. Oper. Res. Decis. 34, 185–209 (2024).
Siweiec, D., Gawlik, R. & Pacana, A. Triangular fuzzy numbers for satisfactory quality-environmental decisions in product development. Oper. Res. Decis. 34, 185–209 (2024).
Kaufmann, A. & Gupta, M. M. Introduction Fuzzy Arithmetic: Theory Appl. 12–14, 18–22 (1985). (Van Nostrand Reinhold.
Chen, S. M. & Chen, J. H. Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Syst. Appl. 36, 6833–6842 (2012).
Adner, R. Match your innovation strategy to your innovation ecosystem. Harv. Bus. Rev. 84, 98–107 (2006).
Cohen, W. M. & Levinthal, D. A. Absorptive capacity: a new perspective on learning and innovation. Adm. Sci. Q. 35, 128–152 (1990).
Cassiman, B. & Veugelers, R. R&d cooperation and spillovers: some empirical evidence from belgium. Am. Econ. Rev. 92, 1169–1184 (2002).
Nonaka, I. A dynamic theory of organizational knowledge creation. Organ. Sci. 5, 14–37 (1994).
Chen, L., Yi, J., Li, S. & Tong, T. W. Platform Governance Design in Platform Ecosystems: Implications for Complementors’ Multihoming Decision. J. Manage. 48, 630–656 (2021).
Griliches, Z. The search for r&d spillovers. Scand. J. Econ. 94, 29–47 (1992).
Malone, T. W. & Crowston, K. The interdisciplinary study of coordination. ACM Comput. Surv. 26, 87–119 (1994).
None On the design of hierarchies: coordination versus specialization. J. Polit Econ. 113, 675–702 (2005).
Houser, D. & Puzzello, D. Transaction cost economics: The comparative contracting perspective. J. Econ. Behav. Organ. 8, 617–625 (1987).
Xu, H. & Wang, J. Knowledge sharing decision-making under stochastic factors in platform ecosystems: thediversified participants’ perspective. Kybernetes 54, 7336–7356 (2024).
Bakos, J. Y. Reducing buyer search costs: implications for electronic marketplaces. Manage. Sci. 43, 1676–1692 (1997).
Pavlou, P. A. & Xue, L. Y. Understanding and mitigating uncertainty in online exchange relationships: a principal-agent perspective. MIS Quart. 31, 105–136 (2007).
Pavlou, P. A. & Gefen D.Building effective online marketplaces with institution-based trust. Inf. Syst. Res. 15, 37–59 (2004).
Adner, R. Ecosystem as structure: an actionable construct for strategy. J. Manage. 43, 39–58 (2016).
Eisenmann, T., Parker, G. & Alstyne, M. W. V. Strategies for two-sided markets. Harv. bus. Rev. 84, 92–101 (2006).
Oliveira, R. & Gonzalez, I. The impact of supply chain integration on the operational process performance: an empirical study under the perspective of resource orchestration theory. Braz Bus. Rev. 19, 227–245 (2022).
Donkor, F., Papadopoulos, T. & Spiegler, V. Supply chain integration and supply chain sustainability relationship: a qualitative analysis of the uk and ghana pharmaceutical industry. Prod. Plan. Control. 35, 535–558 (2024).
Hottenrott, H. & Lopes-Bento, C. R&d partnerships and innovation performance: can there be too much of a good thing? J. Prod. Innovat Manag. 33, 773–794 (2016).
Mohammad, A. & Salam The mediating role of supply chain collaboration on the relationship between technology, trust and operational performance: an empirical investigation. Benchmarking 24, 298–317 (2017).
Shahbaz, M. S., Rasi, R. Z. R. M., Ahmad, M. F. B. & Sohu, S. The impact of supply chain collaboration on operational performance: empirical evidence from manufacturing of malaysia. Int. J. Adv. Appl. Sci. 5, 64–71 (2018).
Wu, A. H., Wang, Z. & Chen, S. Impact of specific investments, governance mechanisms and behaviors on the performance of cooperative innovation projects. Int. J. Proj Manag. 35, 504–515 (2017).
Bouncken, R. B., Clauss, T. & Fredrich, V. Product innovation through coopetition in alliances: singular or plural governance? Ind. Market Manag. 53, 77–90 (2016).
Iida, T. Coordination of cooperative cost-reduction efforts in a supply chain partnership. Eur. J. Oper. Res. 222, 180–190 (2012).
Fu, J. & Fu, Y. An adaptive multi-agent system for cost collaborative management in supply chains. Eng. Appl. Artif. Intel. 44, 91–100 (2015).
Lai, C. S., Chen, C. S., Chiu, C. J. & Pai, D. C. The impact of trust on the relationship between inter-organisational collaboration and product innovation performance. Technol. Anal. Strateg. 23, 65–74 (2011).
Ahin, E., Emberci, M., Civelek, M. E. & Uca, N. The role of agility in the effect of trust in supply chain on firm performance. Manag Stud. 5, 336–345 (2017).
Sjdin, D., Parida, V., Kohtamki, M. & Wincent, J. An agile co-creation process for digital servitization: a micro-service innovation approach. J. Bus. Res. 112, 478–491 (2020).
Bhargava, H. K. Bundling for flexibility and variety: an economic model for multiproducer value aggregation. Manage. Sci. 67, 2365 (2021).
Jiang, Z. & Luo, J. Study on classification of intrapreneurship modes based on organizational context factors. Sci. Sci. Manag S T. 38, 141–158 (2017).
Jones, M. J., Melis, A., Gaia, S. & Aresu, S. Impression management and retrospective sense-making in corporate annual reports: banks’ graphical reporting during the global financial crisis. Int. J. Bus. Commun. 57,474–496 (2020).
Craig, R. J. & Amernic, J. H. Enron discourse: the rhetoric of a resilient capitalism. Crit. Perspect. Accoun. 15, 813–852 (2004).
Funding
This research was funded by Social Science Foundation of Shandong Province (No. 25CSDJ26),the Project of the Department of Education of Liaoning Province (LJ132410166013),the Project of the Department of Education of Liaoning Province( LJ222410142008), and Project of Social Sciences Association of Shandong Province(Award number pending).
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Guo, Y., Zhang, H., Zou, H. et al. Triangular fuzzy game modelling for internal innovation in platform-driven manufacturing enterprises under uncertainty. Sci Rep (2026). https://doi.org/10.1038/s41598-026-47051-2
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DOI: https://doi.org/10.1038/s41598-026-47051-2
