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University","award":["72201063"],"award-info":[{"award-number":["72201063"]}]},{"name":"Open Project of Xi Jinping Thought on Ecological Civilization Research Institute of Fujian Agriculture and Forestry University","award":["STWMSX23-15"],"award-info":[{"award-number":["STWMSX23-15"]}]},{"name":"Open Project of Xi Jinping Thought on Ecological Civilization Research Institute of Fujian Agriculture and Forestry University","award":["STWMSX23-05"],"award-info":[{"award-number":["STWMSX23-05"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Intense market competition has driven small- and medium-sized enterprises (SMEs) in the manufacturing sector to collaborate and form supply chain coalitions, which can improve the information flow and resource sharing and significantly enhance supply chain management efficiency. However, the distribution of cooperative benefits poses a core challenge for the long-term stability of coalitions. This paper addresses the impact of dynamic changes in complex business environments by utilizing triangular fuzzy numbers to represent the value of coalition, effectively depicting the uncertainty and ambiguity in the cooperation process. Compared to traditional models (which do not use triangular fuzzy numbers), this model is better suited to dynamic changes, offering flexible response mechanisms that ensure adaptability and fairness in the decision-making process. In addition, considering the influence of each member\u2019s weight in the coalition, the fuzzy comprehensive evaluation method is used to determine the weights. With the goal of minimizing the dissatisfaction of enterprises in benefit distribution, a least square contribution with triangular fuzzy numbers is constructed to replace the marginal contribution of the classical Banzhaf value, and an improved Banzhaf value based on the player\u2019s triangular fuzzy number-weighted excess contribution is proposed to arrive at a fair and reasonable benefit allocation strategy in order to enhance the long-term stability and cooperative benefits of coalition. By analyzing an example of the supply chain coalition, the effectiveness of the proposed improved Banzhaf value is verified, which satisfies the uniqueness, the individual rationality, and the group rationality. It not only promotes the level of risk management and decision making under the uncertainty conditions of complex business, but also deepens the theoretical foundation of cooperative game theory and expands its possibilities in practical applications and future development.<\/jats:p>","DOI":"10.3390\/sym16121593","type":"journal-article","created":{"date-parts":[[2024,11,29]],"date-time":"2024-11-29T05:02:22Z","timestamp":1732856542000},"page":"1593","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Improved Banzhaf Value Based on Participant\u2019s Triangular Fuzzy Number-Weighted Excess Contributions and Its Application in Manufacturing Supply Chain Coalitions"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1936-2506","authenticated-orcid":false,"given":"Jiacai","family":"Liu","sequence":"first","affiliation":[{"name":"College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou 350108, China"},{"name":"Jinshan College, Fujian Agriculture and Forestry University, Fuzhou 350002, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-0013-3755","authenticated-orcid":false,"given":"Shiying","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou 350108, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rongji","family":"Lai","sequence":"additional","affiliation":[{"name":"College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou 350108, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingfan","family":"Lin","sequence":"additional","affiliation":[{"name":"College of Economics and Management, Fujian Agriculture and Forestry University, Fuzhou 350002, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109174","DOI":"10.1016\/j.ijpe.2024.109174","article-title":"Mitigating closed-loop supply chain risk through assessment of production cost, disruption cost, and reliability","volume":"270","author":"Dou","year":"2024","journal-title":"Int. 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