面向广义梯形模糊数的随机模拟聚合求解方法
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C934

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国家自然科学基金项目 (71901079, 72304075).


Stochastic simulation aggregation solution method for generalized trapezoidal fuzzy numbers
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    摘要:

    在模糊综合评价问题中引入随机模拟技术能够获得带有概率信息的相对排序结果, 对于获取丰富的评价结论具有重要意义. 然而, 不同类型模糊数的随机模拟方式并不相同, 需要针对不同类型模糊数的随机模拟方式分别研究. 基于此, 针对广义梯形模糊数的随机模拟聚合问题展开研究. 首先, 利用广义梯形模糊数的隶属度函数确定其分布函数, 并基于反函数变换法将广义梯形模糊数的非均匀随机抽取问题转换为在其分布函数取值区间的均匀随机抽取问题; 然后, 通过在指标聚类过程中融入评价者偏好信息来确定指标权重系数, 并构建广义梯形模糊数的随机模拟密度中间(SS-DM)算子以求解随机聚合过程中的评价结果; 接着, 以在排序中体现被评价对象间的差异为原则, 通过引入强弱优胜法则确定优胜度概率矩阵并求解最终的排序结果; 最后, 通过算例验证所提出方法的有效性和特色之处.

    Abstract:

    The integration of stochastic simulation techniques into fuzzy comprehensive evaluation systems enables the derivation of probabilistic relative ranking outcomes, which is crucial for obtaining robust assessment conclusions. However, distinct stochastic simulation approaches are required for different types of fuzzy numbers, necessitating specialized research. Building on this foundation, this study focuses on the stochastic simulation aggregation problem for generalized trapezoidal fuzzy numbers (GTrFN). Firstly, the stochastic simulation method of generalized trapezoidal fuzzy number is studied. The random extraction method is determined according to the distribution function which is deduced by the membership function of the GTrFN. Secondly, by integrating the preference information of evaluators into the index clustering process, the index weight coefficient is determined, and the stochastic simulation density middle (SS-DM) operator of generalized trapezoidal fuzzy number is constructed to solve the evaluation results in the random aggregation process. Then, based on the determination method of the superiority degree of probability matrix, the rule of strong and weak superiority is introduced in the process of obtaining the ranking to reflect the difference among the evaluated objects in the ranking. Finally, an example is given to illustrate the effectiveness and characteristics of the proposed method.

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宫诚举,吴涵,韩岳,等.面向广义梯形模糊数的随机模拟聚合求解方法[J].控制与决策,2026,41(3):801-808

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  • 收稿日期:2025-06-29
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  • 在线发布日期: 2026-03-04
  • 出版日期: 2026-03-10
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