基于优势熵矩阵的模糊软集三支决策方法
Three-Way Decision Method of Fuzzy Soft Set Based on Dominant Entropy Matrix
摘要: 讨论了模糊软集上的三支决策问题。通过模糊软集上的模糊优势熵关系来构造模糊优势熵矩阵，从而提出模糊软集上的三支决策方法。首先，介绍了传统的优势关系和优势关系，类比两种优势关系提出了优势熵关系的定义；其次，通过优势熵关系构造了优势熵矩阵及定义了优势熵类，基于优势熵类给出了模糊占优度的定义，依据优势熵矩阵定义模糊软集的损失函数表，计算模糊软集的三支决策阈值，结合模糊占优度来实现模糊软集的三支决策。最后，通过一个算例以及相关的对比分析，验证了本文所提三支决策方法的实用性和有效性。
Abstract: The three-way decision problem on fuzzy soft sets is discussed. The fuzzy dominant entropy matrix is constructed by the fuzzy dominant entropy relationship on the fuzzy soft set, and the three-way decision method on the fuzzy soft set is proposed. Firstly, it introduces the traditional dominance relationship and dominance relationship, and puts forward the definition of dominance entropy relationship by analogy. Secondly, the dominant entropy matrix is constructed and the dominant entropy class is defined based on the dominant entropy class. The fuzzy dominance degree is defined based on the dominant entropy class. The loss function table of the fuzzy soft set is defined based on the dominant entropy matrix, and the three decision thresholds of the fuzzy soft set are calculated. The three decisions of the fuzzy soft set are realized by combining the fuzzy dominance degree. Finally, through a numerical example and relevant comparative analysis, the practicability and effectiveness of the three decision-making methods proposed in this paper are verified.
文章引用：胡凯欣. 基于优势熵矩阵的模糊软集三支决策方法[J]. 应用数学进展, 2024, 13(4): 1399-1414. https://doi.org/10.12677/aam.2024.134131

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