概率双层语言T球形模糊集及其在多属性决策中的应用

Probabilistic Double Hierarchy Linguistic T-Spherical Fuzzy Set and Its Application in Multi-Attribute Decision Making

摘要: 作为模糊集扩展之一的T球形模糊集，由于引入了参数q，使其能够在更大范围内处理不确定信息。相比以往的语言术语集，双层语言术语集在表达决策者意见时，具有优越性。文章在考虑决策者犹豫心理的情况下，提出概率双层语言T球形模糊集的新概念，定义其基本运算、Hamming距离以及排序规则。基于Dombi运算规则，构建加权平均算子，并对其性质进行研究。结合信任度和Shapley值确定决策者的综合权重，利用IDOCRIW方法得到属性的客观权重。进而，提出基于概率双层语言T球形模糊集的多属性决策方法。最后将所提决策框架应用于一个实际案例，并通过对比分析，验证所提方法的有效性。

Abstract: As one of the extensions of fuzzy sets, T-spherical fuzzy sets can deal with uncertain information in a wider range due to the introduction of parameter q. Compared with the previous language term sets, the double hierarchy linguistic term set has advantages in expressing the opinions of decision-makers. Therefore, considering the hesitation of decision makers, the paper proposes a new concept of probabilistic double hierarchy linguistic T-spherical fuzzy sets and defines its basic operation, Hamming distance and ranking rules. Based on the Dombi operation rules, the weighted average operator is proposed, and its properties are investigated. The comprehensive weight of the decision maker is determined by combining the trust degree and the Shapley value, and the objective weight of the attribute is obtained by using the IDOCRIW method. Furthermore, a multi-attribute decision-making method based on probabilistic double hierarchy linguistic T-spherical fuzzy sets is investigated. Finally, the proposed decision-making framework is applied to a practical case, and the effectiveness of the proposed method is verified by comparative analysis.