基于TFNCD算子的三角模糊数多属性群决策

针对属性权重和专家权重全部未知的三角模糊数(triangular fuzzy number,TFN)多属性群决策问题,在TFN熵的基础上构造了确信度指标来量化对决策信息的信任程度,构建了TFN确信度(TFN certitude degree,TFNCD)算子,并证明了其置换不变性、幂等性和有界性等性质,结合支持度确定专家权重,提出了基于TFNCD算子的属性信息集结新方法。最后,通过算例的对比分析验证了TFNCD算子及其集结方法的有效性,该方法充分考虑了TFN类型的数据特征和两种权重完全未知的情况,且属性信息集结更加客观高效,计算相对简便,为TFN多属性决策问题提供了新的信息集结方式和解决思路。

Multi-attribute group decision-making method with triangular fuzzy numbers based on the TFNCD operator

With regarding to the multi-attribute group decision-making problem of the triangular fuzzy number (TFN) with the attribute weights and experts weights being unknown, the confidence index is constructed based on the TFN entropy to quantify the degree of certitude to the decision information, and the TFN certitude degree (TFNCD) operator is introduced and its properties, such as the invariance of displacement transformation, the idempotence and the boundedness are proved. And the expert weights are determined combined with the degree of support. Finally, a method of attribute information aggregation is proposed, and the effectiveness of the TFNCD operator and the aggregated approach are verified by the empirical analysis. Moreover, the approach is built on the independence of experts, where the data features of the TFNs and the completely unknown weights of attributes and experts are fully considered, resulting in the objectivity and high efficiency in the information aggregation with relatively reduced computation. Therefore, it provides an information aggregation mode and solution to the multi-attribute group decision-making problem with TFN.