Intuitionistic fuzzy sets (IFS) are widely used in multi-attribute decision-making (MADM) because of its strong ability to express uncertainty in terms of membership degree, non-membership degree and hesitancy degree. Additionally, Z-number is a novel two-dimension framework to handle uncertainty problems by introducing the reliability of expert evaluation. However, a simple index in the framework of Z-number is not enough to express the evaluation of experts. In order to integrate the uncertainty and reliability expressions of IFS, inspired by Z-number, we propose a two-dimensional intuitionistic fuzzy set (TDIFS) model in this paper. In TDIFS model, the first dimensionality is the evaluation data from experts with regard to attributes, and the second dimensionality represents the reliability of expert in terms of the first component of TDIFS. Moreover, for each dimensionality, it is expressed as an ordered pair of intuitionistic fuzzy set, which can carry more information than a simple index. Furthermore, a novel combination rule is proposed for fusing TDIFSs. The TDIFS combination rule fully integrates expert evaluation and expert reliability, where it can reduce the uncertainty during combination process, so that more convincing results can be obtained. In addition, a new MADM method is proposed based on TDIFS model and TDIFS combination rule. Through comparing with the existing methods in an application of pattern recognition, it is demonstrated that the proposed MADM method is more effective, which can achieve higher robustness and better recognition results.

直觉模糊集（IFS）由于具有较强的表达隶属度，非隶属度和犹豫度的不确定性的能力，因此在多属性决策（MADM）中得到了广泛的应用。此外，Z数是一种新颖的二维框架，可通过引入专家评估的可靠性来处理不确定性问题。然而，在Z数框架内的简单索引不足以表达专家的评价。为了整合IFS的不确定性和可靠性表达，受Z启发数，我们提出了一个二维直觉模糊集（TDIFS）模型。在TDIFS模型中，第一维是专家在属性方面的评估数据，第二维是TDIFS的第一部分，代表了专家的可靠性。此外，对于每个维，它表示为有序直觉模糊集对，它可以承载比简单索引更多的信息。此外，提出了一种新颖的组合规则来融合TDIFS。TDIFS组合规则完全整合了专家评估和专家可靠性，可以减少组合过程中的不确定性，从而获得更具说服力的结果。另外，基于TDIFS模型和TDIFS组合规则，提出了一种新的MADM方法。