TDIFS: Two dimensional intuitionistic fuzzy sets

Abstract 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.