Interval-valued intuitionistic fuzzy multi-attribute second-order decision making based on partial connection numbers of set pair analysis

Multi-attribute decision making (MADM) with attribute values as interval-valued intuitionistic fuzzy numbers (IVIFNs) is essentially a second-order decision making problem with uncertainty. To this end, the partial connection number (PCN) of set pair analysis is applied to MADM with IVIFNs. The PCN is an adjoin function of the connection number (CN), and its calculation process reflects the contradictory movement of the connection component in the CN at various micro-levels. It is the main mathematical tool of multi-level analysis method for the macro state and micro-trend. First, we convert IVIFNs into ternary connection numbers (TCNs); then, we calculate the first-order and second-order total PCNs for TCNs. According to the uncertainty analysis of the first-order total PCN, the possible ranking (first-order ranking) of the schemes in the uncertain environment is given, and the deterministic ordering (second-order ranking) of the schemes is given according to the value of the second-order total PCN to meet the needs of different decision making levels. The practical application shows that the method presented is novel, and the results are in line with the uncertainty decision making. Furthermore, the current status and development trend of schemes are taken into account to make decision making progress more reasonable and operable.