New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis

Triangular intuitionistic fuzzy numbers (TIFNs) are one of the extensions of intuitionistic fuzzy sets and triangular fuzzy numbers, and they have been applied to fault-tree analysis in many studies. The arithmetic operations and logic operations of TIFNs have been addressed in relevant studies. However, the arithmetic operations of TIFNs in these studies all have defects. Based on information from the existing studies, this paper proposes new arithmetic operations and logic operators for TIFNs and applies them to fault analysis of a printed circuit board assembly system. The proposed operations are then compared to the existing ones to confirm their feasibility and rationality.