The $n$-polygonal interval-valued fuzzy set is an effective tool to deal with multi-attribute group decision-making problems, which can represent fuzzy information. Aggregating multiple evaluation values in the decision-making process is a key challenge. In this study, new operations are proposed for $n$-polygonal interval-valued fuzzy numbers based on the algebraic sum and the Einstein sum. The arithmetic mean operators and geometric mean operators are constructed, and the related properties of the constructed operator are explored. The newly proposed aggregation operators have clear fuzzy logic semantics, which can accurately express the "or" logic and compensation between attributes, and reflects the decision intention by which "any attribute can improve the overall evaluation". In view of the fact that graph theory can intuitively depict various attributes, it has significant practical value in promoting more accurate evaluation of alternatives. The path analysis can abstract a complex system into a graph structure and simplify the problem. We develop a decision-making method that combines path and graph strategies. This method is relatively simple to operate and can represent the path between the scheme and all attributes. In order to illustrate the effectiveness of the method, it is applied to supplier selection. Finally, the practicability and stability of the method are verified by comparative experiments and a sensitivity analysis.