Precursor Selection for Sol–Gel Synthesis of Titanium Carbide Nanopowders by a New Cubic Fuzzy Multi-Attribute Group Decision-Making Model

In this paper, we construct an extended version of the TOPSIS method by using cubic information, and provide a numerical application to verify and demonstrate the practicality of the method. A new extension of the gray relation analysis (GRA) method is introduced by using cubic information. We also propose the cubic fuzzy multi-attribute group decision-making model, and the relation between the cubic TOPSIS method and the cubic gray relation analysis (CGRA) method is introduced. Finally, the proposed method is used for selection in sol–gel synthesis of titanium carbide nanopowders. We analyzed the proposed method by using a numerical application to sol–gel synthesis of titanium carbide nanopowders.