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.