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In this paper, we describe the new idea of trapezoidal linguistic uncertain cubic fuzzy number. We discuss some basic operational laws of trapezoidal linguistic uncertain cubic fuzzy number and hamming distance of TrLUCFNs. We introduce the new concept of trapezoidal linguistic uncertain cubic fuzzy TOPSIS method. Furthermore, we extend the classical trapezoidal linguistic uncertain cubic fuzzy TOPSIS method to solve the MCDM method based on trapezoidal linguistic uncertain cubic fuzzy TOPSIS method. The new ranking method for TrLUCFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]