The properties of fuzzy tensor and the product of fuzzy tensor and fuzzy vector are studied in the paper. The concept of fuzzy tensor is defined through expanding the fuzzy matrix. The product of fuzzy tensor and fuzzy vector is proved to be a fuzzy linear transformation. The general form of the fuzzy synthetic evaluation model is established to solve multiple attribute group decision making problems. Finally, two numerical examples of multiple attribute group decision making are provided to demonstrate the feasibility and efficiency of the fuzzy synthetic evaluation.

中文翻译：

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模糊张量的性质及其在多属性群决策中的应用


本文研究了模糊张量的性质以及模糊张量与模糊向量的乘积。模糊张量的概念是通过模糊矩阵的展开来定义的。证明了模糊张量和模糊向量的乘积是模糊线性变换。建立了模糊综合评价模型的一般形式来解决多属性群决策问题。最后，提供了两个多属性群决策的数值例子，证明了模糊综合评价的可行性和有效性。