Abstract:

Multi-Criteria Decision Making（MCDM） issues involve a large amount of inaccurate, incomplete and inconsistent information. The Single Valued Triangular Neutrosophic numbers（SVTrN-numbers） as a branch of Neutrosophic Numbers（NN） can effectively deal with such problems. At the same time, cross entropy is very suitable for measuring the degree of difference in decision information, but the existing cross entropy measure is unreasonable. Considering the advantages of SVTrN-numbers, combined with TOPSIS theory, a new cross-entropy measure is proposed and its properties are proved. Based on this, a new method is proposed for solving MCDM problem in SVTrN-numbers environment. A case is shown to improve the rationality of the cross-entropy formula.

Key words: single-valued triangular Neutrosophic number, cross entropy, relative closeness, TOPSIS method

摘要：

多准则决策（Multi-Criteria Decision Making，MCDM）问题涉及到大量不精确、不完整和不一致的信息，而单值三角Neutrosophic数（Single Valued Triangular Neutrosophic Numbers，SVTrN-numbers）作为Neutrosophic数（Neutrosophic Numbers，NN）的一个分支可以有效地处理这类问题。同时交叉熵很适合度量决策信息的差异程度，但是现有的交叉熵测度存在不足。考虑到SVTrN-numbers具有的优势，结合TOPSIS理论，提出一种新的交叉熵测度，并对其性质进行证明，据此提出了一个SVTrN-numbers环境下解决MCDM问题的新方法。通过一个案例表明交叉熵公式的合理性。

关键词: 单值三角Neutrosophic数, 交叉熵, 相对贴近度, TOPSIS方法