基于Z-number的PROMETHEE多属性决策方法

针对Z-number能够模拟带有不确定信息的自然语言,却没有有效的应用方法这一问题,提出了已知部分权重时以Z-number为信息环境的多属性决策方法。首先,在Z-number理论基础上利用模糊性限制和可靠性限制之间的关系,建立了两个非线性模型计算Z-number的潜在概率;其次,结合模糊数的交叉熵和KL散度,构造了离散Z-number交叉熵公式,并且提出了基于Z-number的PROMETHEE多属性决策方法;该方法结合级别高于关系理论,建立了取值为0～1的优先函数,利用优先函数公式获得优先指数矩阵,进一步计算出净流,然后根据净流大小对各方案进行排序;最后,通过一个实例的应用与分析说明提出方法的有效性和可行性。

Approach to Multi-attribute Decision Making with PROMETHEE Based on Z-Numbers

Aiming at the fact that Z-number can simulate natural language with uncertain information, but there is no effective application method, a multi attribute decision making method with Z-number as information environment with known partial weight is proposed. Firstly, based on Z-number theory, two nonlinear models are established to calculate the potential probability of Z-number by using the relationship between fuzzy restriction and reliability restriction. Secondly, combining the cross entropy and KL divergence of fuzzy numbers, the discrete Z-number cross entropy formula is constructed, and the PROMETHEE multi attribute decision approach based on Z-number is proposed. In this method, combining the theory of outranking relation, a priority function of taking a value from 0 to 1 is established, a priority index matrix is obtained by using a priority function formula, further, the net flow is calculated, and then the schemes are sorted according to the net flow. Finally, the effectiveness and feasibility of the proposed method are illustrated by the application and analysis of an example.