基于新交叉熵的灰关联双向投影多属性决策方法

Grey Relational Bidirectional Projection Multi-attribute Decision-making Method Based on New Cross Entropy

文章针对属性权重完全未知的犹豫模糊多属性决策问题,提出一种基于新交叉熵的灰关联双向投影多属性决策方法。首先,结合基本不等式概念提出犹豫模糊数中新的交叉熵公式,并证明其满足熵的基本性质。其次,以新的交叉熵公式为距离公式,应用离差最大化方法求得属性权重。再次,将灰关联双向投影法拓展到一般犹豫模糊环境下,提出了基于新交叉熵的灰关联双向投影多属性决策方法。最后,通过一个算例验证了所提方法的可行性和有效性。该方法为解决犹豫模糊信息中属性权重完全未知的决策问题提供了新的方法和思路,且具有较高的区分度和灵敏度,提高了决策可信度。

Aiming at the hesitant fuzzy multi-attribute decision-making with completely unknown attribute weights,this paper proposes a grey relational bidirectional projection multi-attribute decision-making method based on a new cross entropy.Firstly,combined with the concept of fundamental inequalities,a new cross entropy formula in hesitant fuzzy numbers is proposed,and it is proved that the new cross entropy formula satisfies the basic properties of entropy.Secondly,the new cross entropy formula is used as the distance formula,which is applied to the deviation maximization method to obtain the attribute weights.Thirdly,the grey relational bidirectional projection method is extended to the general hesitant fuzzy environment,and the grey relational bidirectional projection multi-attribute decision-making method based on the new cross entropy is proposed.Finally,the feasibility and effectiveness of the proposed method are verified by applying a study.This method provides a new method and idea for solving the decision-making problem with completely unknown attribute weights in hesitant fuzzy information,and also has high discrimination and sensitivity,which improves the credibility of decision-making.