基于犹豫区间直觉语言型Z-Number熵和决策者风险态度的多属性群决策分析

Multi-Attribute Group Decision-Making Analysis based on Hesitant Interval Intuitionistic Linguistic Z-Number Entropy and Decision-Maker’ Risk Attitude

犹豫区间直觉语言型Z-number(HIILZN)是在语言型Z-number基础上拓展而来的,在处理现实世界决策上扮演重要的作用。本文主要提出了在以犹豫区间直觉语言型Z-Number为信息环境下决策者有风险偏好的多属性群决策模型,探究决策者不同风险态度对权重和方案排序的影响,对于进行金融投资以及风险投资等方面的决策均有一定的参考价值。本文首先提出了两种新的语言尺度函数,并基于语言尺度函数,提出了HIILZNs新型距离公式,并利用与HIILZNs正理想点的距离提出了HIILZNs的排序值公式。进一步地基于距离公式提出HIILZNs距离相似度公式,并利用距离相似度构造最优模型求解最优专家权重。接下来提出HIILZNs熵公式度量HIILZNs自身的不确定性,并基于决策者风险态度提出风险偏好因子,然后利用风险偏好因子和熵公式定义了风险偏好函数。最后构造排序值加风险偏好函数最大化的最优决策模型求解最优权重,然后利用WAA算子集结每个方案的属性值得到综合排序值并排序,并探究不同风险偏好下属性权重的变化以及对方案排序的影响。最后,通过一个实例验证该方法的科学性和有效性。

Hesitant interval intuitionistic linguistic Z-number (HIILZN) is an extension of linguistic Z-number and plays an important role in dealing with real world decision-making. In this paper, a multi-attribute group decision-making model with risk preference for decision-makers is proposed under information environment of hesitant interval intuitionistic Z-number to explore the influence of different risk attitude of decision-maker on the weights and the ranking of alternatives, which has certain reference value for financial investment and risk investment decision-making. Firstly, two novel linguistic scale functions are proposed, and a novel distance formula of HIILZNs is put forward based on the linguistic scale functions, and then the ranking formula of HIILZN is proposed by using the distance from the positive ideal point of hesitant interval intuitionistic linguistic Z-numbers (HIILZNs). Furthermore, distance similarity formula of HIILZNs is put forward, and the optimal model is constructed by using the distance similarity to solve the optimal experts’ weights. Secondly, the entropy formula of HIILZNs is proposed to measure the uncertainty of HIILZNs, and risk preference factor is presented based on the decision maker’s risk attitude, then the risk preference function is defined by using the risk preference factor and entropy formula. Finally, an optimal decision model is established to maximize the ranking value pluses the risk preference function, and the optimal weights are obtained by aggregating the ranking values of each alternative under each attribute with the WAA operator, and the influence of different risk preference of decision-maker on the weights and the ranking of alternatives is explored. Finally, an example is given to demonstrate the scientificity and effectiveness of the method proposed in this paper.