基于调和犹豫模糊信息的多属性决策方法

Multi-attribute decision-making method based on the reconciled hesitant fuzzy information

实践中发现,犹豫模糊信息和概率犹豫模糊信息在计算过程中存在着计算繁琐、与数量运算规则不相容等问题.对此,提出一套基于调和犹豫模糊元的解决方法.通过定义调和犹豫模糊元为一组概率分布相同的概率犹豫模糊元,在犹豫模糊信息和概率犹豫模糊信息之间架起一座桥梁,将它们纳入统一处理框架.在此基础上,定义调和犹豫模糊信息的基本运算规则、信息集成算子、距离测度和混合熵测度,构建基于调和犹豫模糊信息的多属性决策方法,并将其应用于陆军合成旅指挥控制能力评估.数值实验表明:调和犹豫模糊决策理论克服了已有理论的缺陷,具有计算量可控、易于编程实现、与数量运算规则相容等优势.

It has been found that hesitant fuzzy information and probabilistic hesitant fuzzy information have some problems with calculating, such as cumbersome calculations and incompatibility with quantitative calculation rules. In this work, we propose a set of solutions, based on the reconciled hesitant fuzzy elements(RHFEs), to solve these problems. By defining the RHFEs as a set of probabilistic hesitant fuzzy elements(PHFEs) with the same probability distribution, this work bridges the gap between hesitant fuzzy information and probabilistic hesitant fuzzy information,and incorporates them into a unified processing framework. Based on this, we build a reconciled hesitant fuzzy multi-attribute decision-making(MADM) method, by developing the operation rules, the information aggregation operators, the distance measures and the hybrid entropy measure for RHFEs, and further apply it to evaluate the command and control(C2) capability of the army’s combined brigades. Numerical experiments show that the theory of reconciled hesitant fuzzy decision-making overcomes the shortcomings of existing theories, and has some advantages of controllable calculations, easy to program and compatible with quantitative calculation rules.