基于区间对偶犹豫不确定语言广义Banzhaf Choquet积分算子的多属性决策方法

Muti-criteria decision making based on interval-valued dual hesitant uncertain linguistic generalized Banzhaf Choquet integral operator

基于将对偶犹豫模糊集和语言变量相结合定义对偶犹豫模糊语言集的思路,提出了区间对偶犹豫不确定语言集的概念,研究了区间对偶犹豫不确定语言变量相关的基本理论与方法,并针对属性值为区间对偶犹豫不确定语言信息的关联多属性决策问题,提出了相应的决策方法.首先,定义了区间对偶犹豫不确定语言变量的概念、运算法则、得分函数、精确函数、海明距离以及排序方法.然后,提出了区间对偶犹豫不确定语言广义Banzhaf Choquet积分算子并证明了该算子的一些性质.为了确定属性集的模糊测度,建立了基于离差最大化方法以及Banzhaf函数的模型.进而,给出一种用于解决属性权重部分未知,属性值为区间对偶犹豫不确定语言变量的关联多属性决策方法.最后,通过算例验证了该方法的有效性.

The concept of dual hesitant fuzzy linguistic set is based on dual hesitant fuzzy set and linguistic variables. Motivated by this idea, this paper proposes the concept of interval-valued dual hesitant uncertain linguistic set used to solve more complex decision making. Firstly, this paper studies the concept,operations, score function, accuracy function, Hamming distance, and ranking method of interval-valued dual hesitant uncertain linguistic variables. Then, the interval-valued dual hesitant uncertain linguistic generalized Banzhaf Choquet integral operator is proposed. Meantime, some properties of this operator are investigated. To determine the optimal fuzzy measure on criteria set, the model based on maximization deviation method and Banzhaf function is established. Furthermore, an approach to muti-criteria decision making problem with incomplete weight information and interactive condition under interval-valued dual hesitant uncertain linguistic environment is developed. Finally, an example is shown to verify the effectiveness of the given method.