新Schweizer Sklar范数图模糊算子与决策应用

New Schweizer Sklar Norm Picture Fuzzy Operator and Decision Application

现有的图模糊运算法则不满足运算封闭性,并且对于图模糊聚合算子多通过单个算子聚合评价信息进行决策,无法全面考虑决策信息间的关系。在Schweizer Sklar(SS)范数条件下定义一种图模糊运算法则。由于幂平均算子可以降低异常评价信息对决策结果的影响,Muirhead平均算子能够体现属性间关联性的影响,因此通过对幂平均算子和Muirhead平均算子进行复合,设计图模糊SS范数聚合算子以及其加权的形式,根据所提的图模糊运算法则推导聚合算子的数学表达式并验证其具有幂等性、交换性和有界性。基于所提的图模糊SS范数聚合算子构建一种图模糊多属性决策方法。实验结果表明,所提的图模糊SS范数聚合算子具有可行性和有效性,决策者可以依据自身风险偏好调节参数向量Q和λ的取值,以满足不同的决策需求。相比PFWA、PFWG、PFWMM等单个算子,所提的复合算子可以更加有效、稳定地聚合评价信息来获得决策结果。

Existing picture fuzzy operational laws do not satisfy the closure and picture fuzzy aggregation operators,mostly aggregating the evaluation information through a single operator,which interferes with the comprehensive consideration of the relationship between decision information.Under the Schweizer Sklar(SS)norm condition,a picture fuzzy operational law is proposed.Because the power mean operator can reduce the impact of abnormal evaluation information on the decision results,and the Muirhead mean operator can reflect the impact of the correlation between attributes,by combining these two operators with the picture fuzzy SS norm aggregation operator,a weighted form can be designed for the mathematical expression of the aggregation operator that is derived according to the proposed picture fuzzy operational law thereby verifying its idempotence,commutativity,and boundedness.Based on the proposed picture fuzzy SS norm aggregation operator,a picture fuzzy Multi-Attribute Decision Making(MADM)method is constructed.The experimental results show that the proposed picture fuzzy SS norm aggregation operator is feasible and effective,and decision-makers can adjust the value of parameter vector Q andλaccording to their own risk preference to meet different decision-making needs.Compared with the single operator PFWA,PFWG,PFWMM,the composite operator can more effectively and stably aggregate evaluation information to reach decision.