基于GBM算子扩展的时序广义模糊软集决策模型

在不确定环境下，决策环境的复杂性使决策信息并非完全精确，同时也可能使决策信息存在着时序上的动态变化性。在广义模糊软集的基础上提出了时序广义模糊软集，并定义其并运算、交运算和数乘运算。针对不同时间点决策信息的相互关联性和不同属性间的内在联系，根据几何Bonferroni平均算子（GBM算子）与S范数，提出了时序广义模糊软集几何加权Bonferroni平均算子（TGFSSGBM算子），并证明了其相关性质，在此基础上提出了考虑不同决策时间点权重的TGFSSGWBM算子。最后，构建了基于TGFSSGWBM算子的时序广义模糊软集决策模型，算例分析以及不同算子间的比较分析验证了该决策模型的可行性和有效性。

Decision-Making Model of Time Series Generalized Fuzzy Soft Sets Based on Extended GBM Operator

Under uncertain conditions, information for decision-making may be inexact and constantly changes with times series because of the complexity of circumstance. Based on generalized fuzzy soft sets, this paper presents the Time series Generalized Fuzzy Soft Set（TGFSS） and its union operation, intersection operation and scalar multiplication operation. Secondly, according to Geometrical Bonferroni Mean（GBM） operator and S-norm, TGFSSGBM operator is provided to deal with  the relevance of  different decision-making attributes and the relevance of information from different time points, and some properties of TGFSSGBM operator are also proofed. Subsequently, TGFSSGWBM operator considering weights of different time points is given. On the basis of definitions and proofs mentioned above, a dynamic decision-making model based on TGFSSGWBM operator is put forward. Finally, a numerical example and comparisons among different operators verify the feasibility and effectiveness of the decision-making model provided.