基于三角模糊数犹豫直觉模糊集的多属性智能决策

Multi-attribute intelligent decision-making method based on triangular fuzzy number hesitant intuitionistic fuzzy sets

通过剖析现实生活中数据对象复杂性以及决策人思考的犹豫模糊性,提出了基于三角模糊数的犹豫直觉模糊集决策方法。首先,给出了三角模糊数犹豫直觉模糊集的定义,构建并证明了三角犹豫直觉模糊元及模糊数的基本运算法则和集成算子。其次,通过对三角犹豫直觉模糊元的得分函数和精确函数的定义,实现了三角犹豫直觉模糊数下的对象间的取值比较,针对三角犹豫直觉模糊数下多属性决策分析中的不确定性权重求解难题,提出了一种基于得分函数和最大熵理论的最优权重求解模型,并构建遗传算法模型实施最优化求解。最后,给出了三角犹豫直觉模糊数下的多属性智能决策算法,并以算例证明了所提方法的可行性和有效性。

By analyzing complexities of realistic data objects and the hesitate fuzziness in decision-maker＇s thinking, a hesitant intuitionistic fuzzy sets decision-making method based on triangular fuzzy number is pro- posed. Firstly, triangular fuzzy number hesitant intuitionistic fuzzy sets are defined. Also, some basic operation rules and aggregation operators of triangular hesitant intuitionistic fuzzy elements are constructed under formal proofs. Furthermore, the score function and the accuracy function of triangular hesitant intuitionistic fuzzy ele- ments are defined to realize the data comparison between objects of triangular hesitant intuitionistic fuzzy num- ber. Aiming at the uncertainty weight solving problem of multi-attribute decision making based on triangular hesitant intuitionisfie fuzzy numbers, an optimal weight solving model based on the score function and maximum entropy （ME） principle is innovatively proposed, and a genetic algorithm （GA） model is constructed to get the optimal solution. Finally, a multi-attribute intel-ligent decision-making method based on triangular hesitant in- tuitionistic fuzzy number is presented. The example demonstrates the feasibility and effectiveness of the pro- posed method.