区间直觉模糊幂加权算子的动态多属性决策

Dynamic multi-attribute decision-making method with interval-valued intuitionistic fuzzy power weighted operators

为了解决集结算子处理动态多属性决策问题时,现有的区间直觉模糊(interval-valued intuitionistic fuzzy,IVIF)加权平均算子未考虑集结数据之间的相互关系、决策结果精度不高的不足,利用幂加权几何平均(power weighted geometric average,PWGA)算子的非线性特性将集结数据之间相互关系联系起来,提出了IVIF PWGA算子的动态多属性决策方法。首先,将实数形式的PWGA算子扩展到区间直觉模糊集(IVIF set,IVIFS),利用数学归纳法证明了数据融合后的综合集结值是区间直觉模糊数(interval-valued intuitionistic fuzzy number,IVIFN)的结论。然后,定义了IVIF条件下,处理动态多属性决策问题的PWGA算子。通过动态PWGA算子集结多个时间点的单一集结值得到综合集结值,根据综合集结值的得分函数和精确函数,对各方案排序。最后,通过实例说明了该算法的有效性。

With respect to that the traditional geometric average operator in dynamic multi-attribute decision making method with integrated data expressed in interval-valued intuitionistic fuzzy number(IVIFN)fails to consider the relationships between the integrated data,and the overall precision of the final decision result is not high enough,an improved multi-attribute decision making method based on the new proposed dynamic power weighted geometric average(PWGA)operator of IVIFN is proposed.The ability to display nonmonotonic behavior provides one of the useful features of these operators to establish a connection between the integrated data.Firstly,the PWGA operator of real numbers is extended to PWGA of IVIFN and a proof that the final collective value is still a IVIFN is given as well.Besides,a dynamic interval-valued intuitionistic fuzzy PWGA(DIIFPWGA)operator is proposed at the same time.Thereby,applying the DIIFPWGA operator,the individual overall evaluation values at each time point of alternatives are then integrated into collective ones,which are used to rank the alternatives based on the score function and accuracy function of IVIFN.Finally,a numerical example is given to illustrate and validate the proposed approaches.