广义区间值Pythagorean三角模糊集成算子及其决策应用

Generalized interval-valued Pythagorean triangular fuzzy aggregation operator and application in decision making

针对连续集合上决策变量的隶属度和非隶属度之和超过1的决策问题,提出区间值Pythagorean三角模糊数,并且分析其广义集成算子的决策应用。首先,引入区间值Pythagorean三角模糊数的概念,得到其运算法则。其次,推导区间值Pythagorean三角模糊数的加权平均算子、加权几何算子、有序加权平均算子、有序加权几何算子、广义有序加权平均算子以及广义有序加权几何算子,介绍它们的相关性质。最后,构建出基于广义区间值Pythagorean三角模糊集成算子的多属性决策模型,并且根据实例对广义有序加权平均算子和广义有序加权几何算子进行稳定性分析,运用图像直观地证明在处理决策问题时前者优于后者,说明决策模型的有效性和可行性。

In this article,the interval-valued Pythagorean triangular fuzzy number is proposed for the decision making problems when the sum of membership degree and non-membership degree of decision variables exceeds 1 on continuous sets,and the decision application of its generalized aggregation operator is analyzed.Firstly,the concept of interval-valued Pythagorean triangular fuzzy numbers is given,and its algorithm is obtained.Secondly,the weighted average operator,weighted geometric operator,ordered weighted average operator,ordered weighted geometric operator,generalized ordered weighted average operator and generalized ordered weighted geometric operator of interval-valued Pythagorean triangular fuzzy numbers are defined,and their related properties are introduced.Finally,a multi-attribute decision making model based on generalized interval-valued Pythagorean triangular fuzzy aggregation operator is constructed,and the stability of generalized ordered weighted average operator and generalized ordered weighted geometric operator is analyzed according to an example.The figures are used to prove intuitively that the former is superior to the latter when dealing with decision making problems.The effectiveness and feasibility of the decision making model are illustrated.