毕达哥拉斯犹豫模糊集成算子及其决策应用

针对毕达哥拉斯犹豫模糊多属性决策中，集成算子的重要作用以及集成算子不完善的情况，较为系统地研究了毕达哥拉斯犹豫模糊集成算子。为此，在毕达哥拉斯模糊数的运算和运算法则基础上，定义了毕达哥拉斯犹豫模糊有序加权平均算子（PHFOWA）、广义有序加权平均算子（GPHFOWA）和混合平均算子（PHFHA），以及毕达哥拉斯犹豫模糊有序加权几何平均算子（PHFOWG）、广义有序加权几何平均算子（GPHFOWG）和混合几何平均算子（PHFHG），并结合数学归纳法，分别给出了它们的计算公式，讨论了它们的有界性、单调性和置换不变性等性质。建立了基于毕达哥拉斯犹豫模糊集成算子的多属性决策方法，并应用算例和相关方法比较说明了决策方法的可行性与有效性。

Pythagorean hesitant fuzzy aggregation operators and their applications in decision making

Pythagorean hesitant fuzzy set as a new generalization of Pythagorean fuzzy and hesitant fuzzy set can handle fuzzy information more flexibly in multiple attribute decision making. In view of the important role of aggregation operator in multiple attribute decision making and under the condition of the imperfect aggregation operator in Pythagorean hesitant fuzzy decision environment, this paper systematically investigated Pythagorean hesitant fuzzy aggregation operators. It defined some Pythagorean hesitant fuzzy aggregation operators based on the operational laws of Pythagorean hesitant fuzzy numbers, including Pythagorean hesitant fuzzy ordered weighted average operator(PHFOWA), generalized ordered weighted average operator(GPHFOWA), hybrid average operator(PHFHA), Pythagorean hesitant fuzzy ordered weighted geometric average operator(PHFOWG), generalized ordered weighted geometric average operator(GPHFOWG) and hybrid geometric average operator(PHFHG). It gave the mathematical expression of these operators by derivation and discussed in detail some desirable properties such as boundedness, nonotonicity and commutativity. Finally, this paper proposed a decision making method based on Pythagorean hesitant fuzzy aggregation operators, and used an applied example to illustrate the feasibility and applicability of the proposed method.