The Maclaurin symmetric mean (MSM) and dual Maclaurin symmetric mean (DMSM) operators are two aggregation operators to aggregate the cubic Pythagorean linguistic fuzzy number. The cubic Pythagorean linguistic fuzzy structure is more real to designate fuzzy data in real decision-making problems. The cubic Pythagorean linguistic fuzzy number is more superior and difficult information in the environment of the fuzzy set theory. We describe the score and accuracy function of CPLFN. We define some aggregation operators, including the CPLFAA, CGPLFAA, CPLFGA, CPLFMSM, and CPLFWMSM operators. We present some operators, with the CPLFDWMSMA, CPLFDOWMSMA, CPLFDHWMSMA, CPLFDWMSMG, CPLFDOWMSMG and CPLFDHWMSMG operators. Moreover, some properties and special cases of our proposed methods are also introduced. Then we present multi-attributive group decision-making based on proposed methods. Further, a numerical example is provided to illustrate the flexibility and accuracy of the proposed operators. Last, the proposed methods are compared with existing methods to examine the best developing skill initiatives.

Maclaurin对称均值（MSM）和对偶Maclaurin对称均值（DMSM）算子是两个聚合算子，用于聚合三次Pythagorean语言模糊数。在实际决策问题中指定模糊数据时，三次毕达哥拉斯的语言模糊结构更为真实。在模糊集理论的环境中，三次毕达哥拉斯的语言模糊数是更优越和更困难的信息。我们描述了CPLFN的得分和准确性函数。我们定义了一些聚合运算符，包括CPLFAA，CGPLFAA，CPLFGA，CPLFMSM和CPLFWMSM运算符。我们介绍了一些运算符，包括CPLFDWMSMA，CPLFDOWMSMA，CPLFDHWMSMA，CPLFDWMSMG，CPLFDOWMSMG和CPLFDHWMSMG运算符。此外，还介绍了我们提出的方法的一些特性和特殊情况。然后，我们提出了基于所提出方法的多属性群体决策。此外，提供了一个数值示例来说明所提出的算子的灵活性和准确性。最后，将提出的方法与现有方法进行比较，以检验最佳开发技能的计划。