The linguistic Pythagorean fuzzy sets (LPFSs), which employ linguistic terms to express membership and non-membership degrees, can effectively deal with decision makers’ complicated evaluation values in the process of multiple attribute group decision-making (MAGDM). To improve the ability of LPFSs in depicting fuzzy information, this paper generalized LPFSs to cubic LPFSs (CLPFSs) and studied CLPFSs-based MAGDM method. First, the definition, operational rules, comparison method and distance measure of CLPFSs are investigated. The CLPFSs fully adsorb the advantages of LPFSs and cubic fuzzy sets and hence they are suitable and flexible to depict attribute values in fuzzy and complicated decision-making environments. Second, based on the extension of power Hamy mean operator in CLPFSs, the cubic linguistic Pythagorean fuzzy power average operator, the cubic linguistic Pythagorean fuzzy power Hamy mean operator as well as their weighted forms were introduced. These aggregation operators can effectively and comprehensively aggregate attribute values in MAGDM problems. Besides, some important properties of these operators were studied. Finally, we presented a new MAGDM method based on CLPFSs and their aggregation operators. Illustrative examples and comparative analysis are provided to show the effectiveness and advantages of our proposed decision-making method.

语言的毕达哥拉斯模糊集（LPFS）使用语言术语来表示成员资格和非成员资格程度，可以在多属性组决策（MAGDM）过程中有效地处理决策者的复杂评估值。为了提高LPFS描述模糊信息的能力，本文将LPFS广义化为立方LPFS（CLPFS），并研究了基于CLPFS的MAGDM方法。首先，研究了CLPFS的定义，操作规则，比较方法和距离度量。CLPFS充分吸收了LPFS和三次模糊集的优点，因此它们适合并灵活地描述模糊和复杂决策环境中的属性值。其次，基于CLPFS中幂Hamy均值算子的扩展，三次语言毕达哥拉斯模糊幂平均算子，介绍了三次语言毕达哥拉斯模糊能力哈米均值算子及其加权形式。这些聚合运算符可以有效且全面地聚合MAGDM问题中的属性值。此外，还研究了这些算子的一些重要性质。最后，我们提出了一种基于CLPFS及其聚集运算符的MAGDM新方法。提供了说明性示例和比较分析，以显示我们提出的决策方法的有效性和优势。我们提出了一种基于CLPFS及其聚合运算符的MAGDM新方法。提供了说明性示例和比较分析，以显示我们提出的决策方法的有效性和优势。我们提出了一种基于CLPFS及其聚合运算符的MAGDM新方法。提供了说明性示例和比较分析，以显示我们提出的决策方法的有效性和优势。