The paper’s aims are to present a novel concept of linguistic interval-valued Pythagorean fuzzy set (LIVPFS) or called a linguistic interval-valued intuitionistic type-2 fuzzy set, which is a robust and trustworthy tool, and to accomplish the imprecise information while solving the decision-making problems. The presented LIVPFS is a generalization of the linguistic Pythagorean fuzzy set, by characterizing the membership and non-membership degrees as the interval-valued linguistic terms to represent the uncertain information. To explore the study, we firstly define some basic operational rules, score and accuracy functions, and the ordering relations of LIVPFS with a brief study of the desirable properties. Based on the stated operational laws, we proposed several weighted averages and geometric aggregating operators to aggregate the linguistic interval-valued Pythagorean fuzzy information. The fundamental inequalities between the proposed operators and their properties are discussed in detail. Finally, a multiple attribute group decision-making (MAGDM) algorithm is promoted to solve the group decision-making problems with uncertain information using linguistic features and the proposed operators. The fundamental inequalities between the proposed operators and their properties are discussed in detail. Also, the illustration of the stated algorithm is given through several numerical examples and compared their performance with the results of the existing algorithms. Based on the stated MAGDM algorithm and the suitable operators, the decision-makers’ can be selected their best alternatives with their own attitude character towards optimism or pessimism choice. The presented LIVPFS is an extension of the several existing sets and is more generalized to utilize the uncertain and imprecise information with a wider range of information. Based on the presented aggregation operators, a decision-maker can select the desired one as per their choices to access the finest alternatives.

本文的目的是提出一种新的语言区间值勾股模糊集（LIVPFS）或称为语言区间值直觉2型模糊集的概念，它是一种健壮且值得信赖的工具，并且可以在求解时完成不精确信息决策问题。通过将隶属度和非隶属度表征为表示不确定信息的区间值语言术语，提出的LIVPFS是语言毕达哥拉斯模糊集的概括。为了进行研究，我们首先定义了一些基本的操作规则，得分和准确性函数，以及LIVPFS的有序关系，并简要研究了所需的属性。根据规定的运营法律，我们提出了几种加权平均值和几何聚合算子来聚合语言区间值勾股模糊信息。详细讨论了所提议的算子及其性质之间的基本不等式。最后，提出了一种多属性群决策算法（MAGDM），利用语言特征和拟议的算子来解决信息不确定的群体决策问题。详细讨论了所提议的算子及其性质之间的基本不等式。另外，通过几个数值示例给出了所述算法的说明，并将其性能与现有算法的结果进行了比较。基于陈述的MAGDM算法和合适的运算符，决策者可以根据自己对乐观或悲观选择的态度来选择最佳选择。所提出的LIVPFS是几个现有集合的扩展，并且更广泛地利用不确定信息和不精确信息以及更广泛的信息。基于提出的聚合运算符，决策者可以根据自己的选择选择所需的运算符，以访问最佳方案。