The motivation of this paper is to build up a new technique to manage multi-attribute decision-making (MADM) issues with interval-valued Pythagorean fuzzy (IVPF) set according to the concepts of Hamacher t-norm and t-conorm, and give its application in MADM problems. To begin with, we integrate the Hamacher operations on IVPF sets. Then, in view of these operations, we formulate a few IVPF aggregation operators, for example, IVPF Hamacher weighted average operator, IVPF Hamacher order weighted average operator, IVPF Hamacher hybrid average operator, IVPF Hamacher weighted geometric operator, IVPF Hamacher order weighted geometric operator, and IVPF Hamacher hybrid geometric operator. We investigate the distinguished features of these suggested operators. Moreover, we carry out the proposed aggregation operators to produce a method for solving MADM issues under IVPF data. We present an example of the emerging software system selection to elaborate on its practicality and effectiveness. We investigate the impact of the parameter for different values on decision-making outcomes. The main advantage of utilizing the suggested operator lies in the fact that this operator provides an increasingly complete perspective on the issue to the decision-makers. The technique suggested in this study gives progressively broad, improve the accuracy and exact outcomes when contrasted with the existing related methods. Therefore, this technique performs an important function in real-life MADM issues.

本文的目的是根据Hamacher t -norm和t的概念，建立一种新技术，以区间值勾股勾股模糊（IVPF）集管理多属性决策（MADM）问题。-conorm，并将其应用于MADM问题。首先，我们将Hamacher操作集成到IVPF集合上。然后，针对这些操作，我们制定一些IVPF聚合算子，例如IVPF Hamacher加权平均算子，IVPF Hamacher阶加权平均算子，IVPF Hamacher混合平均算子，IVPF Hamacher加权几何算子，IVPF Hamacher阶加权几何算子，以及IVPF Hamacher混合几何运算符。我们调查了这些建议的运算符的显着特征。此外，我们执行提出的聚合算子以产生一种解决IVPF数据下的MADM问题的方法。我们以新兴软件系统选择为例，详细说明其实用性和有效性。我们调查了不同值的参数对决策结果的影响。利用建议的运算符的主要优点在于，该运算符为决策者提供了关于此问题的日益完整的观点。与现有的相关方法相比，本研究中提出的技术可以逐步扩大范围，提高准确性和精确结果。因此，该技术在现实生活中的MADM问题中起着重要的作用。