Imprecision in the decision-making process is an essential consideration. In order to navigate the imprecise decision-making framework, measuring tools and methods have been developed. Pythagorean fuzzy soft sets are one of the new methods for dealing with imprecision. Pythagorean fuzzy soft topological spaces is an extension of intuitionistic fuzzy soft topological spaces. These sets generalizes intuitionistic fuzzy sets for a broader variety of implementations. This work is a gateway to study such a problem. The concept of Pythagorean fuzzy soft topological spaces(PyFSTS), interior, closure, boundary, neighborhood of Pythagorean fuzzy soft spaces PyFSS, base and subspace of PyFSTSs are presented and its properties are figured out. We established an algorithm under uncertainty based on PyFSTS for multi-attribute decision-making (MADM) and to validate this algorithm, a numerical example is solved for suitable brand selection. Finally, the benefits, validity, versatility and comparison of our proposed algorithms with current techniques are discussed.The advantage of the proposed work is to detect vagueness with more sizably voluminous valuation space than intuitionistic fuzzy sets.

中文翻译：

---

关于勾股模糊软拓扑空间

决策过程中的不精确性是一个重要的考虑因素。为了在不精确的决策框架中导航，已经开发了测量工具和方法。勾股模糊软集是处理不精确性的新方法之一。勾股模糊软拓扑空间是直觉模糊软拓扑空间的扩展。这些集合将直觉模糊集概括为更广泛的实现。这项工作是研究此类问题的门户。提出了勾股模糊软拓扑空间(PyFSTS)的概念、勾股模糊软空间的内部、闭包、边界、邻域PyFSS、PyFSTS的基和子空间，并计算了其性质。我们建立了一种基于 PyFSTS 的不确定性下多属性决策 (MADM) 算法，并为验证该算法，解决了一个适合品牌选择的数值例子。最后，讨论了我们提出的算法与当前技术的好处、有效性、通用性和比较。所提出的工作的优点是用比直觉模糊集更庞大的估价空间来检测模糊性。