This study introduces a new family of soft separation axioms and a real-life application utilizing partial belong and natural non-belong relations. First, we initiate the concepts of w-soft \(T_i\)-spaces \((i=0, 1, 2, 3, 4)\) with respect to distinct ordinary points. These concepts generate a wider family of soft spaces compared with soft \(T_i\)-spaces, p-soft \(T_i\)-spaces and e-soft \(T_i\)-spaces. We illustrate the relationships between w-soft \(T_i\)-spaces with the help of examples and discuss some sufficient conditions of soft topological spaces to be w-soft \(T_i\)-spaces. Additionally, we point out that stable or soft regular spaces are sufficient conditions for the equivalence among the concepts of soft \(T_i\), p-soft \(T_i\) and w-soft \(T_i\). We highlight on explaining the links between w-soft \(T_i\)-spaces and their parametric topological spaces and studying the role of enriched spaces in these links. Furthermore, we prove that w-soft \(T_i\)-spaces are hereditary and topological properties, and they are preserved under finite product soft spaces. Finally, we propose an algorithm to bring out the optimal choices. This algorithm is based on dividing the whole parameters set into parameter sets and then apply a partial belong relation in the favorite soft sets. This application is supported with an interesting example to show how to implement this algorithm.

这项研究介绍了一个新的软分离公理家族，并利用部分归属和自然非归属关系在现实生活中的应用。首先，我们针对不同的普通点提出w-soft \（T_i \）- spaces \（（i = 0，1，2，3，4）\）的概念。与软\（T_i \）-空间，p-soft \（T_i \）-空间和e-soft \（T_i \） -空间相比，这些概念产生了更大范围的软空间。说明我们的关系之间的W-软\（T_i \）与示例的帮助-spaces并讨论软拓扑空间的充分条件是W-软\（T_i \）-空间。另外，我们指出，稳定的或软的规则空间对于软\（T_i \），p-soft \（T_i \）和w-soft \（T_i \）的概念而言是相等的。我们着重介绍w-soft \（T_i \）-空间及其参数化拓扑空间之间的链接，并研究富集空间在这些链接中的作用。此外，我们证明w-soft \（T_i \）空间是遗传和拓扑属性，并且在有限产品软空间下得以保留。最后，我们提出了一种算法，可以得出最佳选择。该算法基于将整个参数集划分为参数集，然后在收藏夹软集中应用部分所属关系。有趣的示例支持该应用程序，以演示如何实现此算法。