The T-Spherical Fuzzy set (T-SPHFS) is one of the core simplifications of quite a lot of fuzzy concepts such as fuzzy set (FS), intuitionistic fuzzy set (ITFS), picture fuzzy set (PIFS), Q-rung orthopair fuzzy set (Q-RUOFS), etc. T-SPHFS reveals fuzzy judgment by the degree of positive membership, degree of abstinence, degree of negative membership, and degree of refusal with relaxed conditions, and this is a more powerful mathematical tool to pair with inconsistent, indecisive, and indistinguishable information. In this article, several novel operational laws for T-SPFNs based on the Schweizer–Sklar t-norm (SSTN) and the Schweizer–Sklar t-conorm (SSTCN) are initiated, and some desirable characteristics of these operational laws are investigated. Further, maintaining the dominance of the power aggregation (POA) operators that confiscate the ramifications of the inappropriate data and Heronian mean (HEM) operators that consider the interrelationship among the input information being aggregated, we intend to focus on the T-Spherical fuzzy Schweizer–Sklar power Heronian mean (T-SPHFSSPHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power geometric Heronian mean (T-SPHFSSPGHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted Heronian mean (T-SPHFSSPWHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted geometric Heronian mean (T-SPHFSSPWGHEM) operator, and their core properties and exceptional cases in connection with the parameters. Additionally, deployed on these newly initiated aggregation operators (AOs), a novel multiple attribute decision making (MADM) model is proposed. Then, the initiated model is applied to the City of Penticton (British Columbia, Canada) to select the best choice among the accessible seven water reuse choices to manifest the practicality and potency of the preferred model and a comparison with the proffered models is also particularized.

中文翻译：

---

一种基于T-Spherical Fuzzy Schweizer-Sklar Power Heronian平均算子的新方法，用于评估不确定条件下的水再利用应用

T-Spherical Fuzzy集（T-SPHFS）是模糊集（FS）、直觉模糊集（ITFS）、图片模糊集（PIFS）、Q-rung orthopair等相当多模糊概念的核心简化之一模糊集（Q-RUOFS）等。T-SPHFS通过宽松条件下的正隶属度、禁欲度、负隶属度和拒绝度来揭示模糊判断，这是一种更强大的数学配对工具具有不一致、优柔寡断和无法区分的信息。在本文中，基于 Schweizer-Sklar t-norm (SSTN) 和 Schweizer-Sklar t-conorm (SSTN) 的 T-SPFNs 的几个新运算法则被启动，并研究了这些运算法则的一些理想特性。更多，保持功率聚合 (POA) 算子的主导地位，没收不适当数据的分支和 Heronian 均值 (HEM) 算子，考虑被聚合的输入信息之间的相互关系，我们打算专注于 T-Spherical 模糊 Schweizer-Sklar幂 Heronian 均值 (T-SPHFSSPHEM) 算子、T-Spherical 模糊 Schweizer-Sklar 幂几何 Heronian 均值 (T-SPHFSSPGHEM) 算子、T-Spherical 模糊 Schweizer-Sklar 幂加权 Heronian 均值 (T-SPHFSSPWHEM) 算子、T - 球面模糊 Schweizer-Sklar 幂加权几何 Heronian 均值 (T-SPHFSSPWGHEM) 算子，以及它们的核心属性和与参数相关的例外情况。此外，部署在这些新启动的聚合运营商 (AO) 上，提出了一种新颖的多属性决策（MADM）模型。然后，将启动的模型应用于彭蒂克顿市（加拿大不列颠哥伦比亚省），在可访问的七个水回用选择中选择最佳选择，以体现首选模型的实用性和效力，并与提供的模型进行比较。 .