<p>Smart healthcare facilities are essential in the administration of the contemporary problems such as rising healthcare costs, the variation in healthcare service delivery, and the demands of sustainable healthcare medical operations. This paper constructs a novel decision-making framework to evaluate and select smart healthcare schemes depending on t-spherical hesitant fuzzy (t-SHF) data. The t-SHF sets are more adaptable and flexible that allows the professionals to express their preferences. Through the use of Dombi norms we can determine the basic laws of operation of t-SHF numbers and discuss their theoretical properties. A set of generalized aggregation operators is presented in order to aggregate t-SHF effectively, which includes Dombi norms, Heronian mean, and power average principles. Based on this, two sets of novel operators are proposed, including the t-SHF Dombi power Heronian mean (and weighted version), and the t-SHF Dombi power geometric Heronian mean (and weighted version), which is capable of handling extreme or outlier values in the decision-making process. The theoretic analysis of the proposed operators with the identification of their efficiency is supported by the case study of the selection of options of the most effective smart healthcare facilities. Sensitivity analyses are extensively performed to explore the effect of the most significant parameters, and comparative analyses with the existing decision-making models are provided to show the superior quality, and feasibility of the suggested MADM model.</p>