Improving human health and comfort in buildings requires efficient temperature regulation. Temperature control system has a significant contribution in minimizing the impact of climate change. Temperature control system is used in industry to control temperature. The polar form of complex Pythagorean fuzzy set is a limited notion because when decision makers take the value for membership degree as 0.71+ι0.81 then we can observe that the basic condition for complex Pythagorean fuzzy set fails to hold that is r=0.71²+0.81²=1.3661∉[0,1]. Moreover, we can observe that the Cartesian form of a complex Pythagorean fuzzy set is also a limited notion because it can never discus advance data. Hence keeping in mind these limitations of the existing notions, in this article, we have explored the Cartesian form of a complex q-rung orthopair fuzzy set. Moreover, we have developed the Yager operational laws based on a Cartesian form of complex q-rung orthopair fuzzy set. We have introduced aggregation theory named complex q-rung orthopair fuzzy Yager weighted average and complex q-rung orthopair fuzzy Yager weighted geometric aggregation operators in Cartesian form. Based on these aggregation operators, we have initiated a multi-attribute group decision-making (MAGDM) approach to define the reliability and authenticity of the developed theory. Furthermore, we have utilized this device algorithm in the selection of a temperature control system. The comparative study of the delivered approach shows the advancement and superiority of the delivered approach.

The proposed research fills a significant gap in the decision-making technique for evaluating geothermal energy systems in industrial processes by introducing a new approach involving Hesitant Bipolar Fuzzy (HBF) Sets (HBFSs) with Dombi operators. The existing literature has mostly focused on uncertainty only, overlooking the aspect that decisions tend to be imprecise, bipolar, and hesitant in reality. To overcome this gap, we first introduce Dombi operators in the context of HBFSs, thereby improving the parametric flexibility in handling more complex uncertain information. Based on these operators, we establish an HBF Multi-Criteria Decision-Making (MCDM) method for the ranking of geothermal energy systems. The applicability of our proposed methodology for prioritizing different types of geothermal energy systems for industrial applications is illustrated in a detailed case study that supports the theoretical framework. The benefit of the suggested method is also supplemented by the comparison of the proposed method with the previous methods and evidence of the capability to handle uncertainty and make more precise and confident decisions. This study offers an important theoretical as well as practical contribution to decision-making practices and the choice of sustainable energy systems for geothermal energy options under uncertainty, offering decision-makers a robust framework of analysis. Moreover, we have the following key findings or outcomes of proposed research. • Development of HBF Dombi Weighted Averaging (HBFDWA) operators. • Development of HBF Dombi Ordered Weighted Averaging (HBFDOWA) operators. • Development of HBF Dombi Weighted Geometric (HBFDWG) operators. • Development of HBF Dombi Ordered Weighted Geometric (HBFDOWG) operators. • A case study is performed based on the developed operators to rank geothermal energy systems. • A comparative analysis is performed to show the superiority of the proposed approach. • A sensitivity analysis is discussed to show the influences of the parameter.