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.

The rapid growth of Internet of Things (IoT) technologies has made real-time data processing a critical component for efficient monitoring, analysis, and intelligent decision-making in dynamic and large-scale environments. IoT systems continuously generate massive volumes of heterogeneous data that must be processed with minimal latency to ensure timely responses and reliable system performance. Effective real-time data processing enables IoT applications to adapt to changing conditions, enhance operational efficiency, improve safety and reliability, and support time-sensitive services in domains such as smart cities, healthcare monitoring, industrial automation, and intelligent transportation systems. This study presents a comprehensive mathematical framework for the analysis of real-time data processing methods for IoT applications based on hesitant bipolar fuzzy (HBF) Dombi power operators. The proposed model is designed to effectively capture uncertainty, hesitation, and bipolar information that naturally arise in real-world IoT environments due to incomplete, imprecise, and conflicting data sources. By incorporating a multi-criteria decision-making (MCDM) approach, multiple real-time data processing techniques are systematically evaluated and prioritized with respect to several performance-related attributes. The proposed HBF Dombi power-based framework offers a reliable and transparent mechanism for comparing competing real-time data processing strategies and selecting the most suitable method for specific IoT scenarios. The results indicate that the proposed approach improves decision accuracy and supports better alignment between data processing methods and the complex operational requirements of modern IoT systems. This work contributes both theoretical insights and practical guidance for the design and evaluation of efficient, adaptive, and intelligent real-time IoT data processing architectures.