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 current definition of the Complex Hesitant Fuzzy Set (CHFS), derived from the Ramot form of complex numbers, cannot process information as in Tamir’s complex fuzzy form. We have data with uncertainty and extra information that cannot be described by any other structure than Tamir’s complex fuzzy form. Hence, in this article, we initiated the idea of CHFS based on Tamir’s complex fuzzy form and established its operational laws. Since Decision-Making (DM) theory is central to nearly all disciplines, we have proposed a novel complex hesitant fuzzy Multi-Criterion Decision-Making (MCDM) model. This method can handle all sorts of real-life MCDM problems, where the data contains uncertainty, hesitancy, and extra fuzzy information. While developing this method, we also develop and apply Dombi aggregation operators in this manuscript. After that, we discussed a case study that concerns energy storage system selection for AI-controlled microgrids and discussed how the theory we have developed can be applied to real-world challenges. Last, we conferred on how this proposed theory is superior to other theories and why it should be adopted.