## 1 Introduction  
Decision making (DM) is a helpful technique for choosing the best option from multiple lists of options. To acquire the best findings, several researchers gave a variety of concepts. MADM is an important part of decision sciences that can offer ranking outcomes for limited options based on the attribute values of various alternatives. In the last few years, the growth of construction businesses and social DM in all aspects have been linked to the issue of MADM. Therefore, it has become extensively used on various grounds, such as the assessment of sustainable housing affordability by [PERSON] et al. [1] and fuzzy hybrid techniques for management of construction engineering by [PERSON] [2]. An important difficulty in the real-world DM process is expressing attribute value more accurately and efficiently. [PERSON] [3] presented the fuzzy set (FS) notion to fill this gap. It was a significant accomplishment with several applications in various ambiguous environments. FS is essentially composed of just membership degree (MD) that fall into the \([0,\ 1]\) range. FS is a helpful tool for analyzing uncertain ambiguous data. Researchers have been paying increasing attention to these approaches in recent decades and have effectively used them in the DM process in several situations. The concept of FS was further developed by [PERSON] [3], intuitionist fuzzy set (IFS). It consists of MD '\(\alpha\)' and non-membership degree (NMD) '\(\beta\)' such that \(0\leq\alpha+\beta\leq 1\). Whenthe value of MD is 0.3 and NMD is 0.8, then IFS cannot clearly define how to handle such a circumstance. Then, [PERSON] [4] developed the concept of the Pythagorean fuzzy set (PyFS) to address these issues by providing the condition for MD \({}^{\prime}\alpha^{\prime}\) and NMD \({}^{\prime}\beta^{\prime}\) such that \(0\leq\alpha^{2}+\beta^{2}\leq 1\). In addition, [PERSON] [5], the q-ROF set (q-ROFS) can be used to generalize IFS and PyFS. The q-ROFS gives greater freedom for expressing their opinions and gives the conditions on MD \({}^{\prime}\alpha^{\prime}\) and NMD \({}^{\prime}\beta^{\prime}\) such that \(0\leq\alpha^{q}+\beta^{q}\leq 1\). The q-ROFS structure has the ability to deal with the sum of \(q\)th power of MD and NMD, and it always gives the answer within the range of \([0,\ 1]\). The results of this fuzzy structure are more accurate than previous fuzzy structures. Due to this important factor, we select this structure for the data aggregation. In MADM, a hot debate is generated when trying to select the best option from ambiguous data or information. For MADM issues, the aggregation of data is the primary technique. A variety of AOs is based on different TCN and TN. The debate on arithmetic AOs has a long history among these AOs; many AOs have been examined in numerous contexts. For example, various authors have investigated [PERSON] AOs based on [PERSON] TNs, such as [PERSON] et al. [6], who studied [PERSON]'s interactive AOs of a t-Spherical fuzzy set (TSFS), and [PERSON] and [PERSON] [7], who investigated [PERSON] geometric AOs of IFS. Intuitionistic fuzzy (IF) hybrid arithmetic AOs are proposed by [PERSON] et al. [8], and [PERSON] [9] proposed picture fuzzy Maclaurin symmetric AOs. [PERSON] [10] studied the applications of bipolar soft sets in MADM, and [PERSON] [11] proposed IF trapezoidal fuzzy arithmetic AOs. The concept of Hamacher TNs, which led to the invention of Hamacher AOs and their use in MADM issues, has also been researched by several researchers in fuzzy mathematics. Hamacher AOs for IFSs based on Entropy are developed by [PERSON] [12], while [PERSON] et al. [13] analyze the t-spherical fuzzy (TSF), Hamacher AOs for analyzing the performance of rescue robots. Various other TNs and TCNs, such as Dombi TNs and Dombi TCNs by [PERSON] [14], have been extensively investigated and led to the invention of Dombi AOs. [PERSON] and [PERSON] [15] and [PERSON] et al. [16] developed the concepts of Dombi AOs in the context of IFSs and Dombi AOs in the Pythagorean fuzzy (PyF) system, respectively.