The paper aims is to present a multi-criteria decision-making algorithm for solving decision-making problems with the utilization of the C-IFSs (circular intuitionistic fuzzy sets) features. In it, the uncertainties present in the data are handled with the help of C-IFSs in which we considers the circular rating of each object within a certain radius. Later on, we propose a novel algebraic framework for C-IFSs based on Archimedean t-norm operations, including addition, multiplication, subtraction, and division. These operations enable the aggregation of preferences from multiple experts into a single ranking. Also, we propose an extended EDAS (Evaluation Based on Distance from Average Solution) method, which utilizes weighted aggregation operators and defuzzification techniques to rank alternatives. To validate our approach, we provide a numerical example and compare the results with existing methods. Additionally, we discuss the time complexity of the algorithm. The proposed methodology offers decision-makers the flexibility to analyze the influence of different ratings on the final decision and select suitable parameters.