International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2801 2020 2020 Department of Mathematics, College of Education for Pure Science, University of Tikrit, Tikrit, Iraq Mohanad Mohanad Department of Mathematics, College of Education for Pure Science, University of Tikrit, Tikrit, Iraq Sinan O. Al Al-Salihi Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq; College of Engineering, National University of Science and Technology, Dhi Qar, Iraq Faisal Al Al-Sharqi In actual life, dealing with uncertain information has become a challenge for researchers who strive day after day to develop more accurate mathematical tools for better dealing with this information. The Q-Fuzzy soft model can process uncertain information in two dimensions by dealing with the subjective judgments of users effectively. Therefore, this article aims to increase the effectiveness of the Q-fuzzy soft model and address the challenges of design-making under uncertain information by proposing a new model called the interval-valued Q-fuzzy soft (IV-Q-FSS) model. Under the IV-Q-FSSs, we discuss strongly set-theory operations such as subset, union of two IV-Q-FSSs, intersection of two IV-Q-FSSs, complement of IV-Q-FSS, AND operation, and OR operation for IV-Q-FSSs, and some operations like the possibility and necessity operations of an IV-Q-FSS. In addition, we hand over numerous properties held up by numerical examples that describe how they toil. Finally, this recently developed model has been successfully trying out in dealing with one of the design-making problems based on hypothetical data for a respiratory disease. This algorithm is built based on the aggregation operator for IV-Q-FSS data to break this issue (i.e., selecting the optimal alternative). 2024 2024 65 76 10.54216/IJNS.240306 https://www.americaspg.com/articleinfo/21/show/2801