The emergency situation of COVID-19 is a very important problem for emergency decision support systems. Control of the spread of COVID-19 in emergency situations across the world is a challenge and therefore the aim of this study is to propose a q-linear Diophantine fuzzy decision-making model for the control and diagnose COVID19. Basically, the paper includes three main parts for the achievement of appropriate and accurate measures to address the situation of emergency decision-making. First, we propose a novel generalization of Pythagorean fuzzy set, q-rung orthopair fuzzy set and linear Diophantine fuzzy set, called q-linear Diophantine fuzzy set (q-LDFS) and also discussed their important properties. In addition, aggregation operators play an effective role in aggregating uncertainty in decision-making problems. Therefore, algebraic norms based on certain operating laws for q-LDFSs are established. In the second part of the paper, we propose series of averaging and geometric aggregation operators based on defined operating laws under q-LDFS. The final part of the paper consists of two ranking algorithms based on proposed aggregation operators to address the emergency situation of COVID-19 under q-linear Diophantine fuzzy information. In addition, the numerical case study of the novel carnivorous (COVID-19) situation is provided as an application for emergency decision-making based on the proposed algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID-19.

The Objectives of this study is to extend the concept of q-rung linear Diophantine fuzzy sets (q-RLDFSs), followed by the Near-Earth Asteroids (NEAs) deflection detector. The q-RLDFS is more superior than the linear Diophantine fuzzy sets (LDFSs) because of the qth power of reference parameters (RPs). In the present work first, we have recall the q-RLDFS and named it Non-linear Diophantine Fuzzy set (N-LDFS) further, introduce some operational rules on N-LDFS under Hamacher sum and Hamacher product. Hamacher Norms were commonly referred to as Hamacher operations, but their applications might be better expressed if they are presented with a new level of flexibility within the general parameter. Hamacher operations have not yet been applied in N-LDFS in a suitable form. Therefore we apply the Hamacher operators for N-LDFS and develop a new area of research in decision making problems. We apply Hamacher operators to develop Non-linear Diophantine fuzzy aggregation operators from geometric point of view such as non-linear Diophantine fuzzy Hamacher weighted geometric (N-LDFHWG), non-linear Diophantine fuzzy Hamacher ordered weighted geometric (N-LDFHOWG) and non-linear Diophantine fuzzy Hamacher hybrid weighted geometric (N-LDFHHWG) aggregation operators. We also establish commutativity, idempotency and monotonicity properties which are the most desirable properties for proposed operators. Ultimately, we have implemented a case study regarding the decision support method to pick the best NEA deflection detector. We have construction of an algorithm to solve the problem of multi-attribute decision-making (MADM) problem, followed by a fun application using N-LDFHWG operator. A comparison between the proposed and existing methods is perform from the geometric point of view. Finally, the comparisons demonstrate the effectiveness and superiority of the proposed method.