Fuzzy Decision Support Systems for Selection of NEA Detection Technologies Under Non-Linear Diophantine Fuzzy Hamacher Aggregation Information

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 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 for N-LDFS in a suitable form. Therefore we have apply the Hamacher operators for N-LDFS and develop a new area of research in decision making problems. We have apply the 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 will also establish commutativity, idempotency and monotonicity properties which are the most desirable properties for proposed operators. Ultimately, we have implement a case study regarding the decision support method to pick the best NEA deflection detector. We construct an algorithm to solve the problem of multi-attribute decision-making (MADM) problem, followed by a fun of application using the 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.