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

Abstract

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 multiattribute 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.INDEX TERMS Hamacher Norms, q-rung linear Diophantine fuzzy set (q-RLDFS), Non-linear Diophantine fuzzy Hamacher weighted geometric (N-LDFHWG) operators, Near-Earth Asteroid (NEA), MADM. I. INTRODUCTIONA STEROIDS are rocky worlds that are too small, revolving around the sun, to be considered planets.Sometimes, they are also referred to as planetoids or minor planets. Asteroids were leftovers from the emergence of our solar system about 4.6 billion years ago [1]. Early