Nonlinear Diophantine Rough Fuzzy Sets-Based Multicriteria Group Decision-Making in Uncertain Environments

Abstract

Several operational laws, Hamacher operations, and creative aggregation techniques for handling Nonlinear Diophantine Rough Fuzzy data are thoroughly examined in this work. We present NLDRFHWG, NLDRFHOWG, and NLDRFHHWG, three new arithmetic averaging operators created especially to improve the accuracy and dependability of arithmetic aggregation. These operators are thoroughly examined, emphasizing their characteristics and connections to current aggregation techniques. We also illustrate how these operators are related to hamacher-type operations and how the suggested models broaden their use. For the suggested operators, three essential mathematical properties are established: idempotency, monotonicity, and boundedness. Additionally, the practical utility of the NLDRFHWG operator is demonstrated by applying it to multiple attribute decision-making situations employing NLDRF data. The results of this work provide sophisticated methods for combining and analyzing complicated, ambiguous, or inconsistent data, which adds insightful information. The usefulness and practicality of the suggested operators are further illustrated by a numerical example, which validates their possible importance in future research and decision-making.