Reference parameter mapping (passing arguments by reference) is a technique where the reference (like to find physical meaning, memory address) of a parameter is passed to a function or procedure, rather than a copy of the parameter's value. This approach enables changes made to the parameter within the function to affect the original data. In decision-making systems, reference parameter mapping (passing arguments by reference) offers several key advantages that enhance flexibility, consistency, and efficiency. This is especially useful in scenarios where decisions are based on shared data, complex interactions, and iterative updates. In this paper, a new class of fuzzy set was introduced that is known as the $ \left({q}_{1}^{}, {q}_{2}^{}\right) $-rung Diophantine fuzzy set, where $ {q}_{1} $ and $ {q}_{2} $ are reference parameter mappings. Most of the classical and new generalized fuzzy sets are exceptional classes of $ \left({q}_{1}^{}, {q}_{2}^{}\right) $-rung Diophantine fuzzy set ($ \left({q}_{1}^{}, {q}_{2}^{}\right) $-$ RDFS $) like intuitionistic fuzzy set ($ IFS $), Pythagorean fuzzy Sets ($ P\mathrm{y}FS $s) and $ \mathfrak{q} $-rung Orthopair fuzzy sets ($ \mathfrak{q} $-$ ROFS $s), linear Diophantine fuzzy sets ($ LDFS $), and so on. It is commonly seen in multi-criteria decision-making ($ MCDM $) scenarios that the presence of imprecise information and ambiguity in the decision maker's judgment affects the resolution technique. Fuzzy models that are now in use are unable to effectively manage these uncertainties to provide an appropriate balance during the decision-making process. Using control (reference) parameter mappings, $ \left({q}_{1}^{}, {q}_{2}^{}\right) $-$ RDFS $s are potent fuzzy model that can handle these challenging problems. Two more novel ideas are presented in this work: $ \left({q}_{1}^{}, {q}_{2}^{}\right) $-rung Diophantine fuzzy averaging and geometric aggregation operators with newly defined score and accuracy functions. An agricultural field robot $ MCDM $ framework was proposed, incorporating $ \left({q}_{1}^{}, {q}_{2}^{}\right) $-rung Diophantine fuzzy averaging and geometric aggregation operators. This strategy's efficacy and adaptability in addressing real-world issues were demonstrated by its application to get more benefits. This study has a lot of potential to handle difficult socioeconomic issues and offer vital information to academic, government, and analysts searching for fresh approaches in a variety of fields.