Construction and analysis of Aczel-Alsina t-norm based (p,q)-rung linear diophantine fuzzy aggregation operators with multi-criteria decision making

Aggregation operators ( $ \mathbb {AO} $ AOs) are employed in various fuzzy environments to accommodate uncertain information. Aczel-Alsina ( $ \mathcal {AA} $ AA) t-norm and t-conorm inherently flexible endows Aczel-Alsina $ \mathbb {AO} $ AOs with greater adaptability and robustness in the aggregation process than operators rooted in other t-norm and t-conorm families. Further, $ (\mathfrak {p, q}) $ (p,q)-rung linear Diophantine fuzzy set ( $ (\mathfrak {p, q}) $ (p,q)- $ \mathbb {RLDFS} $ RLDFS) is one of the advanced versions of the fuzzy set ( $ \mathbb {FS} $ FS), which has been revealed to be very successful at combating uncertain information and has grown in prominence in decision analysis. The article aims to establish $ \mathcal {AA} $ AA operations laws for $ (\mathfrak {p, q}) $ (p,q)- $ \mathbb {RLDFS} $ RLDFSs. Furthermore, we expose the $ (\mathfrak {p, q}) $ (p,q)-rung linear Diophantine fuzzy Aczel-Alsina weighted average ( $ (\mathfrak {p, q}) $ (p,q)-RLDFAAWA), $ (\mathfrak {p, q}) $ (p,q)-rung linear Diophantine fuzzy Aczel-Alsina weighted geometric ( $ (\mathfrak {p, q}) $ (p,q)-RLDFAAWG) operators and systematically analyze their unique features and results with concrete examples. Additionally, based on the devised $ \mathbb {AO} $ AOs, a multi-criteria decision making ( $ \mathbb {MCDM} $ MCDM) approach is designed to choose optimal agricultural technological systems under the $ (\mathfrak {p, q}) $ (p,q)- $ \mathbb {RLDFS} $ RLDFS framework. The proposed model is subjected to a comprehensive comparison against various existing studies to demonstrate its superiority in terms of reliability and accuracy. Moreover, the influence of key parameters, designated as Λ, $ \mathfrak {p} $ p, and $ \mathfrak {q} $ q, on the ranking outcomes is thoroughly examined to assess the applicability and robustness of the results derived from the developed method.