Sustainable practices to reduce environmental impact of industry using interaction aggregation operators under interval-valued Pythagorean fuzzy hypersoft set

Optimization techniques can be used to find the optimal combination of inputs and parameters and help identify the most efficient solution. Aggregation operators (AOs) play a prominent role in discernment between two circulations of prospect and pull out anxieties from that insight. The most fundamental objective of this research is to extend the interaction AOs to the interval-valued Pythagorean fuzzy hypersoft set (IVPFHSS), the comprehensive system of the interval-valued Pythagorean fuzzy soft set (IVPFSS). The IVPFHSS adroitly contracts with defective and ambagious facts compared to the prevalent Pythagorean fuzzy soft set and interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS). It is the dominant technique for enlarging imprecise information in decision-making (DM). The most important intention of this exploration is to intend interactional operational laws for IVPFHSNs. We extend the AOs to interaction AOs under IVPFHSS setting such as interval-valued Pythagorean fuzzy hypersoft interactive weighted average (IVPFHSIWA) and interval-valued Pythagorean fuzzy hypersoft interactive weighted geometric (IVPFHSIWG) operators. Also, we study the significant properties of the proposed operators, such as Idempotency, Boundedness, and Homogeneity. Still, the prevalent multi-criteria group decision-making (MCGDM) approaches consistently carry irreconcilable consequences. Meanwhile, our proposed MCGDM model is deliberate to accommodate these shortcomings. By utilizing a developed mathematical model and optimization technique, Industry 5.0 can achieve digital green innovation, enabling the development of sustainable processes that significantly decrease environmental impact. The impacts show that the intentional model is more operative and consistent in conducting inaccurate data based on IVPFHSS.