Schweizer-Sklar T-Norm Operators for Picture Fuzzy Hypersoft Sets: Advancing Suistainable Technology in Social Healthy Environments

Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life. However, decision-making in such contexts often involves handling vague, imprecise, and uncertain information. To address this challenge, this study presents a novel multi-criteria decision-making (MCDM) approach based on picture fuzzy hypersoft sets (PFHSS), integrating the flexibility of Schweizer-Sklar triangular norm-based aggregation operators. The proposed aggregation mechanisms—weighted average and weighted geometric operators—are formulated using newly defined operational laws under the PFHSS framework and are proven to satisfy essential mathematical properties, such as idempotency, monotonicity, and boundedness. The decision-making model systematically incorporates both benefit and cost-type criteria, enabling more nuanced evaluations in complex social or environmental decision problems. To enhance interpretability and practical relevance, the study conducts a sensitivity analysis on the Schweizer-Sklar parameter ( $\mathrm{\Delta }$). The results show that varying $\mathrm{\Delta }$ affects the strictness of aggregation, thereby influencing the ranking stability of alternatives. A comparative analysis with existing fuzzy and hypersoft-based MCDM methods confirms the robustness, expressiveness, and adaptability of the proposed approach. Notably, the use of picture fuzzy sets allows for the inclusion of positive, neutral, and negative memberships, offering a richer representation of expert opinions compared to traditional models. A case study focused on green technology adoption for environmental sustainability illustrates the real-world applicability of the proposed method. The analysis confirms that the approach yields consistent and interpretable results, even under varying degrees of decision uncertainty. Overall, this work contributes an efficient and flexible MCDM tool that can support decision-makers in formulating policies aligned with sustainable and socially responsible outcomes.