Fermatean fuzziness on decision analysis incorporating weights detection for sustainable forest management strategy assessment

Forest management plays a crucial role in promoting sustainable and environmentally friendly development by delivering both environmental and economic benefits. However, forest managers face the challenge of balancing competing priorities while ensuring long-term ecological resilience. This study introduces five innovative Forest Management Models (FMMs) designed to maximize timber production, water regulation, and carbon sequestration, while considering key factors such as final volume and replantation costs. To evaluate these models under uncertainty, two novel multi-criteria decision analysis (MCDA) approaches — Fermatean fuzzy Simultaneous Evaluation of Criteria and Alternatives (FF-SECA) and Fermatean fuzzy Technique for Order Preference by Similarity to Ideal Solution (FF-TOPSIS) — are developed. These approaches generate preference rankings of forest-related factors and provide strong decision support for selecting the most sustainable FMMs. The results highlight that prioritizing water production under a carbon sequestration constraint is the most effective strategy, whereas maximizing carbon sequestration alone is less efficient. Comparative and sensitivity analyses further confirm the adaptability and reliability of the proposed methodologies. The findings provide actionable insights for policymakers and forest managers, promoting eco-innovation, harnessing green energy potential, and fostering sustainable forest resource governance.