Lattice-Based Decision Models for Green Urban Development: Insights from $$L_{q}*$$ q-Rung Orthopair Multi-fuzzy Soft Set

Location selection is a critical process in decision-making for projects that involve multiple criteria, such as urban planning, industrial site development, or green building projects. Multiple criteria decision making (MCDM) is a systematic approach that evaluates and ranks potential alternatives based on a set of often conflicting criteria. This study focuses on selecting the optimal urban location for a green building project by employing the $$L_{q}*$$ q-rung orthopair multi-fuzzy soft-MCDM( $$L_{q}*$$ q-ROMFS) techniques. The $$L_{q}*$$ q-ROMFS set combines elements from two distinct theories with lattice ordering parameters: q-rung orthopair fuzzy set and multi-fuzzy soft set. It provides a mathematical framework with multiple parameters that effectively represents problems involving multi-dimensional data within a dataset. We expand this concept by establishing the algebraic structures of $$L_{q}*$$ q-ROMFS sets, including properties like modularity and distributivity, while also analyzing their homomorphism under lattice mappings. Finally, leveraging the $$L_{q}*$$ q-ROMFS matrix, we propose both a choice matrix and a weighted choice matrix to effectively address the selection of the optimal urban location for a green building project.