Ciric fixed point theorems of $\mathtt{\pounds }$-fuzzy soft set-valued maps with applications in fractional integral inclusions

This manuscript established the concept of $b$-Ciric $\mathtt{\pounds }$-fuzzy soft contractions (BCLFSC) within $b$-metric spaces, presenting a framework to analyze fixed points of $\mathtt{\pounds }$-fuzzy soft set-valued mappings under these conditions. Leveraging lattice-valued memberships, our framework enables more sophisticated decision-making processes, providing flexibility to structure criteria and relationships hierarchically. An illustrative example was provided to support the theoretical foundations, demonstrating the use of $\mathtt{\pounds }$-fuzzy soft sets in decision-making contexts where nuanced, multi-attribute evaluations are essential. Additionally, our approach was applied to fractional integral equations, showcasing how these results unify and expand current methodologies in both conventional and non-classical fixed point theory. This study built on the foundational work in $b$-metric spaces by incorporating recent advances in fuzzy and soft set theory, particularly within complex decision-making and fractional essential inclusion applications. While our model accommodates intricate, ambiguous datasets, which is advantageous in multi-criteria assessments, we acknowledge computational demands as a limitation. This paper concludes with a discussion of implications for future research, underscoring the potential for further development in lattice-valued decision frameworks and applications to new domains.