@article{Rashid2025, 
author = {Maliha Rashid and Akbar Azam and Maria Moqaddas and Naeem Saleem and Maggie Aphane},
title = {Ciric fixed point theorems of              £      -fuzzy soft set-valued maps with applications in fractional integral inclusions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {4641-4661},
keywords = {£-fuzzy soft set, b-metric space, fixed point, fractional inclusion},
url = {https://www.sciopen.com/article/10.3934/math.2025215},
doi = {10.3934/math.2025215},
abstract = {This manuscript established the concept of    b-Ciric              £      -fuzzy soft contractions (BCLFSC) within    b-metric spaces, presenting a framework to analyze fixed points of              £      -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              £      -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.}
}