@article{Azam2025, 
author = {Akbar Azam and Faryad Ali and Sehar Afsheen and Mohammed Shehu Shagari},
title = {Fuzziness and randomness in fixed point theory: Measurable selections and applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {19335-19356},
keywords = {fixed point, coincidence point, random operators, contractive-type mapping, fuzzy mapping},
url = {https://www.sciopen.com/article/10.3934/math.2025864},
doi = {10.3934/math.2025864},
abstract = {This paper presents a novel fixed point theorem for measurable selections arising from pairs of fuzzy set-valued operators defined on Polish spaces. By establishing conditions under which such selections exist, we provided a rigorous framework for analyzing the solvability of random multivalued operator equations in fuzzy environments. Our approach seamlessly integrated fuzziness and randomness, extending classical fixed point theory into a more realistic setting where uncertainty is both probabilistic and vague. To demonstrate the utility and applicability of our results, we constructed well-structured and insightful examples rooted in engineering-inspired scenarios. These examples not only validate the theoretical framework but also highlight its effectiveness in modeling complex systems affected by dual sources of uncertainty.}
}