Fuzziness and randomness in fixed point theory: Measurable selections and applications

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.