Fuzzy fixed point results for $\alpha$-admissible $\varphi$- $\psi$-set-valued fuzzy contractions

Fixed point theory and fuzzy mathematics offer powerful tools for addressing real-world problems involving uncertainty and imprecision. In this paper, we introduced a generalized framework for $\alpha -$admissible fuzzy set-valued contractive mappings by extending the existing concepts of $\varphi$-set-valued and $\varphi$- $\psi$-set-valued contractions in the setting of $b$-metric spaces. We established several fixed point theorems under these generalized contractive conditions, thereby extending and enriching the existing theory. As an additional contribution, we also explored fixed point results under Kannan-type and Reich-type conditions within the same framework. Notably, several classical fixed point results were recovered as special cases of our findings, demonstrating the unifying nature of our approach. To illustrate the applicability and non-triviality of the results, a concrete example was provided.