Fuzzy set theory can be used to handle the difficulty of estimating the parameters of a nonlinear regression model when the underlying data is ambiguous, imprecise, or only partially known. This paper discussed and compared five estimations for fuzzy nonlinear regression: the One-Step Overall Existence Ranking Index, the Two-Step OERI, the fuzzy least-squares based on shape-preserving operations, the fuzzy least absolute value deviations regression, and a proposed ridge fuzzy nonlinear regression that combines a K-fold optimized cross-validation adaptive ridge-regularization scheme within a unified L-R fuzzy number framework. The study aims to provide researchers with fuzzy nonlinear regression estimates by multiple indexes with a comprehensive methodological reference. The fuzzy power regression model was used in the simulation study. In all twelve tests (n, σ²), the proposed PR-FNR method achieved the lowest root mean squared error, followed by the FLSR-SPO method, while the FLAVDR method produced the highest and least stable errors.