A new class of neutrosophic multivariate exponential-type estimators for climate data in simple random sampling

Classical finite-population mean estimation is typically formulated for point-valued, fully reliable observations. In long-span environmental records, rounding, sensor changes, missingness, and post-processing may motivate interval-valued neutrosophic measurements with an explicit indeterminacy component. We propose a family of neutrosophic multivariate exponential-type estimators that incorporates two auxiliary binary attributes through exponential calibration. Under simple random sampling without replacement, we derive first-order approximations leading to endpoint-wise neutrosophic mean squared error bounds, obtain a closed-form optimal convex weight for each representative member, and define a single class-specific benchmark estimator y¯∗ CSN as the optimal-weight member attaining the smallest first-order minimum MSE within the proposed family. Relative performance is reported through ordered endpoint-wise mean squared error bounds and corresponding PRE bounds relative to y¯∗CSN . Empirically, we study Turkey’s monthly temperatures by treating 1970–2022 as a pseudo-finite population and 2010–2022 as the available sample, implementing all comparisons month-by-month to respect strong seasonality. We also report repeated-sampling Monte Carlo evidence under empirical and calibrated synthetic finite-population scenarios using fixed measurement half-widths. In summary, within the considered finite-population settings with measurement ambiguity, the endpoint-wise benchmark provides a transparent reference for assessing how closely restricted two-attribute exponential specifications approximate the class-specific optimum.