All researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$ Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ Z l , Z u ] . The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.

The current work is one step in filling a large void in the research left by the advent of neutrosophic Statistics (NS), a philosophized variant of classical statistics (CS). The philosophy of NS deals with techniques for investigating data that is ambiguous, hazy, or uncertain. The traditional techniques of estimation utilizing auxiliary information work under specific determinate data, which in the case of neutrosophic data may lead to mistakes (over/ under-estimation). This study presents a generalized neutrosophic ratio-type exponential estimator (NRTEE) for estimating location parameters and achieving the lowest mean square error (MSE) possible for interval neutrosophic data (IND). The offered NRTEE helps to deal with the uncertainty and ambiguity of data. Unlike typical estimators, its findings are not single-valued but rather in interval form, which reduces the possibility of over-or under-estimation caused by single crisp outcomes and also increases the likelihood of the parameter dwelling in the interval. It improves the efficiency of the estimator since we have an estimated interval that contains the unknown value of the population mean with a minimal MSE. The suggested NRTEE’s efficiency is further addressed by utilizing real-life IND of temperature and simulations. A comparison is also performed to establish the superiority of the proposed estimator over the traditional estimators. The limits are calculated and discussed in cases when our suggested estimator is always efficient. The suggested estimator is the most efficient of all estimators and outperformed all others on both IND and classical data.