Over the years, numerous fuzzy time-series forecasting (FTSF) models have been developed to handle the uncertainty and non-determinism in the time-series (TS) data. To handle the non-determinism and indeterminacy, researchers have considered either intuitionistic fuzzy set or hesitant fuzzy set theory. However, in both the fuzzy set theories (FST), the degree of indeterminacy is a dependent value and always lies in the range [0, 1]. Hence, these two fuzzy set theories fail to model the indeterminacy value when the degree of non-membership fluctuates due to hesitancy. Motivated from this, we have considered neutrosophic entropy-based fuzzy time-series forecasting (NEBFTSF) model where the neutrosophic entropy of each observation in the TS is used to capture the indeterminacy. Apart from this, the triangular membership value for each observation is used to illustrate the non-probabilistic uncertainty in the TS. The present research mainly focuses on three concepts such as 1) an adaptive method is used to partition the universe of discourse (UOD) into unequal length of intervals (LOIs), 2) for the first time the fuzzy logical relationships (FLRs) are established by considering the ratio trend variation (RTV) data with mean of aggregated entropy value of each crisp observation, and 3) to obtain the forecasted values both de-trending and de-normalization are employed. To assess the forecasting performance of the proposed model, 11 TS datasets with ten distinct profound forecasting models are considered. The Friedman and Nemenyi hypothesis test and Wilcoxon signed rank test conform the forecasting efficiency and reliability of the NEBFTSF model.

多年来，已经开发了许多模糊时间序列预测 (FTSF) 模型来处理时间序列 (TS) 数据中的不确定性和非确定性。为了处理非确定性和不确定性，研究人员考虑了直觉模糊集或犹豫模糊集理论。然而，在两种模糊集理论 (FST) 中，不确定度都是一个依赖值，并且始终位于 [0, 1] 范围内。因此，当非隶属度由于犹豫而波动时，这两种模糊集理论无法对不确定性值进行建模。受此启发，我们考虑了基于中智熵的模糊时间序列预测 (NEBFTSF) 模型，其中使用 TS 中每个观察的中智熵来捕获不确定性。除此之外，每个观测值的三角隶属度值用于说明 TS 中的非概率不确定性。目前的研究主要集中在三个概念上，例如1）使用自适应方法将话语领域（UOD）划分为不等长的区间（LOI），2）首次建立模糊逻辑关系（FLR）通过考虑具有每个清晰观察的聚合熵值平均值的比率趋势变化 (RTV) 数据，以及 3) 使用去趋势和去规范化来获得预测值。为了评估所提出模型的预测性能，考虑了具有 10 个不同深度预测模型的 11 个 TS 数据集。