Entropy is a standard measure used to determine the uncertainty, randomness, or chaos of experimental outcomes and is quite popular in statistical distribution theory. Entropy methods available in the literature quantify the information of a random variable with exact numbers and lacks in dealing with the interval value data. An indeterminate state of an experiment generally generates the data in interval form. The indeterminacy property of interval-valued data makes it a neutrosophic form data. This research proposed some modified forms of entropy measures for an important lifetime distribution called Weibull distribution by considering the neutrosophic form of the data. The performance of the proposed methods is assessed via a simulation study and three real-life data applications. The simulation and real-life data examples suggested that the proposed methodologies of entropies for the Weibull distribution are more suitable when the random variable of the distribution is in an interval form and has indeterminacy or vagueness in it.

熵是用于确定实验结果的不确定性、随机性或混沌性的标准度量，在统计分布理论中非常流行。文献中可用的熵方法用精确数字量化随机变量的信息，缺乏对区间值数据的处理。实验的不确定状态通常以区间形式生成数据。区间值数据的不确定性使其成为中智形式数据。该研究通过考虑数据的中智形式，为称为威布尔分布的重要寿命分布提出了一些改进形式的熵测度。通过模拟研究和三个现实生活数据应用程序评估所提出方法的性能。