Statistics is the science of learning from data. Data are frequently presented in the form of numbers, vectors, or functions, generally containing measurements of some phenomena. During this process of data collection measurements are recorded as precise numbers, and countless techniques are available to model or to draw inference from these measurements. But in practical situations especially dealing with continuous variables there are two types of uncertainty in daily life data, one is variation among the observations and another is imprecision of single observations. Keep in mind that variation among observations is different from imprecision, which is also called fuzziness. Classical statistical tools are based on precise observations and do nothing with fuzziness. By ignoring fuzziness of the observations we may lose information and get misleading results. Therefore, fuzziness of the single observations should be considered and modeled by fuzzy numbers. To consider fuzziness of the single observations in drawing inference the idea of fuzzy sets was first introduced by Zadeh in 1965. According to him in the physical world many quantities do not have precise values but are more or less fuzzy. Also if we consider some examples in linguistic description like, a class of good or bad teachers, class of goodlooking women, high or low temperature, in all these situations one cannot characterize it in classical mathematical set notation. In the same way there are a lot of situations for which we cannot define precise criteria for the membership to a set. The analysis techniques of life time data can be traced back centuries but the prompt development started about few decades ago, and since then a significant number of books and research papers has been published. Most of these publications are based on precise life time observations. It has already been shown that life time observations are not precise numbers but more or less fuzzy. Therefore, the analysis techniques need to be generalized in such a way that in addition to the stochastic variation, fuzziness of the observations are also integrated. Some work has been done dealing with fuzzy life time data, but still in most of the situations it is ignored. In this study some popular approaches of survival analysis are generalized in such a way that fuzziness of the observations is also considered for the analysis to obtain appropriate results. The proposed estimators are based on fuzzy life time data. In addition to these techniques some parametric and nonparametric techniques from Accelerated Life Testing are also generalized for fuzzy life time data.
