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Top1. Introduction
Our understanding of most physical processes is based largely on vague concepts and imprecise human reasoning. This imprecision is nonetheless a form of information that can be quite useful to humans in decision making, control processes, prediction, etc. Imprecision can be used to describe certain kinds of uncertainty associated with linguistic information or intuitive information. Examples of imprecise information are that the product quality is ‘‘good’’, or that the lifetime of a lamp is ‘‘approximately 
’’, or that the necessary dose of a certain chemical material in a drug must be ‘‘about
’’.
The occurrence of fuzzy random variable makes the combination of randomness and fuzziness more persuasive, since the probability theory can be used to model uncertainty and the fuzzy sets theory can be used to model imprecision. In a complex system, the number of failures and failure times may be recorded imprecisely due to equipment and human errors. For such cases this imprecision also should be quantified in the calculation. Here fuzzy set theory is used to quantify the uncertainty of imprecision. Researchers have stated that probability theory can be used in concert with fuzzy set theory for the modelling of complex systems Zadeh (1995), Barrett and Woodall (1997), Ross, Booker, and Parkinson (2003), and Singpurwalla and Booker (2004).
Several researchers then pay attention to applying the fuzzy set theory to the Bayes approach in lifetime data (Wu 2004; Taheri 2011Viertl and Gurker 1995; Huang et al. 2006; Viertl 2009; for Bayes approaches in fuzzy environments see, for example, Taheri 2003; Taheri and Behboodian 2001; Viertl and Hule 1991).
The main goal of the Bayesian approach, Obtain lifetime estimates under a squared error loss function in fuzzy environment. Fuzzy Bayesian reliability method developed by Wu (2004). We develop models E-Bayesian and Hierarchical Bayesian estimations under censoring data in fuzzy environment. Han Ming gives the definition of E-Bayesian estimation of estate probability and the formulas of E-Bayesian estimation, engineering forecast model and its applications in security investment at (2005) and also Lindley and Smith (1972) first introduced the idea of hierarchical prior distribution. Han (1997) developed methods to construct hierarchical prior distribution and also he (2009) discussed about E-Bayesian estimation and hierarchical Bayesian estimation of failure rate. Zeinhum F. Jaheen, Hassan M. Okasha (2011) obtained E-Bayesian estimation for the Burr type XII model based on type-2 censoring.
The purpose of this study is to obtain estimates fuzzy E-Bayesian and Hierarchical Bayesian under censoring data, when we have observed 
censors from the two parameter Kumaraswamy’s distribution. Kumaraswamy distribution has many of the same properties as the beta distribution but has some advantages in terms of tractability, its density is
(1.1) Where
and
are shape parameters, respectively. Here we assume that
parameter is known. The distribution function
is;