Fuzzy Bayesian estimation on lifetime data

Summary  The Bayesian estimation on lifetime data under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator by invoking the well-known theorem called “Resolution Identity” in fuzzy set theory. On the other hand, we also provide computational procedures to evaluate the membership degree of any given Bayes point estimate. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINDO.