There topics of statistical inference are investigated in fuzzy environment: I) Testing statistical hypotheses with fuzzy information, II) Possibilistic Bayesian inference, and III) Density estimation for fuzzy data. For the first topic, we introduce two approaches to testing fuzzy hypotheses: a fuzzy test statistic based approach and a fuzzy confidence interval based approach. For the second topic, we investigate a possibilistic analogue to Bayes inference. In this regard, we introduce the possibilistic Bayes estimation for crisp and fuzzy data, when the underlying model is probabilistic or possibilistic. Finally, the problem of density estimation for fuzzy data is studied, by the histogram, the empirical c.d.f., and the kernel methods.
