In this paper we define a special interval uncertainty by extending the well known concept of fuzzy intervals (or, fuzzy numbers), defining a new concept of extended fuzzy interval and its subspace: extended linear fuzzy interval. We present some examples and derive basic properties. Then we demonstrate an application of the new concept by formulating the well known Optimal Allocation Problem (OAP) and its solution under uncertainty. We formulate the corresponding optimization problem with the extended fuzzy interval coefficients and also extended fuzzy interval variables and derive its optimal solution in the form of extended fuzzy intervals. Two numerical examples are presented in order to illustrate particular problems and solution concepts.