Abstract
In this paper, we define a new concept of integrals on fuzzy measure, that we call the extended fuzzy integrals. The extended fuzzy integrals can be represented in various ways, and then is shown to be a natural extension of Lebesgue integral and furthermore to include Sugeno's fuzzy integral as a special case. It is necessary to obtain its explicit representation, so we show two new representations of the extended fuzzy integrals.
