Abstract
In this paper an extensive generalization for Sugeno's fuzzy integral is given by defining two families of fuzzy integrals, a normed family and a conormed one. Sugeno's fuzzy integral is a particular case belonging to both families. The purpose of this paper is to study the properties for the mentioned integrals and the relationships existing between those families. The extension of this families to a fuzzy domain is also accomplished. Finally, some possible ways to use the obtained results are suggested in the paper.
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