The conventional extension principle is established on the Euclidean space and defined
by considering the minimum or t-norm operator in which the fuzzy sets are usually
assumed to be normal. The previous work on generalized extension principle was also
based on the normal fuzzy sets. Since the non-normal fuzzy sets occur frequently in
practical applications, in this paper, the generalized extension principle based on
the non-normal fuzzy sets is established in which the general aggregation operator
and Hausforff space are taken into account.