It is known that processing of data under general type-1 fuzzy uncertainty can be reduced to the simplest case -- of interval uncertainty: namely, Zadeh's extension principle is equivalent to level-by-level interval computations applied to alpha-cuts of the corresponding fuzzy numbers.
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Technical Report: UTEP-CS-11-10
Published in Proceedings of the IEEE Symposium on Advances in Type-2 Fuzzy Logic Systems T2FUZZ'2011, part of the IEEE Symposium Series on Computational Intelligence, Paris, France, April 11-15, 2011, pp. ix-xii.