The componentwise decomposition theorem of lattice-valued Sugeno integral is extended. The concepts of interval fuzzy-valued, intuitionistic fuzzy-valued and interval intuitionistic fuzzy-valued Sugeno integrals are introduced. It is shown that the intuitionistic fuzzy-valued Sugeno integrals and the interval fuzzy-valued Sugeno integrals are mathematically equivalent. The interval intuitionistic fuzzy-valued Sugeno integral can be decomposed into the interval fuzzy-valued and intuitionistic fuzzy-valued Sugeno integrals, or the original Sugeno integrals.
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