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Interval cut-set of interval-valued intuitionistic fuzzy sets

In this paper, different types of interval cut-set of interval-valued intuitionistic fuzzy sets (IVIFSs), complement of these cut-sets are defined. Some properties of those cut-set of IVIFSs are investigated. Also three decomposition theorems of IVIFSs are defined. These works can also be used in setting up the basic theory of IVIFSs.