The concept “interval-valued intuitionistic fuzzy sets (IVIFS)” was delivered through Atanassov’s and Gargov [21] in 1989 as a simplification of each IVFS and IFS. Satyanarayana et al. [3, 4] implemented the concept of IVIFSs to BF-sub-algebras and fuzzy ideals of BF-algebras. Further, the notion of an IVIFTS of BF-algebras are also discussed in this work.

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