Highlights • The paper focuses on define newly modal operators over GIVIFSs. • Various properties of these operators have also been investigated in details. • Some applications of operators are one motivation for study. • The validity of the operators is tested based on proofs and numerical examples. Article Info Abstract Interval valued intuitionistic fuzzy set (IVFS) as an extension of intuitionistic fuzzy sets is described by two parameters, namely membership degree and non-membership degree

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... which are expressed in terms of intervals rather than crisp numbers. IVFS can be used to handle uncertainty and vagueness in real world decision making problems and operators of IVFSs have a key role in this filed. Thus, in this work we define newly defined modal operators over generalized interval valued intuitionistic fuzzy sets by modifying the existing operators. The new proposed operators are the integrity and comprehensive. Then, we describe the desirable properties of the proposed operators and discuss the special cases of them in details. Furthermore, the relationship between operators is examined. Finally, an illustrative example is provided for comparison.