Abstract
In this paper, the interval-valued double t-norm \(\widetilde{T}\) induced by an interval t-norm \(\overline{T}\) and an interval t-conorm \(\overline{S}\) is defined. The interval-valued intuitionistic fuzzy subgroup and the interval-valued intuitionistic fuzzy normal subgroup based on the interval-valued double t-norm \(\widetilde{T}\) are introduced. In the meantime, some of its basic properties and structural characteristics are studied. Furthermore, the theorems of the homomorphic image and the inverse image are given.
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