Abstract
The main motivation of this paper to generalize the old concept. In this paper, the concept of the cubic interval-valued intuitionistic fuzzy set which is the extension of the cubic set is applied to semigroup and their related properties such as union, intersection, product, whole function and characteristic function of cubic interval-valued intuitionistic fuzzy sets are investigated. Moreover, the concept of cubic interval-valued intuitionistic fuzzy subsemigroup and cubic interval-valued intuitionistic fuzzy ideas are proposed. Characterizations of cubic interval-valued intuitionistic fuzzy ideas are considered, and how the image or inverse image of cubic interval-valued intuitionistic fuzzy subsemigroups and cubic interval-valued intuitionistic fuzzy ideals become cubic interval-valued intuitionistic fuzzy subsemigroups and cubic interval-valued intuitionistic fuzzy ideals, respectively, is studied.
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