As a combination of an interval-valued intuitionistic fuzzy soft set (IVIFSS) and interval-valued intuitionistic fuzzy set (IVIFS), the existing notion of the generalized interval-valued intuitionistic fuzzy soft set (GIVIFSS) is clarified and reformulated. We define two types of containment in GIVIFSS. With this new perspective, the g-union, g-intersection, g∗-union, g∗-intersection, OR, AND, g-necessity and g-possibility operations are defined for GIVIFSSs. The properties and relations between operations of GIVIFSSs are investigated. An algorithm is proposed for solving MADM problems using GIVIFSS. A descriptive example is presented to see the applicability of the proposed method. Results indicate that the proposed technique is more effective and generalize over the previous models of interval-valued fuzzy sets.
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