Affiliations: [a] Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Thailand
| [b] Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), Thailand
| [c] Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
| [d]
Shandong University of Finance and Economics, Jinan, China
| [e] Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani, Thailand
Abstract: 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.