The multi-attribute decision making method based on interval-valued intuitionistic fuzzy Einstein hybrid weighted geometric operator

This article proposes an approach to multi-attribute decision making (MADM) where individual assessments are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). Firstly, some Einstein geometric operators on interval-valued intuitionistic fuzzy sets, such as Einstein product, Einstein exponentiation etc., and their characteristics are introduced. Secondly, some Einstein geometric operators, such as the interval-valued intuitionistic fuzzy Einstein weighted geometric operator, interval-valued intuitionistic fuzzy Einstein ordered weighted geometric operator and interval-valued intuitionistic fuzzy Einstein hybrid weighted geometric (IVIFHWG(epsilon)) operator, are developed for aggregating the IVIFNs. Moreover, various properties of these operators are established. Finally, an IVIFHWG(epsilon) operator based approach to MADM under interval-valued intuitionistic fuzzy environments is proposed. An illustrative propulsion/manoeuvring system selection problem is employed to demonstrate how to apply the proposed procedure and verify the feasibility and effectiveness of the developed method. (C) 2013 Elsevier Ltd. All rights reserved.