The induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging operator and its application in decision making

The Shapley function is a very effective tool to measure the importance of elements, which can reflect the interactive characteristics among them. In this study we use the Shapley function to propose an induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging (IG-IVIFHSA) operator. This operator does not only globally consider the importance of elements and their ordered positions, but also overall reflect the interaction among them and among their ordered positions. It is worth pointing out that most of the existing hybrid aggregation operators are special cases of our operator. Meantime, some important cases are considered, and some desirable properties are studied. Furthermore, the models for the optimal fuzzy measures on attribute set and ordered set are established, respectively. Moreover, an approach to multi-attribute decision making under interval-valued intuitionistic fuzzy environment is developed. Finally, two numerical examples are given to verify the developed method and demonstrate its practicality and feasibility. (C) 2013 Elsevier B.V. All rights reserved.