A New Approach to Solve Group Decision Making Problems with Attribute Values and Attribute Weights Represented by Interval-Valued Intuitionistic Fuzzy Numbers

The aim of this paper is to develop an approach for solving multiple attribute group decision making (MAGDM) problems under interval-valued intuitionistic fuzzy framework. In the present work, attribute values are characterized by interval-valued intuitionistic fuzzy numbers (IVIFNs). Due to complexity, uncertainty and the lack of information, the attribute weights given by each decision maker are also represented by IVIFNs. In order to develop this approach, firstly, a new order function is proposed for comparing two or more IVIFNs. Then, the optimal attribute weights for a group of decision makers are determined on the basis of the proposed order function and the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator. Using the calculated optimal weights and the IIFHG operator, a single collective weighted decision matrix is obtained. After that, this matrix is transformed into a crisp decision matrix by using the proposed order function. Finally, overall attribute value for each alternative is calculated by utilizing the ordered weighted averaging (OWA) operator to rank alternatives. The developed approach is shown through a numerical example.