A multi-criterion three-way decision-making method under linguistic interval-valued intuitionistic fuzzy environment

How to solve a multi-criterion decision-making (MCDM) problem with linguistic interval-valued intuitionistic fuzzy numbers (LIVIFNs) effectively is an important research topic. So far, a number of methods for solving this problem have been presented within the academia. Each of these methods can work well in specific situation. But they could produce undesirable decision-making results when the information for decision-making is insufficient or acquisition of the information needs a certain cost, since all of them are based on conventional two-way decision model. In this paper, three-way decision model is introduced into linguistic interval-valued intuitionistic fuzzy environment and a multi-criterion three-way decision-making method under this environment is presented. A specific relative loss function derived from an LIVIFN is established and corresponding three-way decision rules are developed. Based on the established function and developed rules, a three-way decision method for solving an MCDM problem with LIVIFNs is proposed. The application of the proposed method is illustrated via a practical example. The effectiveness and advantage of the method are demonstrated via an experimental comparison with some existing methods. The comparison results suggest that the proposed method is as effective as the existing methods and is more flexible than the existing methods in solving an MCDM problem with LIVIFNs.