Multi-attribute three-way decisions based on ideal solutions under interval-valued intuitionistic fuzzy environment

Multi-attribute three-way decision (MA3WD) has been a novel tool to solve multi-attribute decision-making (MADM) problems by considering the transforming relationship between loss functions and decision matrix. However many practical decision-making problems face the information with uncertainty and complexity, which makes it impossible to obtain relative loss functions in MA3WD. By introducing the thinking of ideal solutions (IS), this study extends MA3WD to interval-valued intuitionistic fuzzy environment, giving a more flexible and general model to handle with uncertain MADM problems. In this paper, we firstly propose an interval-valued intuitionistic fuzzy three-way decision (IVIF3WD) model by obtaining relative loss functions derived from evaluation values, and introduce ideal solutions to construct an ideal-solution based three-way decision model with single interval-valued intuitionistic fuzzy attribute. Then in consideration of all the attributes, two multi-attribute IVIF3WD models are proposed in the perspectives of individual ideal solutions and global ideal solutions respectively. Finally, two cases of investment with different fuzzy information are utilized to illustrate the application and superiority of proposed models. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study extends the MA3WD to interval-valued intuitionistic fuzzy environment, providing a more flexible and general model to handle uncertain MADM problems. The IVIF3WD model is proposed by introducing ideal solutions to construct an ideal-solution based three-way decision model, along with two multi-attribute IVIF3WD models.