Abstract
Interval type-2 fuzzy sets (IT2FSs) can provide more flexibility than type-1 fuzzy sets (T1FSs) for depicting uncertain information, and multi-attribute decision making (MADM) problems with interval type-2 fuzzy information have received increasing attention. A new projection-based regret theory method is proposed to solve MADM problems under IT2FSs environments. First, a projection model of IT2FSs is defined that takes both the distance and angle information into consideration. Second, integrating the proposed projection model with regret theory, new utility and regret-rejoice functions are developed, respectively. Finally, a case study is provided to demonstrate the effectiveness of the proposed method. Sensitivity analysis shows the stability of the proposed method, and the ranking order does not change with different parameters. Comparisons are made with existing approaches to illustrate the advantage of the proposed method in reflecting decision makers’ psychological factors.
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