A New Decision-Making Method Based on Interval-Valued Linguistic Intuitionistic Fuzzy Information

In real decision-making, because of the particularity of human cognition activity, it is difficult to depict the decision information by exact numbers, especially, for complex decision information, how to express and aggregate them is an important work for solving these decision-making problems. In order to express the complex fuzzy information accurately, we proposed the concept of interval-valued linguistic intuitionistic fuzzy numbers (IVLIFNs), where their membership function and non-membership function are represented by interval-valued linguistic terms, and then we developed the operational rules, score function, accuracy function, and comparison method of them. Considering that the Maclaurin symmetric mean (MSM) operator has a good characteristic in dealing with the interrelationships among multi-parameters, and it also is a generalization of arithmetic aggregation operator, Bonferroni mean (BM) operator, and geometric aggregation operator, we further proposed the interval-valued linguistic intuitionistic fuzzy MSM (IVLIFMSM) operator, the weighted interval-valued linguistic intuitionistic fuzzy MSM (WIVLIFMSM) operator, and proved some related properties of them. We gave an illustrative example to demonstrate the steps and the effectiveness of the proposed method by the comparison with existing methods. IVLIFNs can more conveniently express the complex fuzzy information in qualitative environment by considering the cognition of decision-makers, and the proposed method can consider the interrelationship among multiple input arguments, so it can make the decision-making results more reasonable. In a word, the proposed method is more scientific and flexible in solving multiple attribute decision-making (MADM) problems than some existing methods.