Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems

Intuitionistic trapezoidal fuzzy multi-numbers (ITFM-numbers) are a special intuitionistic fuzzy multiset on a real number set, which are very useful for decision makers to depict their intuitionistic fuzzy multi-preference information. In the ITFM-numbers, the occurrences are more than one with the possibility of the same or the different membership and non-membership functions. In this paper, we define ITFM-numbers based on multiple criteria decision-making problems in which the ratings of alternatives are expressed with ITFM-numbers. Firstly, some operational laws using t-norm and t-conorm are proposed. Then, some aggregation operators on ITFM-numbers are developed. Also, the ranking order of alternative is given according to the similarity of the alternative with respect to the positive ideal solution. Finally, a numerical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.