Behavioral multi-criteria decision making with multi-granularity 2-dimension fuzzy linguistic variables

Nowadays TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method has been widely used to solve multi-criteria decision making (MCDM) problems for its validity in consideration of psychological behavior of the decision maker (DM). However, the classical TODIM method can only deal with crisp numbers, which fails to respond to the vagueness of the information and hesitancy of the DM in the real life. Thus, in this paper, we propose a concept of multi-granularity2-dimension fuzzy linguistic variable, which can describe the evaluation values provided by DM to the given alternatives and the subjective assessment about the dependability of the provided results simultaneously with fuzzy linguistic variables. Firstly, the background of fuzzy linguistic variable, 2-dimension linguistic variable and the classical TODIM method are introduced. Secondary, we give the definition to multi-granularity 2-dimension fuzzy linguistic variable, and so with some operational laws, the expectation and the distance of multi-granularity 2-dimension fuzzy linguistic variables. Furthermore, we extend the TODIM method to tackle the criterion values with 2-dimension fuzzy linguistic information, and the procedure is provided. Finally, a numerical example is used to illustrate the practicality and the effectiveness of the proposed method.