Extended TODIM method for hybrid multiple attribute decision making problems

TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) is a method for solving the multiple attribute decision making (MADM) problem considering decision maker’s (DM’s) behavior, in which the attribute values are in the format of crisp numbers. It cannot be used to handle hybrid MADM problems with various formats of attribute values. In this paper, an extended TODIM method is proposed to solve the hybrid MADM problem. First, three formats of attribute values (crisp numbers, interval numbers and fuzzy numbers) are expressed in the format of random variables with cumulative distribution functions. Then, according to the concept of the classical TODIM method, the gain and loss matrices concerning each attribute are constructed by calculating the gain and loss of each alternative relative to the others. Further, by calculating the dominance degree of each alternative over the others, the overall value of each alternative can be obtained to rank the alternatives. Finally, two numerical examples are used to illustrate the use of the proposed method.