A study of TODIM in a intuitionistic fuzzy and random environment

• A generalization of TODIM method, named IF-RTODIM, to consider dynamic underlying conditions was proposed.
• A simplification of the method considering underlying states is presented in three versions.
• Each one using different ways of aggregating.
• We apply the three versions of IF-RTODIM for two different types of information.
• The results are consistent.

Nowadays the process of decision making may be very complex. Many methods to support Multi-Criteria Decision Making (MCDM) have been proposed. Recently, the TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) method, which is based on the prospect theory, has received more attention. In this paper we generalize the Fuzzy-TODIM method to deal with intuitionistic fuzzy information and to be capable to consider underlying random vectors that affects the performance of the alternatives. The method makes use of some Bayesian ideas to provide an overall ranking of the alternatives. This work considers information represented by intuitionistic fuzzy number and intuitionistic fuzzy sets (IFS). Also, a new formula of distance between IFS and a new score function to compare IFS are introduced. Examples are discussed and compared with other works, showing the feasibility of the proposed method.