Comparing rankings from using TODIM and a fuzzy expert system

TODIM is, in its original formulation, an MCDA method developed to solve ranking problems. As an MCDA method TODIM combines the use of a multi-attribute value function as well as elements of the Outranking Approach, being founded on Prospect Theory. Recent advances in TODIM incorporate concepts from Fuzzy Sets. Although modelling multicriteria decision problems with Fuzzy Sets has been utilized when the available data are imprecise, their use in MCDA is slightly controversial, because the data fuzzification can invalidate the outcome. Following a mixed qualitative-quantitative research strategy, our aim is to prove that for the ranking problems, TODIM can provide better solutions than Fuzzy Sets. Ranks from TODIM are linear, or strong, in a sense that it has no ties between the alternative solutions. The rank obtained with a Fuzzy Expert System can be weaker, that is, it may be a number of ties. The research strategy extends this result to ranking problems with the occurrence of crisp criteria.