A new FlowSort-based method to deal with information imperfections in sorting decision-making problems

Most real-life decision-making problems can be modeled as sorting problems. As a result, a number of multi-criteria methods have been developed to deal with these types of problems. One of these methods is the FlowSort, which is a multi-criteria sorting method based on the PROMETHEE methodology whose parameters and required input data should be defined precisely, by quantitative and crisp values. This requirement is often difficult to meet, since imperfect data such as interval data, linguistic variables, stochastic and incomplete data are more natural to use in real-life problems. FlowSort-based methods, such as the Fuzzy-Flowsort method, were designed to deal with some, but not all, imperfect data types. In addition, none of the FlowSort-based methods is able to deal with criteria weights elicitation, even though this has been one of the main issues and difficulties in the multi-criteria decision-making field. In this context, our aim is to propose a new method for sorting decision-making problems capable of dealing with multiple imperfect data (interval, stochastic data and linguistic variables) and with criteria weight elicitation. We apply the SMAA method (Stochastic Multicriteria Acceptability Analysis) to the Fuzzy-FlowSort method. A numerical application is presented to illustrate the applicability of the proposed method. Then, two SMAA-FFS comparisons with existing FlowSort-based methods to deal with imperfect data are performed. For each of them, the results and some discussions are presented, and the conclusions point to a consistent model, independent of the imperfect data types used.