Narrow Results

In multi-criteria decision-making, the Choquet integral can handle the interaction between criteria; however, the interaction between criteria is not only related to the criteria themselves but may also depend on the performance values of criteria. We present a further extension of the Choquet integral considering this fact. A classic example is used to illustrate the limitations of the Choquet integral, and a performance-dependent assumption is proposed that describes the interactions influenced by the performance of alternatives on criteria. Based on this assumption, we propose an alternative capacity and construct an improved Choquet integral to obtain alternative’s global utility. A preference model based on the improved Choquet integral with a wider range of applicability and more realistic decision results is proposed. Finally, a numerical example is provided to illustrate the feasibility and validity of our reference model.

Decision-making problems often require characterization of alternatives through multiple criteria. In contexts where some of these criteria interact, the decision maker (DM) must consider the interaction effects during the aggregation of criteria scores. The well-known ELECTRE (ELimination Et Choix Traduisant la REalité) methods were recently improved to deal with interacting criteria fulfilling several relevant properties, addressing the main types of interaction, and retaining most of the fundamental characteristics of the classical methods. An important criticism to such a family of methods is that defining its parameter values is often difficult and can involve significant challenges and high cognitive effort for the DM; this is exacerbated in the improved version whose parameters are even less intuitive. Here, we describe an evolutionary-based method in which parameter values are inferred by exploiting easy-to-make decisions made or accepted by the DM, thereby reducing his/her cognitive effort. A genetic algorithm is proposed to solve a regression-inspired nonlinear optimization problem. To the best of our knowledge, this is the first paper addressing the indirect elicitation of the ELECTRE model’s parameters with interacting criteria. The proposal is assessed through both in-sample and out-of-sample experiments. Statistical tests indicate robustness of the proposal in terms of the number of criteria and their possible interactions. Results show almost perfect effectiveness to reproduce the DM’s preferences in all situations.

Decision-making is one of the significant and inevitable issues in the most real-world problems. Decision criteria interact in many of these problems, and traditional aggregation techniques, which are usually linear methods, cannot be exploited to consider these interactions and exert correlations between criteria. In such cases, nonadditive aggregation methods have attracted the attention of many researchers. This study presents a novel model based on the best-worst method (BWM) and the multi-criteria fuzzy Choquet integral technique to apply the interaction between the criteria. In the proposed model, we have reduced the effect of the inconsistency rate detected on the fuzzy measure (or Choquet capacity) by taking into account the positive or negative interaction between the criteria.