Applying a Genetic Algorithm to Implement the Fuzzy-MACBETH Method in Decision-Making Processes

Abstract

This paper describes the development of an evolutionary algorithm for building cardinal scales based on the Fuzzy-MACBETH method. This method uses a triangular fuzzy numbers scale in the MACBETH method to incorporate the subjectivity of a semantic scale into mathematical modeling, which enables circumventing the cardinal inconsistency problem of the classical method, facilitating its application in complex contexts. A genetic algorithm is used in the fuzzy system developed here to build the basic fuzzy scale in a cardinally inconsistent decision matrix. The proposed technique is inspired by crossover and mutation genetic operations to explore potential solutions and obtain a cardinal scale aligned with the decision maker’s preferences. Finally, an illustrative example of the application of the proposed decision support system is presented. The results confirm that the FGA-MACBETH method aligns with the classical method. This study’s primary contribution is that circumventing the problem of cardinal inconsistency in a semantically consistent decision matrix enabled obtaining a cardinal scale without requiring the decision maker to redo his/her initial assessments.