PyMissingAHP: An Evolutionary Algorithm for Filling Missing Values in Incomplete Pairwise Comparisons Matrices with Real or Fuzzy Numbers via Mono and Multiobjective Approaches

• Published in: Arabian journal for science and engineering (2011) 2024-05, Vol.49 (5), p.7375-7394
• Main Authors: Heymann, Mozart Caetano, Pereira, Valdecy, Caiado, Rodrigo Goyannes Gusmão
• Format: Article
• Language: English
• Subjects: Alternatives; Analytic hierarchy process; Decision analysis; Decision making; Engineering; Evolutionary algorithms; Genetic algorithms; Hierarchies; Humanities and Social Sciences; multidisciplinary; Multiple criterion; Multiple objective analysis; Research Article-Systems Engineering; Science
• ISSN: 2193-567X; 1319-8025; 2191-4281
• DOI: 10.1007/s13369-023-08227-4

The Analytic Hierarchy Process (AHP) is a multi-criteria decision-making method that relies on constructing a pairwise comparison matrix (PCM) based on decision-makers’ (DMs) judgments regarding alternatives and criteria. The objective is to obtain weights and ultimately rank and select alternatives. However, in some cases, DMs may not provide judgments due to a lack of experience, knowledge, or reluctance to express opinions on the subject, resulting in missing pairs in the PCM. Existing techniques for filling these missing pairs have inherent limitations. This paper demonstrates the application of the pymissingAHP algorithm, implemented in Python and available at https://bit.ly/3UFdqSZ , to address missing pairs using mono and multiobjective approaches. The pymissingAHP algorithm employs a Genetic Algorithm (GA) featuring a specialized encoding to address this issue. Our approach can handle mono or multiple objective scenarios, which involve minimizing the consistency index and maintaining the ranking of weights as defined by experts. Additionally, the algorithm accommodates fuzzy numbers within the AHP framework (FAHP). PCMs containing numerous missing values may yield multiple solutions and not accurately reflect experts’ opinions. Although our approach can solve entirely depleted PCMs, obtaining as many comparisons as possible is recommended to ensure a faithful representation of expert opinions for the decision-makers. The pymissingAHP algorithm provides a significant advantage: the capacity to seek solutions that address single or multiple objectives, utilizing continuous or discrete values, and additionally, the ability to solve FAHP problems.