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<p>Maintaining consistency in the Pairwise Comparison Matrix (PCM) is essential for achieving reliable results in the Multicriteria Decision Making (MCDM) process. This article presents a comprehensive, data-driven model based on an autoencoder and the Grey Wolf Optimiser (GWO) to improve the consistency of the PCM in the MCDM method. At the very beginning, we train the system to understand the PCM’s behaviour using an unsupervised neural network, an autoencoder. After that, with the help of the trained Autoencoder and the established consistency threshold, the proposed model is applied to original, unrecognised matrices and classifies them as Error Accumulation (EA) and Unusual and False Observations (UFO). Basically, if the inconsistency in the PCM is due to unusual and false observations (called UFOs), it treats them as UFO-type matrices; if it is due to error accumulation (called EAs), it treats them as EA-type matrices and corrects them accordingly. After characterising the matrices as EA or UFO types, we apply a swarm-intelligence-based optimisation algorithm, the Grey Wolf Optimiser (GWO). Experimental results show the effectiveness of the proposed model to find consistent matrices with slight differences between the original and substitute matrices.</p>

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An autoencoder and Grey Wolf Optimizer-based framework for fixing the inconsistent pairwise comparison matrix in multicriteria decision-making

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月19日

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  • Shalu Kaushik,
  • Aditya Jayesh Aiya,
  • Sangeeta Pant,
  • Anuj Kumar,
  • Lokesh Kumar Joshi

摘要

Maintaining consistency in the Pairwise Comparison Matrix (PCM) is essential for achieving reliable results in the Multicriteria Decision Making (MCDM) process. This article presents a comprehensive, data-driven model based on an autoencoder and the Grey Wolf Optimiser (GWO) to improve the consistency of the PCM in the MCDM method. At the very beginning, we train the system to understand the PCM’s behaviour using an unsupervised neural network, an autoencoder. After that, with the help of the trained Autoencoder and the established consistency threshold, the proposed model is applied to original, unrecognised matrices and classifies them as Error Accumulation (EA) and Unusual and False Observations (UFO). Basically, if the inconsistency in the PCM is due to unusual and false observations (called UFOs), it treats them as UFO-type matrices; if it is due to error accumulation (called EAs), it treats them as EA-type matrices and corrects them accordingly. After characterising the matrices as EA or UFO types, we apply a swarm-intelligence-based optimisation algorithm, the Grey Wolf Optimiser (GWO). Experimental results show the effectiveness of the proposed model to find consistent matrices with slight differences between the original and substitute matrices.