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This document is a correction notice for an article titled "Quantifying and reducing the complexity of multi-line charts as a visual aid in multi-criteria decision-making." The original article contained errors, particularly with the figures, which have now been updated. The corrected article is available online and is licensed under a Creative Commons Attribution 4.0 International License. Springer Nature, the publisher, remains neutral regarding jurisdictional claims and institutional affiliations. [Extracted from the article]

Multi-line charts are commonly used in multi-criteria decision-making (MCDM) to represent multiple data series on the same graph. However, the presence of conflicting criteria or divergent viewpoints introduces the challenge of accurately interpreting these charts, necessitating thoughtful design to improve their comprehensibility. In this paper, we model these multi-line charts as connected perfect matching bipartite graphs. We propose a metric called the Coefficient of Complexity (CoC) to quantify the complexity of these multi-line charts. In order to reduce the visual complexity of these charts, we propose to minimize the CoC by modeling it as an integer linear optimization problem (reminiscent of the traveling salesman problem). We demonstrate our techniques through multiple real-life case studies, wherein multi-line charts serve as data visualization across various MCDM software tools. Additionally, multi-line charts with specific requirements have been optimized using our approach, showcasing the adaptability and efficacy of our technique. We also formulate the radar chart as a specialized form of the multi-line chart, and adapt our technique to improve its comprehensibility. The proposed CoC and its optimization are important contributions to the field of analytics, as a number of methods use multi-line charts for visual aid. Consequently, enhancing their comprehensibility can facilitate the decision-making process and help decision-makers gain insights. [ABSTRACT FROM AUTHOR]

Although Multi-criteria Decision Making methods have been extensively used for choice problems, their descriptive use has rarely been considered. The descriptive component is important because it allows decision makers to better understand the problem. In this paper, we add the descriptive method GAIA as an extension to the AHPSort method that helps policy makers to gain insights into their decision problems, through the portraying of a case in the food and drink industry. This descriptive component is implemented as a visual analysis. The proposed extension has been implemented in an open-source software tool that allows users to visualise the different performances of food suppliers within a review process and provide feedback for improvements within the food and drink industry. [ABSTRACT FROM AUTHOR]