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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]

The analytic hierarchy process is a widely used multi-criteria decision-making method that involves the construction of pairwise comparison matrices. To infer a decision, a consistent or near-consistent matrix is desired, and therefore, several methods have been developed to control or improve the overall consistency of the matrix. However, controlling the overall consistency does not necessarily prevent having strong local inconsistencies. Local inconsistencies are local distortions which can lead to rank reversal when a new alternative is added or deleted. To address this problem, we propose an algorithm for controlling the inconsistency during the construction of the pairwise comparison matrix. The proposed algorithm assists decision makers whilst entering their judgments and does not allow strong local inconsistencies. This algorithm is based on the transitivity rule and has been verified through statistical simulations. Appropriate thresholds of acceptable evaluations have been inferred from these simulations. We demonstrate that the proposed algorithm is a helpful decision aid to decision makers when entering pairwise comparison judgments. [ABSTRACT FROM AUTHOR]

Channel bonding (CB) is a technique used to provide larger bandwidth to users. It has been applied to various networks such as wireless local area networks, wireless sensor networks, cognitive radio networks, and cognitive radio sensor networks (CRSNs). The implementation of CB in CRSNs needs special attention as primary radio (PR) nodes traffic must be protected from any harmful interference by cognitive radio (CR) sensor nodes. On the other hand, CR sensor nodes need to communicate without interruption to meet their data rate requirements and conserve energy. If CR nodes perform frequent channel switching due to PR traffic then it will be difficult to meet their quality of service and data rate requirements. So, CR nodes need to select those channels which are stable. By stable, we mean those channels which having less PR activity or long remaining idle time and cause less harmful interference to PR nodes. In this paper, we propose two approaches remaining idle time aware intelligent channel bonding (RITCB) and remaining idle time aware intelligent channel bonding with interference prevention (RITCB-IP) for cognitive radio sensor networks which select stable channels for CB which have longest remaining idle time. We compare our approaches with four schemes such as primary radio user activity aware channel bonding scheme, sample width algorithm, cognitive radio network over white spaces and AGILE. Simulation results show that our proposed approaches RITCB and RITCB-IP decrease harmful interference and increases the life time of cognitive radio sensor nodes. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simulation model for cognitive radio sensor networks (CRSNs) which is an attempt to combine the useful properties of wireless sensor networks and cognitive radio networks. The existing simulation models for cognitive radios cannot be extended for this purpose as they do not consider the strict energy constraint in wireless sensor networks. Our proposed model considers the limited energy available for wireless sensor nodes that constrain the spectrum sensing process—an unavoidable operation in cognitive radios. Our model has been thoroughly tested by performing experiments in different scenarios of CRSNs. The results generated by the model have been found accurate which can be considered for realization of CRSNs. [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]