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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]

Using multi-criteria decision making (MCDM) technique to rank alternatives is a well-known area of study in which aggregation operators, such as ordered weighted averaging (OWA) and induced OWA (IOWA) operators, play an important role in merging information and producing an overall ranking. The distance measures from ideal argument values in aggregation operators have gained attention in recent literature. Distance measures are traditionally used as argument variables, which leads to the depiction that the attribute cannot be aggregated directly. In this paper, a generalized form of distance-induced OWA (DIOWA) operators is proposed with distance measures used as order-inducing variables. A distinctive benefit of DIOWA operators is that they permit us to consider ideal argument values while simultaneously also taking the attribute values as argument variables. Three variants of DIOWA operators are proposed and investigated, namely a) the Hamming distance-induced OWA (HDIOWA) operator, b) the normalized Hamming distance-induced OWA (NHDIOWA) operator, and c) the weighted Hamming distance-induced OWA (WHDIOWA) operator. We highlight their important properties and provide proofs to necessary theorems, and also suggest the determination methods for calculating their associated weights. We discuss further extensions of the proposed DIOWA operators with the help of generalized and quasi-arithmetic means. We discuss the use of our proposed family of operators for two different decision making situations, and demonstrate their validity by an illustrative numerical example. Finally, we apply the proposed operators to a real-life problem of ranking Chinese provinces for their science and technology (S&T) development levels. The proposed operators are shown to be a useful addition to the aggregation toolbox for decision analysts. [ABSTRACT FROM AUTHOR]

Highlights • A new decision-making methodology called Simulated Uncertainty Range Evaluations (SURE) for handling uncertainty is proposed. • A real-world case study for a pharmaceutical company is used to test the methodology. • Only SURE correctly identified the alternative eventually chosen by the company. Abstract Managerial decision-making often involves the consideration of multiple criteria with high levels of uncertainty. Multi-attribute utility theory, a primary method proposed for decision-making under uncertainty, has been repeatedly shown to be difficult to use in practice. This paper presents a novel approach termed Simulated Uncertainty Range Evaluations (SURE) to aid decision makers in the presence of high levels of uncertainty. SURE has evolved from an existing method that has been applied extensively in the pharmaceutical and speciality chemical sectors involving uncertain decisions in whole process design. The new method utilises simulations based upon triangular distributions to create a plot which visualises the preferences and overlapping uncertainties of decision alternatives. It facilitates decision-makers to visualise the not-so-obvious uncertainties of decision alternatives. In a real-world case study for a large pharmaceutical company, SURE was compared to other widely-used methods for decision-making and was the only method that correctly identified the alternative eventually chosen by the company. The case study demonstrates that SURE can perform better than other existing methods for decision-making involving multiple criteria and uncertainty. [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 in energy planning, their descriptive use has been rarely considered. In this paper, we add an evolutionary description phase as an extension to the AHP (analytic hierarchy process) method that helps policy makers to gain insights into their decision problems. The proposed extension has been implemented in an open-source software that allows the users to visualize the difference of opinions within a decision process, and also the evolution of preferences over time. The method was tested in a two-phase experiment to understand the evolution of opinions on energy sources. Participants were asked to provide their preferences for different energy sources for the next twenty years for the United Kingdom. They were first asked to compare the options intuitively without using any structured approach, and then were given three months to compare the same set of options after collecting detailed information on the technical, economic, environmental and social impacts created by each of the selected energy sources. The proposed visualization method allow us to quickly discover the preference directions, and also the changes in their preferences from first to second phase. The proposed tool can help policy makers in better understanding of the energy planning problems that will lead us towards better planning and decisions in the energy sector. [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]

The growing issue of demand-supply management between the prosumers and the local energy market requires an efficient and reliable energy management model. The microlayers, such as prosumers, energy districts, and macro players, namely retail dealers and wholesale dealers play a pivotal role in achieving mutual benefits. The stochastic nature of renewable energy generation in energy districts requires an effective model that can contemplate all stochastic complexities. Therefore, this paper proposes a mutual trade model between energy districts and smart grid to authorize the prosumers for mutual energy transactions under the stochastic adaptive-service level agreement. Moreover, multiple smart contacts are developed between the stakeholders to design adaptability and stochastic behavior of wind speed and solar irradiance. The real-time adaptations of the stochastic adaptive-service level agreement are based on technical beneficial feasibility and achieved through stochastic and adaptive functions. The optimized solution based on a genetic algorithm is proposed for the energy cost and energy surplus of prosumers and output parameters of the mutual trade model (grid revenue). In the context of mutual benefits associated with balanced demand and supply, the economic load dispatch and simplex method maximization are used for optimized demand-supply energy management. Moreover, the effectiveness of the proposed adaptive and stochastic mutual trade model is validated through simulation and statistical analysis. [ABSTRACT FROM AUTHOR]

Recommender Systems (RS) are widely used to help people or group of people in finding their required information amid the issue of ever-growing information overload. The existing group recommender approaches consider users to be part of a single group only, but in real life a user may be associated with multiple groups having conflicting preferences. For instance, a person may have different preferences in watching movies with friends than with family. In this paper, we address this problem by proposing a Hybrid Two-phase Group Recommender Framework (HTGF) that takes into consideration the possibility of users having simultaneous membership of multiple groups. Unlike the existing group recommender systems that use traditional methods like K-Means, Pearson correlation, and cosine similarity to form groups, we use Fuzzy C-means clustering which assigns a degree of membership to each user for each group, and then Pearson similarity is used to form groups. We demonstrate the usefulness of our proposed framework using a movies data set. The experiments were conducted on MovieLens 1M dataset where we used Neural Collaborative Filtering to recommend Top-k movies to each group. The results demonstrate that our proposed framework outperforms the traditional approaches when compared in terms of group satisfaction parameters, as well as the conventional metrics of precision, recall, and F-measure. [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]