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Pearson correlation coefficients (ρ) (significance level = 0.05) between the 12 indicators of the RIfAO. Colours and ellipses represent strength and direction of the correlation. Numbers in grey background represents non-significant correlations. Asterisks represent significance levels, accordingly: * = 0.05, ** = 0.01, *** = 0.001.
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Composite Indicators (CIs, a.k.a. indices) are increasingly used as they can simplify interpretation of results by condensing the information of a plurality of underlying indicators in a single measure. This paper demonstrates that the strength of the correlations between the indicators is directly linked with their capacity to transfer information...
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... where X ji is the raw country value in the ith indicator X i , i = 1, 2, …, n. This procedure results in a linear transformation of the data, ranging from 0 (min) to 1 (max), and is performed on all indicators to render them comparable. Table 1 gives an overview of each of the 12 indicators that are included in the RIfAO framework, and Fig. 4 shows the Pearson correlation coefficients (ρ) between them (step 2 in Fig. 3). For conciseness, the indicators are labelled according to their ID number (e.g., IND 1), as defined in Table 1, in all graphs and ...
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... Thus, they are not equally influential in representing countries across the concept measured by RIfAO. The normalized correlation ra- Table 2 further showcase this discrepancy (see "Deviation ratio" column), with values ranging from 64% overrepresentation (IND 10 ) to 77% underrepresentation (IND 7 ). By re-examining the correlation matrix in Fig. 4, a connection between correlation strength and information transfer is evident: the information in the highly correlated indicators (e.g., IND 3,8,10,12 ) tends to be overrepresented, whereas the opposite holds true for the poorly, non-or negatively correlated indicators (e.g., IND 5,6,7,11 ). These findings are especially relevant in ...
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... ratios in Fig. 8, the information contained within the zeroweighted indicators is still captured by the CI simply through correlation. Judging from previous observations, it can be assumed that these indicators (excluding IND 2 ) are sufficiently represented by the inclusion of IND 4 , with which they are all highly positively correlated (see Fig. ...
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... In R, the package COINr enables users to develop CIs with all standard operations, including criteria selection, data treatment, normalization, aggregation, and sensitivity analysis (Becker et al., 2022). Other packages, such as compind, focus specifically on weighting and aggregation (Fusco et al., 2018), while MATLAB tools like CIAO (Lindén et al., 2021) offer specialized capabilities for parts of CI development. ...
... Composite indicators, based on multi-criteria decision-making (MCDM) methods, are frequently applied to summarize information, with the aim of capturing underlying concepts [20][21][22]. These indicators often rely on reference-based aggregation formulas, such as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) [23][24][25][26][27][28] or Hellwig methods [29,30], to synthesize data across multiple criteria. ...
With rapid urbanization, maintaining a high quality of life (QoL) for city residents has become a critical challenge for policy-makers and urban planners. Smart cities, leveraging advanced technologies and data analytics, present a promising pathway to enhance urban services and promote sustainability. This paper introduces an innovative adaptation of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, integrating a Belief Structure (BTOPSIS) to improve the evaluation and interpretation of survey data. Our approach effectively addresses the distribution of responses across categories and the uncertainty often present in such data, including missing or ambiguous answers. Additionally, we perform a sensitivity analysis to assess the stability of the BTOPSIS rankings under varying utility function parameters, further validating the robustness of our method. We apply this framework to the 2023 ‘Quality of Life in European Cities’ survey, analyzing diverse urban factors such as public transport, healthcare, cultural facilities, green spaces, education, air quality, noise levels, and cleanliness. Additionally, our study offers a comparative analysis of BTOPSIS against other multi-criteria methods used for evaluation data from this report, showcasing its strengths and limitations in addressing the dataset’s complexity. Our findings reveal significant variations in residents’ perceived QoL across European cities, both between cities and within countries. Zurich and Groningen rank highest in satisfaction, while Tirana, Skopje, and Palermo are ranked lowest. Notably, residents of cities with populations under 500,000 report higher satisfaction levels than those in larger cities, and satisfaction levels are generally higher in EU and EFTA cities compared to those in the Western Balkans, with the highest satisfaction observed in northern and western Member States. To aid urban planners and policy-makers, we propose a ranking tool using the BTOPSIS method, capturing nuanced resident perceptions of living conditions across cities. These insights provide valuable guidance for strategic urban development and advancing the smart city agenda across Europe.
... A recent and growing application of MCDM is in the construction of composite indicators. As indicated by Lindén et al. [49], the objective of constructing a synthetic measure is "to condense and summarize the information contained in a number of underlying indicators, in a way that accurately reflects the underlying concept". A literature review by Greco et al. [50] highlights the substantial expansion of this research field, emphasizing its relevance and practical significance within the realm of MCDM. ...
This paper presents an original and comprehensive investigation into the Taxonomic Measure of Development (TMD), introduced by Hellwig in 1968, enriching both its theoretical foundations and practical applications. It provides an overview of various variants of the Hellwig method, including their extensions and applications, while also exploring recent trends across multiple research domains. Primarily developed as a method for multidimensional analysis, TMD has evolved into a pivotal tool in multi-criteria decision-making. It is widely used for evaluating and ranking alternatives, particularly in the analysis of complex socio-economic phenomena and decision-making scenarios involving multiple criteria. This study systematically reviews the original algorithm and its subsequent extensions and modifications, including adaptations for fuzzy sets, intuitionistic fuzzy sets, and interval-valued fuzzy sets. Furthermore, it explores an integrated multi-criteria approach based on Hellwig’s method and its practical applications across various domains. This paper introduces an original approach by conducting a detailed, step-by-step analysis of the TMD framework. This process-oriented analysis is a novel contribution that sets this study apart from typical reviews based on statistical or bibliometric data. By examining key steps in the TMD framework—such as data collection, criterion weighting, data normalization, ideal value determination, distance calculation, and normalization factor—this paper highlights the method’s versatility in addressing complex, real-world decision-making problems. Although similar to the widely used Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method in its reliance on distance to evaluate alternatives, Hellwig’s approach is unique in focusing exclusively on proximity to an ideal solution, without considering distance from a negative ideal. This distinctive emphasis has led to numerous adaptations and extensions that address specific issues such as criterion dependencies, uncertainty, and rank reversal. The findings underscore the continued relevance of the Hellwig method, its recent extensions, and its growing international recognition.
... 12,58 Considering that all the indicators were chosen to be statistically independent, no adjustments to the weights are necessary. 51 Table 2 presents the decision-making tree defined for this case study, including the weight established for each requirement (W R ), criterion (W C ), and indicator (W I ), as well as the total global weight (W t ). ...
The global construction industry is experiencing significant growth, driving the demand for building floor area. However, this expansion comes with substantial environmental consequences, including high‐energy consumption and greenhouse gas (GHG) emissions, together with economic and social impacts. To address these challenges, this research aims at providing designers and decisions‐makers with an approach that will aid the quantification of those impacts relevant for the sustainability performance of flooring systems. A holistic sustainability assessment was performed considering economic, environmental, and social aspects using the Integrated Value Model for Sustainability Evaluations. This study focused on various flooring typologies, including reinforced concrete (RC) and fiber‐RC (FRC) slabs with solid and waffle (for RC solution) configurations. The most representative criteria and indicators of sustainability for concrete column‐supported slabs were identified, measured, and weighted—aggregated in a decision‐making tree—in order to obtain a representative a sustainability index (SI) for each alternative. The results of the analysis evidence that the RC solid slab has a higher overall SI than the other alternatives, the FRC alternatives performing with similar SI of that quantified for the RC solid slab solution and the RC waffle slab being that with the lower sustainability performance among those flooring systems considered in this study. The results of a sensitivity analysis showed that those alternatives using FRC have potential for improving the overall sustainability performance.
... * Core area is measured across the woodland parcel that the FOBI woodland unit sits within, rather than the 1 km landscape buffer. conceptually weak groupings (Lindén et al 2021, Freni-Sterrantino et al 2022. Metrics were also removed if they were collinear (ρ ⩾ 0.92; (Casabianca et al 2022)) with another metric deemed to be more integral to the FOBI, as they highlight sources of redundancy or 'double counting' . ...
... The weighting options proposed by the project team (Step 1.2) were tested to understand their outcomes for the FOBI. The effective weight of individual metrics on a composite index is determined by the weightings assigned to each metric and the number of metrics in a grouping at each level; the final influence of a metric is driven by its effective weight and the strength of its correlation with the composite index (Becker et al 2017, Greco et al 2019, Lindén et al 2021. Two opposing strategies to account for the unequal number of metrics that the Level 2 subindices contain were put forward for comparison: (i) Equal Level 2 Subindex Weights (manual): enforcing each subindex to be equally weighted at Level 2, so that metrics in larger groupings are attributed a lower effective weight, (ii) Equal Metric Weights (manual): enforcing equal weights across metrics, so that Level 2 subindices with a higher number of metrics are attributed a higher effective weight. ...
... Two opposing strategies to account for the unequal number of metrics that the Level 2 subindices contain were put forward for comparison: (i) Equal Level 2 Subindex Weights (manual): enforcing each subindex to be equally weighted at Level 2, so that metrics in larger groupings are attributed a lower effective weight, (ii) Equal Metric Weights (manual): enforcing equal weights across metrics, so that Level 2 subindices with a higher number of metrics are attributed a higher effective weight. Alongside this manual weighting approach, a non-linear weighting optimisation procedure was also explored to find and compare the set of weights that balances (i) the influence of the Level 2 subindices (Equal Level 2 Subindex Weights (optimised)), or (ii) metrics (Equal Metric Weights (optimised)) (Lindén et al 2021). The 'best' weighting system was selected in consideration of the highest Cronbach's Alpha (an indicator of the internal consistency of an index (JRC, OECD 2008)) achieved across Level 2 (with metrics) and Level 3 (with Level 2 subindices); the highest correlation between the subindices at Level 3; the best balance between the correlation of Level 2 subindices with the Level 3 subindex. ...
Public forest agencies are obligated to take steps to conserve and where possible enhance biodiversity, but they often lack information and tools that support and evidence their decision making. To help inform and monitor impact of management actions and policies aimed at improving forest biodiversity, we have co-developed a quantitative, transparent and repeatable approach for assessing the biodiversity potential of the United Kingdom's (UK) publicly owned forests over space and time. The FOrest Biodiversity Index (FOBI) integrates several forest biodiversity indicators or 'metrics' , which characterise management-sensitive woodland and landscape features associated with biodiversity. These are measured or modelled annually using spatially comprehensive forest survey data and other well-maintained spatial environmental datasets. Following metric normalisation and a correlation analysis, a statistically robust selection of these metrics is aggregated using a hierarchical procedure to provide composite index scores. The FOBI metric and index results are provided for every individual public forest, and can be summarised across any reporting region of interest. Compared to existing indicators that rely on sample-based forest data, the results thus better support decisions and obligations at a range of scales, from locally targeted action to national, long-term biodiversity monitoring and reporting. We set out how the FOBI approach and associated bespoke online interfaces were co-developed to meet public forest agency needs in two constituent countries of the UK (England and Scotland), whilst providing a conceptual framework that can be adapted and transferred to other geographic areas and private forests. Example results are reported for England's public forests for four annual timestamps between 2014 and 2021, which indicate improvements to the biodiversity potential of public forests and surrounding landscapes over this time via increases in their diversity, extent, condition and connectivity.
... On the one hand, Shannon's [34] information Entropy Index offers a valuable measure of informational diversity [35,36] with high applicability in the endogenous sub-indicator weights definition [37,38] and in reducing informational loss arising from the sub-indicators aggregation [28,39]. Other examples of informational diversity measures are the Gini and the variation coefficients [40]. ...
This research offers a solution to a highly recognized and controversial problem within the composite indicator literature: sub-indicators weighting. The research proposes a novel hybrid weighting method that maximizes the discriminating power of the composite indicator with objectively defined weights. It considers the experts’ uncertainty concerning the conceptual importance of sub-indicators in the multidimensional phenomenon, setting maximum and minimum weights (constraints) in the optimization function. The hybrid weighting scheme, known as the SAW-Max-Entropy method, avoids attributing weights that are incompatible with the multidimensional phenomenon’s theoretical framework. At the same time, it reduces the influence of assessment errors and judgment biases on composite indicator scores. The research results show that the SAW-Max-Entropy weighting scheme achieves greater discriminating power than weighting schemes based on the Entropy Index, Expert Opinion, and Equal Weights. The SAW-Max-Entropy method has high application potential due to the increasing use of composite indicators across diverse areas of knowledge. Additionally, the method represents a robust response to the challenge of constructing composite indicators with superior discriminating power.
... Number of scientific research workersIn other words, let's normalize the indicators and calculate the science index based on the average value of the normalized values of these indicators(Lindén et al. 2021). ...
... The obtained regression equations and statistics are given inTable 4.3. A linear regression model was constructed for the following indicators(Lindén et al. 2021): -G13 -Number of students per 1000 people; -G23 -unemployment rate, %; -G41 -Number of mobile phone subscribers per 1000 people. ...
The purpose of the article is to assess innovation activity taking into account the role of innovation in the economic development of the region. As the object of the study, the authors took 10 economic regions, grouped according to their economic characteristics on the territory of Azerbaijan. This paper reviewed international experience in assessing innovation activities taking into account regional characteristics. In the article, as a result of the analysis of the factors determining innovative activity, factors suitable for Azerbaijan were selected. The region's innovative activity was assessed taking into account international criteria for calculating the innovation index. As a result, it can be used when calculating the innovation index of the Republic of Azerbaijan, when assessing regional economic development based on the innovation factor.
... To identify a relationship between resilience, globalisation and the efficiency of the use of ICT by a state to increase competitiveness and well-being, it is necessary to use composite indicators, due to their characteristic of quantifying multidimensional concepts that cannot be measured directly because of their complexity (Oțoiu and a Grădinaru, 2018; Lindén et al., 2021). ...
Rethinking the concept of resilience in the post-pandemic period is urgently needed considering an uncertain and unpredictable future. To identify the necessary solutions for the recovery of the economy, the involvement of all actors in the socioeconomic and political environment is vital. Consolidating regional development, intensifying global cooperation, and developing sustainable business models in the field of digital entrepreneurship are necessary pillars in revitalising the economy and creating a sustainable economy. In this context, using data for the countries of the European Union, it was shown, using statistical methods of multivariate analysis, that globalisation and digitalisation are necessary to achieve resilience. Thus, new opportunities are opening up for creating development strategies that can prepare socioeconomic systems for future shocks and uncertainties.
... The expedient of resorting to not weighting, for example, corresponds to the tacit assumption that all variables have equal status (European Commission 2020, in the section 'Weighting'). The application of sensitivity analysis to CI in many cases also reveals inconsistencies in the way weights are interpreted as measures of importance (Paruolo, Saisana, and Saltelli 2013, Becker et al. 2017, Lindén et al. 2021a). ...
... An additional problem appears when the synthetic measure includes negatively correlated variables, pointing to a logical inconsistency in the measure (Saisana and Philippas 2012). Paruolo, Saisana, and Saltelli (2013) and Lindén et al. (2021a) discuss ways to improve the assignment of weights in CI built via linear aggregation. Due to its intuitive appeal, linear aggregation is often chosen in the construction of indices. ...
... This will allow internally consistent measures to be obtained, as well as in some cases reducing the set of diagnostic variables. Additionally, where there are reasons to suspect that the weighting has introduced inconsistencies, the approaches suggested in Paruolo, Saisana, and Saltelli (2013) and Lindén et al. (2021a) could be considered. ...
Climate change and COVID-19 have brought mathematical models into the forefront of politics and decision-making, where they are now being used to justify momentous and often controversial decisions. Such models are technically very complex, and sources of political authority. Yet disagreement among experts fuels a growing uneasiness about the quality and significance of the numbers that models produce. This multidisciplinary volume takes a critical look at the intersections of the technical and the political aspects of models. Our goal is to help unravel the meanings and implications of models in the real world, for readers that include decision makers, policy analysts, journalists, scholars … and even modellers.
... In many cases, global composite metrics are often deployed to compare regions or countries based on Environmental, Social, and Governance (ESG) outlooks (Global, 2020). Few papers have emerged recently focusing on building composite resilience indicators for engineering systems such as energy systems (Lindén et al., 2021), wastewater management systems (Sun et al., 2020), and transportation infrastructure (Vajjarapu and Verma, 2021). ...
The impact of climate change and the dynamic nature of environmental conditions underscore the critical need to enhance resilience of systems and process safety considerations. The efficacy of such efforts primarily depends on how resilience is measured. Among the myriad efforts to quantify resilience, composite indicators have emerged as promising tools. However, these indicators typically employ statistical methods to derive weights for aggregation and rely on statistical homogeneity among indicators which can limit their scope and fidelity. In this study, we propose an alternative novel resilience index derived from a system’s structure and the essential conditions for safe operation during and after disruptions. The proposed measure reflects the systems’ ability to resist and respond to failures by addressing possibilities of impact propagation to other infrastructure systems. Moreover, it eliminates the need for weights and allows for compensability among its leading indicators. Using a case study based on the on-site wastewater treatment and disposal systems (OSTDS) in South Florida that faces increasing risks due to rising sea levels, we investigate the validity of the proposed index and perform a comparative analysis with statistically-driven measures. Furthermore, we demonstrate the adaptation of the proposed index for decision making within a generalized optimization framework.