Aggregation Formula Research Articles

Two Approaches to Ranking Aggregation in The Methodology of Multiple-Level, Multiple Criteria Evaluation of Urban Transportation Projects

Purpose: The objective of the study was to propose an alternative approach to aggregating rankings in a multi-level, multi-criteria methodology for assessing urban transport projects (UTP). A gap in the literature: In the literature, only one approach (so-called horizontal) is presented for aggregating rankings in a multi-level, multi-criteria methodology for assessing UTPs, implemented at two levels: operational (level II) based on the normalization formula for aggregating the substantive utility – local (in a given class) of individual UTPs of an appropriate nature to the substantive utility – global of all UTPs in the entire population, and a global assessment of UTPs, leading to obtaining the final ranking of all projects (level V) based on the aggregation formula for hierarchizing UTPs according to their global utility. Methodology/Approach used in the study: The study used the multi-level, multi-criteria methodology for assessing UTPs, including the horizontal approach to aggregating rankings; the multi-criteria decision support (MCDS) methodology, the AHP method, which is used to conduct computational experiments; and Spearman’s rank correlation coefficient used to evaluate the vertical approach. Summary of findings: This article develops and presents a new approach to aggregating rankings in the multi-level, multi-criteria UTP evaluation methodology. This approach aggregates rankings only at one, level V of the methodology and is based: firstly on the original aggregation formula for prioritizing UTPs according to their global utilities obtained within predefined project classes based on their partial utilities (substantive, sectoral, strategic); and secondly on the original formula for normalizing the aggregation of global UTP utilities from predefined classes to prioritize UTPs in the final ranking according to their global utilities of all UTPs in the entire population (irrespective of the project class they were in). This article also evaluates the proposed vertical approach to aggregating rankings in the multi-level, multi-criteria UTP evaluation methodology.

A Gaussian interval type-2 fuzzy characterization method based on heterogeneous big data and its application in forest ecological assessment

The under-forest economy is a new agricultural and forestry production mode. It can improve the utilization efficiency of forest land and make full use of forest resources, forest space, and forest ecological environment through different forms of industries such as understory planting and breeding. The under-forest economy has important ecological and economic benefits, significant to rural revitalization and industrial structure adjustment. It has been widely discussed by people in recent years. The forest ecological security level is a core factor to be considered in selecting sites for the under-forest economy. In practice, some forest ecological security evaluation indexes usually show heterogeneous forms. To comprehensively evaluate the level of forest ecological security, this study constructs a new multi-indicator fuzzy evaluation method based on heterogeneous big data. Firstly, a new linguistic scale function is defined to realize the consistent conversion of multi-granularity linguistic information. A Gaussian interval type-2 fuzzy aggregation formula for heterogeneous large-scale data is proposed. This formula is used to describe the differences in evaluation information between individuals caused by different knowledge backgrounds of evaluators. Then, the Gaussian interval type-2 fuzzy cross-entropy is defined, and it is verified to satisfy the excellent properties. This cross-entropy is applied to determine the objective weights of evaluation indexes. Considering the risk-averse psychology of experts and combining the prospect theory, the MULTIMOORA method in the Gaussian interval type-2 fuzzy environment is proposed. Finally, the applicability of the constructed Gaussian interval type-2 fuzzy comprehensive evaluation method (GIT2FCE) is verified through a case study conducted on the site selection of the under-forest economic industry.

Efficient Pareto based approach for IoT task offloading on Fog–Cloud environments

In recent times, a new paradigm has emerged in the field of Cloud computing, namely Fog computing. This paradigm has proven to be highly useful in a wide range of domains where both delay and cost were important metrics. Notably, the Internet of Things (IoT) strongly benefits from this, as small devices can gain access to strong computation power quickly and at a low cost. To achieve this, task offloading is used to decide which task should be executed on which node. The development of an efficient algorithm to address this problem could significantly enhance the sustainability of systems in various industrial, agricultural, autonomous vehicle, and other domains. This paper proposes a new variant of the Niche Pareto Genetic Algorithm (NPGA) called Local search Drafting-NPGA (LD-NPGA) to optimize resource allocation in a Cloud/Fog environment, with the objective of minimizing makespan and cost simultaneously. It generates Pareto solutions allowing the user to make choices closer to its intentions. Thus, it addresses various shortcomings identified in the state of the art, including scalability and aggregation formula. A drafting step is implemented to maintain diversity in the population of solutions, resulting in a more varied Pareto set than basic NPGA. LD-NPGA significantly outperforms state-of-the-art metaheuristics in makespan and cost by 15%. Finally, the scalability of our approach and the variety of solutions generated are confirmed in the different experiments.

Application of The Aggregation and Multicriteria Optimization Method in Assessing the Level of the Knowledge Economy of World Regions in Industry 4.0

The article proposes a new methodology for determining the level of the knowledge economy of countries in terms of the possibilities of using Industry 4.0 technologies. The relevance of the study is due to the transition to a new technological structure – “Industry 4.0” in the world. The aim of the study is to analyze data on the main sub-indices of the knowledge economy associated with Industry 4.0 for countries around the world based on the author’s methodology. As a tool for this analysis, the k-means++ clustering method was used to classify countries according to their characteristics. The assessment of the potential of Industry 4.0 is determined on the basis of 5 criteria characterizing various aspects of the development of countries at the level of economic knowledge. In the calculation process, determining the extent to which the indicators used describe the level of the knowledge economy, and the use of the aggregation formula and multi-criteria optimization, constitutes the scientific novelty of the study. It was concluded that as a result of clustering the countries of the world using the formula Aggregation and Multicriteria Optimization, the number of clusters decreased and the distribution of countries between clusters began to more adequately reflect reality. The results of the study can be used in the process of assessing the competitiveness of countries during the transition to the Industry 4.0 economy, as well as in developing strategies and concepts for countries.

Non-gain asymmetry for dissipativity framework for positive systems exhibiting interior equilibria

This paper aims to formulate a new approach to dissipative modeling of nonlinear positive systems with interior equilibria. Processing positivity separately from stability becomes unnecessary. For asymmetric state spaces on which systems evolve, this paper proposes a supply rate of non-gain-type asymmetry and develops formulas of their aggregation, which is not as trivial as aggregating L 2 gain and passivity supply rates. The novelty of their proofs is that the involved treatment of asymmetric functions is reduced to the evaluation of directed graphs carrying balance information between variables. The dissipativity on asymmetric spaces and the aggregation formulas qualify a single logarithmic storage function to establish stability and positivity simultaneously for an interconnected system. The usefulness is illustrated by examples.

Three-way group consensus method based on probabilistic linguistic preference relations with acceptable inconsistency

In the realm of addressing consensus challenges within group decision-making (GDM) that encompass individual preferences, this article presents an innovative approach. This article introduces a three-way group consensus methodology grounded in probabilistic linguistic preference relations (PLPRs) that ensures an acceptable level of inconsistency by applying the three-way decision (TWD) principle. This methodology is referred to as the TWD-GC-AIC approach. The TWD-GC-AIC approach consists of two core components, each dedicated to distinct aspects: ensuring the internal consistency of individual expert preference relations and achieving consensus within the expert group. The first component is dedicated to enhancing the consistency of individual expert preferences. This process commences with the determination of expert weights and the development of a novel aggregation formula. Subsequently, the consistency metric is refined through the incorporation of a newly devised distance formula. Once the predefined consistency threshold is reached, this study seamlessly integrates a planning model with an iterative algorithm. This integration serves a dual purpose: minimizing adjustment costs while retaining as much of the original information provided by the experts as possible. In the consensus-reaching phase, known as the consensus reaching process (CRP) of the expert group, this study employs iterative algorithms that incorporate TWD within the feedback mechanism. This strategic approach aims to comprehensively consider the emotional attitudes of the experts when adjusting the evaluation information, ultimately leading to a more informed and rational final decision outcome. Finally, this paper empirically validates the effectiveness and efficiency of the TWD-GC-AIC method, particularly in scenarios involving probabilistic linguistic term sets (PLTSs). The method is applied to a practical example and rigorously benchmarked against various other consensus methodologies to assess its performance.

Evaluating chemometric strategies and machine learning approaches for a miniaturized near-infrared spectrometer in plastic waste classification

Optimizing the sorting of plastic waste plays a crucial role in improving the recycling process. In this contribution, we report on a comparative study of multiple machine learning and chemometric approaches to categorize a data set derived from the analysis of plastic waste performed with a handheld spectrometer working in the Near-Infrared (NIR) spectral range. Conducting a cost-effective NIR study requires identifying appropriate techniques to improve commodity identification and categorization. Chemometric techniques, such as Principal Component Analysis (PCA) and Partial Least Squares - Discriminant Analysis (PLS - DA), and machine learning techniques such as Support- Vector Machines (SVM), fine tree, bagged tree, and ensemble learning were compared. Various pre-treatments were tested on the collected NIR spectra. In particular, Standard Normal Variate (SNV) and Savitzky-Golay derivatives as signal pre-processing tools were compared with feature selection techniques such as multiple Gaussian Curve Fit based on Radial Basis Functions (RBF). Furthermore, results were combined into a single predictor by using a likelihood-based aggregation formula. Predictive performances of the tested models were compared in terms of classification parameters such as Non-Error Rate (NER) and Sensitivity (Sn) with the analysis of the confusion matrices, giving a broad overview and a rational means for the selection of the approach in the analysis of NIR data for plastic waste sorting.

How to Use Natural Experiments to Estimate Misallocation

We propose a method to estimate the effect of firm policies (e.g., bankruptcy laws) on allocative efficiency using (quasi-)experimental evidence. Our approach takes general equilibrium effects into account and requires neither a structural estimation nor a precise assumption on how the experiment affects firms. Our aggregation formula relies on treatment effects of the policy on the distribution of output-to-capital ratios, which are easily estimated. We show this method is valid for a large class of commonly used models in macrofinance. We apply it to the French banking deregulation episode of the mid- 1980s and find an increase in aggregate TFP of 5 percent. (JEL G21, G24, G28, G31, G32, H25)

Assessing the effect of new data sources on the consumer price index: a deterministic approach to uncertainty and sensitivity

Abstract One of the greatest challenges facing official statistics in the 21st century is the use of alternative sources of data about prices (scanned and scraped data) in the analysis of price dynamics, which also involves selecting the appropriate formula of the price index at the elementary group (5-digit) level. When consumer price indices of goods and services are constructed, a number of subjective decisions are made at different stages, e.g. regarding the choice of data sources and types of indices used for the purpose of estimation. All of these decisions can affect the bias of consumer price indices, i.e. the extent to which they contribute to the overall uncertainty about the resulting index values. By measuring how robust consumer price indices are, one can assess the impact that the decisions made at the different stages of index construction have on the index values. This assessment involves analysing uncertainty and sensitivity. The purpose of the study described in the article was to determine how much and in which direction the consumer price index changes when including scanner and scraped data in the analysis, in addition to the data on prices collected by enumerators. The impact of these new data sources was assessed by analysing uncertainty and sensitivity under the deterministic approach. To the best of the authors’ knowledge, it is a novel application of robustness analysis to measure inflation using new data sources. The empirical study was based on data for February and March 2021, while scanner and scraped data about selected categories of food products were obtained from one retail chain operating hundreds of points of sale in Poland and selling products online. It was found that the choice of a data source has the most significant impact on the final value of the index at the elementary group level, while the choice of the aggregation formula used to consolidate different data sources is of secondary importance.

Take it with a pinch of salt—ESG rating of stocks and stock indices

This paper investigates the environmental, social, and governance (ESG) ratings of 20 leading stock exchange indices by analyzing and aggregating ratings of underlying stocks. ESG ratings are increasingly important inputs to sustainable investments in the European Union and United States with the phasing-in disclosure regulations. We find that ratings from two different rating providers (Sustainalytics and Refinitiv) for the same listed stocks are only weakly correlated, even if the scaling differences of the ratings are adjusted. Monte Carlo simulations are conducted to estimate how the choice of major ESG rating inputs (i) aggregation formula, (ii) weighting scheme and (iii) data provider influence the uncertainty of ratings and thus indirectly the sustainable investment process. The simulations reveal that the uncertainty is primarily related to choice of the ESG rating provider. We found that the popular best-in-class portfolio selection could be built on ESG scores. In lower segments of the ESG asset universe, investment selection becomes more challenging due to the increasing uncertainty of ratings. Finally, the paper shows that exchanges in the European Union provide relatively good ESG investment opportunities in international comparison.

Belief aggregation for representative agent models

AbstractRepresentative agent models pin down equilibrium asset prices of an underlying heterogeneous agents economy through the utility maximization problem of a representative agent evaluated at aggregate endowment levels. This paper considers a complete markets asset exchange economy in which all economic agents are expected utility maximizers who share the same risk preferences but may have heterogeneous endowments and beliefs. For arbitrary well‐behaved Bernoulli utility functions we derive belief aggregation formulas that characterize the beliefs of an expected utility maximizing representative agent.

MULTIVARIATE DISTRIBUTIONS WITH TIME AND CROSS-DEPENDENCE: AGGREGATION AND CAPITAL ALLOCATION

AbstractThis paper investigates risk aggregation and capital allocation problems for an insurance portfolio consisting of several lines of business. The class of multivariate INAR(1) processes is proposed to model different sources of dependence between the number of claims of the portfolio. The total capital required for the whole portfolio is evaluated under the TVaR risk measure, and the contribution of each line of business is derived under the TVaR-based allocation rule. We provide the risk aggregation and capital allocation formulas in the general case of continuous and strictly positive claim sizes and then in the case of mixed Erlang claim sizes. The impact of both time dependence and cross-dependence on the behavior of risk aggregation and capital allocation is numerically illustrated.

The impact of the aggregation formula on indicator-based method for the assessment of building susceptibility to hydro-meteorological hazards

A crucial variable in risk and vulnerability assessment procedures is the ability of the built environment to resist in case of hazard impact. This component, referred to as “susceptibility”, can be assessed in different ways, among which indicator-based methods are preferable when no data about past hazardous events are available. This type of methodology, considering the building susceptibility independent from the hazard magnitude, relies on the selection of indicators meaningful for the investigated area and their combination via an aggregation formula, leading to a susceptibility index for each building.The current study aims at reviewing and comparing different approaches used in literature to combine the indicators for calculating the susceptibility index. To this end, five indicators, previously selected for a mountainous case study area, are applied and implemented in a GIS platform, generating just as many specific susceptibility maps. Further, the indicators are weighed and combined in different scenarios with two aggregation formulae, which are integrated into the GIS environment so as to spatially display and compare the results. Last, but not least, the HBIM model and a GIS/BIM database of the studied area are created. Results suggest that the aggregation formula and the assigned weights are crucial ingredients, and therefore they should be chosen carefully according to the aim of the study and the needs of the stakeholders.

Quantitative Toxicity Prediction via Meta Ensembling of Multitask Deep Learning Models.

Toxicity prediction using quantitative structure–activity relationship has achieved significant progress in recent years. However, most existing machine learning methods in toxicity prediction utilize only one type of feature representation and one type of neural network, which essentially restricts their performance. Moreover, methods that use more than one type of feature representation struggle with the aggregation of information captured within the features since they use predetermined aggregation formulas. In this paper, we propose a deep learning framework for quantitative toxicity prediction using five individual base deep learning models and their own base feature representations. We then propose to adopt a meta ensemble approach using another separate deep learning model to perform aggregation of the outputs of the individual base deep learning models. We train our deep learning models in a weighted multitask fashion combining four quantitative toxicity data sets of LD50, IGC50, LC50, and LC50-DM and minimizing the root-mean-square errors. Compared to the current state-of-the-art toxicity prediction method TopTox on LD50, IGC50, and LC50-DM, that is, three out of four data sets, our method, respectively, obtains 5.46, 16.67, and 6.34% better root-mean-square errors, 6.41, 11.80, and 12.16% better mean absolute errors, and 5.21, 7.36, and 2.54% better coefficients of determination. We named our method QuantitativeTox, and our implementation is available from the GitHub repository https://github.com/Abdulk084/QuantitativeTox.

An integrated method for the assessment of social sustainability in public-works procurement

Today, critical deficiencies hinder the effective inclusion of social criteria in public-works procurement. The primary reasons for this are the lack of information and objective social assessment methods in the construction industry. Hence, this paper proposes a method to assist agencies in including indicators and objective assessments of social sustainability in public-works procurement. This method applies to civil engineering projects in the infrastructure life-cycle construction stage using design-bid-build delivery. Eight social categories and 22 factors are organized into two organizational levels (project and company). Quantitative and semi-quantitative indicators are proposed to assess the social commitment of construction companies in their organizations and projects. Additionally, two aggregation formulas are established as assessment criteria in public-works procurement. The results highlight that the indicators' importance in assessing social commitment in a project can be defined depending on the local context. Moreover, the method to assess corporate social responsibility can also measure and compare a company's performance, regardless of size. The proposed method can be used in procurement procedures, helping public-works procurers develop transparent decision processes.

Consensus-based robust decision making methods under a novel study of probabilistic uncertain linguistic information and their application in Forex investment

The probabilistic uncertain linguistic terms set (PULTS) is an effective tool to depict uncertain linguistic opinions of individuals or groups in the procedure of decision making. Motivated by the power of PULTS and the linguistic scale function, this study aims to propose robust techniques to solve multi-attribute group decision making problems with uncertain linguistic evaluations. To enrich calculation and enhance the flexibility of PULTS, we first generalize the aggregation formula to fuse opinions of decision makers represented as PULTSs and secondly derive adjusting rule of probability to adjust the probability distribution of two or more than two probabilistic uncertain elements (PULEs) into the same probability distribution. Novel operations of PULTSs are designed based on the adjusting rule of probability distribution and linguistic scale function for the semantics of linguistic terms. Many related properties of these operations are also discussed. New score function and deviation degree of PULEs are also developed to compare PULEs. Two aggregation operators i.e., probabilistic uncertain linguistic averaging (PULWA) operator and probabilistic uncertain linguistic geometric (PULWG) operator are also redefined in terms of novel operations. In addition, a series of distance measure is defined to overcome the shortcomings of existing ones. After defining a correlation measure, the probabilistic uncertain linguistic (PUL)-consensus reaching method (in which two specific consensus approaches are described separately) is put forward to refine the consensus level of a group. To suit the needs of different semantics, two robust decision making methods named as consensus-based PUL-gained and lost dominance score method and consensus-based PUL-aggregation method are proposed. Finally, a case study concerning the selection of the best commodity for investment in Forex is conducted to illustrate the practicality of the proposed methods. Lastly, a detailed comparative analysis is done with the existing technique to highlight the improvements and advantages of proposed work.

RESTING ENERGY EXPENDITURE IN PARKINSON'S DISEASE PATIENTS UNDER DOPAMINERGIC TREATMENT

Weight homeostasis is complex in Parkinson's disease (PD) and body weight changes substantially throughout the course of the disease. We designed a case-control study to i) investigate whether PD is associated with changes in resting energy expenditure (REE), ii) to assess the accuracy of REE predictive equations for healthy people in PD and iii) to eventually construct a new formula. Measured REE (mREE) was compared between 122 PD patients and 122 gender and body mass index (BMI)-matched controls. The accuracy of estimated REE by 5 common equations (Harris/Benedict-1919, Harris/Benedict-1984, Mifflin St. Jeor, WHO/FAO and aggregate formula) was investigated in PD using Bland-Altman analysis and reported as the frequency of accurate predictions (±10%). Concordance correlation coefficients (CCC) were also calculated. Then, we regressed a new REE equation - using gender, age, weight, height and Hoehn-Yahr stage - and validated it in an independent sample (N=100). No significant difference in mREE was recorded between the whole PD sample and healthy controls. However, mREE was increased in patients with BMI≥30 kg/m2 and Hoehn-Yahr stage≥3. Available REE equations showed limited accuracy (accurate prediction [±10%] frequency, <60% for all). For the new equation the proportion of accurate prediction was 67.0% (overestimation, 24.0%) and CCC was 0.77. PD patients are not commonly characterized by an increase in REE. This is limited to patients suffering from obesity and more severe disease. Common REE equations appear to be inaccurate. The new formula provided better REE estimates and its use can be proposed.

Resting energy expenditure in Parkinson’s disease patients under dopaminergic treatment

ABSTRACT Background: Weight homeostasis is complex in Parkinson’s disease (PD) and body weight changes substantially throughout the course of the disease. We designed a case–control study to (i) investigate whether PD is associated with changes in resting energy expenditure (REE), (ii) to assess how accurately REE could be predicted for individuals with PD utilizing the equations constructed for healthy individuals, and (iii) to eventually construct a new equation. Materials & Methods: Measured REE (mREE) was compared between 122 PD patients and 122 gender and body mass index (BMI)-matched controls. The accuracy of estimated REE by 5 common equations (Harris/Benedict-1919, Roza/Shizgal-1984, Mifflin St. Jeor, WHO/FAO and aggregate formula) was investigated in PD using Bland–Altman analysis and reported as the frequency of accurate predictions (±10%). Concordance correlation coefficients (CCC) were also calculated. Then, we regressed a new REE equation – using gender, age, weight, height and Hoehn-Yahr stage – and validated it in an independent sample (N = 100). Results: No significant difference in mREE was recorded between the whole PD sample and healthy controls. However, mREE was increased in patients with BMI ≥ 30 kg/m2 and Hoehn-Yahr stage ≥ 3. Limited accuracy was present in the available REE equations (accurate prediction [±10%] frequency, <60% for all). For the new equation, the proportion of accurate prediction was 67.0% (overestimation, 24.0%) and CCC was 0.77. Conclusion: PD patients are not commonly characterized by an increase in REE. This is limited to patients suffering from obesity and more severe disease. Common REE equations appear to be inaccurate. The new predictive equation proposed in this study provided better REE estimates.

Capital allocation and RORAC optimization under solvency 2 standard formula

Solvency II Directive 2009/138/EC requires an insurance and reinsurance undertakings assessment of a Solvency Capital Requirement by means of the so-called “Standard Formula” or by means of partial or full internal models. Focusing on the first approach, the bottom-up aggregation formula proposed by the regulator allows for a capital reduction due to the diversification effect, according to the typical subadditivity property of risk measures. However, once the overall capital has been assessed no specific allocation formula is provided or required in order to evaluate the contribution of each risk source on the overall Solvency Capital Requirement. The aim of this paper is twofold. First, we provide a closed formula for capital allocation fully compliant with the Solvency II Capital Requirement assessed by means of the Standard Formula. The solution enables a top-down approach to assess the allocated Solvency Capital Requirement among the risks considered in the Solvency II multilevel aggregation scheme; we demonstrate that the allocation formula adopted is consistent with the Euler allocation principle. Second, a solution is found as a result of an optimum capital allocation problem based on a Return On Risk Adjusted Capital measure; we establish the equivalence between the Return On Risk Adjusted Capital optimization, when the risk adjusted capital is calculated according to the Standard Formula, and the Markowitz mean-variance optimization.

JEEA-FBBVA Lecture 2018: The Microeconomic Foundations of Aggregate Production Functions

AbstractAggregate production functions are reduced-form relationships that emerge endogenously from input–output interactions between heterogeneous producers and factors in general equilibrium. We provide a general methodology for analyzing such aggregate production functions by deriving their first- and second-order properties. Our aggregation formulas provide nonparametric characterizations of the macroelasticities of substitution between factors and of the macrobias of technical change in terms of microsufficient statistics. They allow us to generalize existing aggregation theorems and to derive new ones. We relate our results to the famous Cambridge–Cambridge controversy.