Aggregation Functions Research Articles

Forest fire risk zoning based on fuzzy logic and analytical network process.

Forest fires have a significant impact on human life, property safety, and ecological environment. Deve-loping high-quality forest fire risk maps is beneficial for preventing forest fires, guiding resource allocation for firefighting, assisting in fire suppression efforts, and supporting decision-making. With a multi-criteria decision analysis (MCDA) method based on geographic information systems (GIS) and literature review, we assessed the main factors influencing the occurrences of forest fires in Youxi County, Fujian Province. We analyzed the importance of each fire risk factor using the analytic network process (ANP) and assigned weights, and evaluated the sub-standard weights using fuzzy logic assessment. Using ArcGIS aggregation functions, we generated a forest fire risk map and validated it with satellite fire points. The results showed that the areas classified as level 4 or higher fire risk accounted for a considerable proportion in Youxi County, and that the central and northern regions were at higher risk. The overall fire risk situation in the county was severe. The fuzzy ANP model demonstrated a high accuracy of 85.8%. The introduction of this novel MCDA method could effectively improve the accuracy of forest fire risk mapping at a small scale, providing a basis for early fire warning and the planning and allocation of firefighting resources.

A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

Demand Response Strategy Based on the Multi-Agent System and Multiple-Load Participation

In order to improve the utilization of user-side power resources in the distribution network and promote energy conservation, this paper designs a distributed system suitable for power demand response (DR), considering multi-agent system (MAS) technology and consistency algorithms. Due to the frequent changes in the power system structure caused by changes in the load of a large number of users, this paper proposes using cluster partitioning indicators as communication weights between agents, enabling agents to utilize the distribution network for collaborative optimization. In order to achieve the integration of multiple load-side power resources and improve the refinement level of demand-side management (DSM), two types of agents with load aggregator (LA) functions are provided, which adopt the demand response strategies of Time-of-Use (TOU) or Direct Load Control (DLC) and model the uncertainty of individual device states using Monte Carlo method, so that the two typical flexible loads can achieve the target load-reduction requirements under the MAS framework. The research results demonstrate that this method achieves complementary advantages of the two types of loads participating in DR on a time scale, reducing the costs of power companies and saving customers’ electricity bills while peak shaving.

Novel adaptive DCOPA using dynamic weighting for vector of performances indicators optimization of IoT networks

Clustering in the Internet of Things (IoT) involves organizing devices into groups to streamline network management and optimize resource utilization, including Internet connections, energy usage, coverage, quality of service, and connectivity. DCOPA (A Distributed Clustering Based on Objects Performances Aggregation for Hierarchical Communications in IoT Applications) is a recent distributed clustering protocol based on a timer for cluster formation where the election of Cluster Heads (CHs) is modeled as a multicriteria problem. In this paper, three contributions are presented. Firstly, the DCOPA protocol is analyzed with a focus on its multi-criteria aggregation function T(i) which directly contributes to the election of the CHs and the formation of the network’s clusters. This is then followed by an in-depth analysis of the impact and the variation of the weights assigned to the two aggregated criteria which are the energy and the distance from the base station. A verification of the scalability, load balancing and distribution of the clusters and CHs will follow. Secondly, a new formal notation for the performance analysis, specifically focusing on the mortality and lifetime based on the Vector of Performance Indicators (VPI), will be introduced for IoT. As a third contribution, a revised version of DCOPA is introduced called ADCOPA (Adaptive DCOPA Using Dynamic Weighting for Vector of Performances Indicators Optimization of IoT Networks). ADCOPA is based on a new property which is the dynamicity or the variability of the weights of the criteria used in the election function of CHs. The simulation results show that the ADCOPA algorithm, which dynamically adjusts the weights of the criteria during the network’s lifetime, outperforms the DCOPA algorithm. The latter uses static weights for the criteria that remain unchanged for the entire lifetime of the network. This confirms that the ability to dynamically adjust the weighting of the criteria is an important factor in achieving better performance.

Stress-constrained topology optimization for multi-material thermo-hyperelastic compliant mechanisms based on inverse motion

A stress-constrained topology optimization design for the multi-material thermo-hyperelastic compliant mechanism is investigated in this article, using inverse motion analysis. Through the inverse motion analysis approach, precise control over the geometry of the deformed structure is achieved. A topology optimization model is established for the multi-material thermal hyperelastic compliant mechanism, incorporating constraints on volume, cost and stress, while maximizing displacement as the objective function. Filtering is implemented using an improved partial differential equation, and the stress problem is addressed using the ϵ-relaxation method and the p-norm aggregation function. The sensitivity analysis of the displacement objective function and the stress constraint is conducted. Considering the multi-material thermally actuated actuator as an example, the influence of the stress constraint on the topology optimization design is studied. The results indicate that inverse motion analysis allows for effective control of the output end position of the deformed compliant mechanism.

The maximal coordination principle in regulatory Boolean networks

We introduce a coordination index in regulatory Boolean networks and we expose the maximal coordination principle (MCP), according to which a cohesive society reaches the dynamics characterized by the highest coordination index. Based on simple theoretical examples, we show that the MCP can be used to infer the influence graph from opinion dynamics/gene expressions. We provide some algorithms to apply the MCP and we compare the coordination index with existing statistical indexes (likelihood, entropy). The advantage of the coordination approach is its simplicity; in particular, we do not need to impose restrictions on the aggregation functions.

Strength-based topology optimisation of anisotropic continua in a CAD-compatible framework

In this paper, a new method to address strength-based topology optimisation (TO) problems is proposed. Specifically, failure criteria for anisotropic materials are integrated into a TO algorithm making use of Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent the pseudo-density field describing the topology of the continuum, thus providing solutions that can be easily exported to any computer-aided design software. The notion of failure load factor is introduced to obtain optimised topologies that do not depend on the magnitude of the applied loads. A unified formulation of the main phenomenological criteria for anisotropic materials, i.e., Tsai–Wu, Hoffman and Tsai–Hill criteria, is used and typical issues related to stress-based TO problems, such as local behaviour and singularity of stresses, are handled thanks to: the properties of NURBS blending functions, a special adaptive χ-norm aggregation function that avoids overflow/underflow issues, and a modified pq relaxation approach. The effectiveness of the proposed approach is demonstrated on 2D and 3D problems. A sensitivity analysis of the optimised topologies to the integer parameters involved in the definition of the NURBS entity is performed. Moreover, the influence of the penalisation scheme used for the elasticity and the stress tensors, the failure criterion, and the orientation of the material on the optimal solution is also investigated.

Aggregation of random elements over bounded lattices

Aggregation functions are widely used to fuse information from different sources in a unique value. In many cases, the aggregated information is related to some experimental measure or random sampling of a population. In this direction, it is reasonable to consider aggregation of random elements. In this paper, the concept of aggregation functions of random elements over bounded lattices, which are measurable functions from a probability space to a bounded lattice, is presented. In particular, starting from a partially ordered set, a measurable space is constructed. Random elements are considered to be measurable functions from a probability space to the measurable space. The concept of aggregation of random elements over bounded lattices is defined by generalizing the monotonicity and the boundary conditions in terms of stochastic orders. Several types, such as the induced, random and degenerated aggregations of random elements over bounded lattices are defined and some coherence properties are studied. Particular examples regarding the aggregation of random variables, random graphs and random semi-positive matrices are provided.

Enhancing Solar Radiation Forecasting in Diverse Moroccan Climate Zones: A Comparative Study of Machine Learning Models with Sugeno Integral Aggregation

Hourly solar radiation (SR) forecasting is a vital stage in the efficient deployment of solar energy management systems. Single and hybrid machine learning (ML) models have been predominantly applied for precise hourly SR predictions based on the pattern recognition of historical heterogeneous weather data. However, the integration of ML models has not been fully investigated in terms of overcoming irregularities in weather data that may degrade the forecasting accuracy. This study investigated a strategy that highlights interactions that may exist between aggregated prediction values. In the first investigation stage, a comparative analysis was conducted utilizing three different ML models including support vector machine (SVM) regression, long short-term memory (LSTM), and multilayer artificial neural networks (MLANN) to provide insights into their relative strengths and weaknesses for SR forecasting. The comparison showed the proposed LSTM model had the greatest contribution to the overall prediction of six different SR profiles from numerous sites in Morocco. To validate the stability of the proposed LSTM, Taylor diagrams, violin plots, and Kruskal–Wallis (KW) tests were also utilized to determine the robustness of the model’s performance. Secondly, the analysis found coupling the models outputs with aggregation techniques can significantly improve the forecasting accuracy. Accordingly, a novel aggerated model that integrates the forecasting outputs of LSTM, SVM, MLANN with Sugeno λ-measure and Sugeno integral named (SLSM) was proposed. The proposed SLSM provides spatially and temporary interactions of information that are characterized by uncertainty, emphasizing the importance of the aggregation function in mitigating irregularities associated with SR data and achieving an hourly time scale forecasting accuracy with improvement of 11.7 W/m2.

Admissible OWA operators for fuzzy numbers

Ordered Weighted Averaging (OWA) operators are some of the most widely used aggregation functions in classic literature, but their application to fuzzy numbers has been limited due to the complexity of defining a total order in fuzzy contexts. However, the recent notion of admissible order for fuzzy numbers provides an effective method to totally order them by refining a given partial order. Therefore, this paper is devoted to defining OWA operators for fuzzy numbers with respect to admissible orders and investigating their properties. Firstly, we define the OWA operators associated with such admissible orders and then we show their main properties. Afterward, an example is presented to illustrate the applicability of these AOWA operators in linguistic decision-making. In this regard, we also develop an admissible order for trapezoidal fuzzy numbers that can be efficiently applied in practice.

The Online Saddle Point Problem and Online Convex Optimization with Knapsacks

We study the online saddle point problem, an online learning problem where at each iteration, a pair of actions needs to be chosen without knowledge of the current and future (convex-concave) payoff functions. The objective is to minimize the gap between the cumulative payoffs and the saddle point value of the aggregate payoff function, which we measure using a metric called saddle point regret (SP-Regret). The problem generalizes the online convex optimization framework, but here, we must ensure that both players incur cumulative payoffs close to that of the Nash equilibrium of the sum of the games. We propose an algorithm that achieves SP-Regret proportional to [Formula: see text] in the general case, and [Formula: see text] SP-Regret for the strongly convex-concave case. We also consider the special case where the payoff functions are bilinear and the decision sets are the probability simplex. In this setting, we are able to design algorithms that reduce the bounds on SP-Regret from a linear dependence in the dimension of the problem to a logarithmic one. We also study the problem under bandit feedback and provide an algorithm that achieves sublinear SP-Regret. We then consider an online convex optimization with knapsacks problem motivated by a wide variety of applications, such as dynamic pricing, auctions, and crowdsourcing. We relate this problem to the online saddle point problem and establish [Formula: see text] regret using a primal-dual algorithm.

Classification aggregation without unanimity

A classification is a surjective mapping from a set of objects to a set of categories. A classification aggregation function aggregates every vector of classifications into a single one. We show that every citizen sovereign and independent classification aggregation function is essentially a dictatorship. This impossibility implies an earlier result of Maniquet and Mongin (2016), who show that every unanimous and independent classification aggregation function is a dictatorship. The relationship between the two impossibilities is reminiscent to the relationship between Wilson’s (1972) and Arrow’s (1951) impossibilities in preference aggregation. Moreover, while the Maniquet-Mongin impossibility rests on the existence of at least three categories, we propose an alternative proof technique that covers the case of two categories, except when the number of objects is also two. We also identify all independent and unanimous classification aggregation functions for the case of two categories and two objects.

Personalized neural network-based aggregation function in multi-criteria collaborative filtering

Modeling an effective aggregation function to improve the accuracy of recommendations remains an issue in model-based multi-criteria collaborative filtering (MCCF). The total-based aggregation function is efficient, but it lacks personalization. The user-based aggregation function is personal, but it faces computational and scalability issues. We propose a new personalized neural network-based aggregation function in MCCF to answer the challenges. We enhance the total-based aggregation function by considering not only criteria ratings but also dynamic personal features. The features are extracted from the user's rating history, including rating tendencies and experience. The empirical results of four real-world datasets confirmed the superiority of our method compared to baselines. It achieved the best ROC AUC for all data sets, with an average improvement of 12%. When recommending items with moderate likelihood to users, three out of four datasets witnessed an improvement of up to 6% in the macro F1-score. Additionally, for the most likely items, the macro F1-score increased by up to 12% in all datasets. These findings indicate that our approach has the potential to provide more effective and promising recommendations that are applicable in various domains. Furthermore, it can lead to higher user engagement and satisfaction, which also benefits businesses.

An Adaptive Spatio-temporal Global Sampling for Presentation Attack Detection

Without developing dedicated countermeasures, facial biometric systems can be spoofed with printed photos, replay attacks, silicone masks, or even a 3D mask of a targeted person. Thus, the threat of presentation attacks needs to be addressed to strengthen the security of the biometric systems. Since a 2D convolutional neural network (CNN) captures static features from video frames, the camera motion might hinders the performance of modern CNNs for video-based presentation attack detection (PAD). Inspired by the egomotion theory, we introduce an adaptive spatiotemporal global sampling (ASGS) technique to compensate the camera motion and use the resulting estimation to encode the appearance and dynamics of the video sequences into a single RGB image. This is achieved by adaptively splitting the video into small segments and capturing their global motion within each segment. The proposed global motion is estimated based on four key steps: dense sampling, FREAK feature extraction and matching, similarity transformation, and aggregation function. This allows using deep models pre-trained on images for video-based PAD detection. Moreover, the interpretation of ASGS reveals that the most important parts for supporting the decision on PAD are consistent with motion cues associated with the artifacts, i.e., hand movement, material reflection, and expression changes. Extensive experiments on four standard face PAD databases demonstrate its effectiveness and encourage further study in this domain.

The cost management of civil and agro-industrial construction project in the scope of information model

The necessary conditions for the existence of an effective cost management system of investment and construction projects are established in the article. Stated aim of the study is to develop methodological provisions of the cost engineering using information modeling technologies. The methodological blocks for parameterization, goal-setting and algorithmization of the information model of an investment and construction project are developed by the author. A list of aggregative cost parameters and an aggregative cost function of an investment and construction project, which is based on aggregative cost parameters, are presented. The processes of budgeting, control and managerial decision-making were considered by the author as functional blocks. The tasks of project budgeting in the scope of an information model, the comprehensive budget model of an investment and construction project and its system parameterization are presented in the article. The main provisions of project cost control and a list of basic cost indicators for control purposes are considered. The requirements of information modeling compatibility with the current subject activity and other software are determined. The author has developed the main provisions of project change management in the scope of information model and recommendations for rational making management decision. An algorithm for a decision-making regarding the realization of an investment and construction project is presented. The prospects of adaptive management of investment and construction projects particularly cost is determined and the vector model of the project behavior under the management action is developed. The main customer requirements to the information model of the investment and construction project are presented. The advantages of using the 5D model in the cost management system for the implementation of an investment and construction project are revealed.

Optimal utilization of multicore processors with PLINQ in .NET applications

This article explores the utilization of Parallel Language Integrated Query (PLINQ) as a powerful tool for enhancing the processing of large datasets through parallelism in .NET applications. PLINQ leverages the capabilities of modern multicore processors to accelerate data operations, thereby enabling developers to significantly reduce processing time while efficiently managing computational resources. The discussion begins with an overview of PLINQ’s integration within the .NET framework, emphasizing its ability to parallelize standard LINQ queries seamlessly. The article then delves into practical applications of PLINQ, illustrating through examples how it can optimize tasks such as financial data analysis and image processing. The core concepts and architecture of PLINQ, including its support for complex query capabilities and advanced aggregation functions, are examined to highlight how PLINQ manages data partitioning, load balancing, and thread safety. Further, the article addresses the strategic design considerations necessary for maximizing the efficiency of PLINQ, focusing on the importance of thoughtful system design to overcome potential limitations. Best practices for employing PLINQ are discussed to ensure optimal performance and effective use of parallel programming constructs.Finally, the conclusion underscores the significance of PLINQ in modern software development, particularly for applications that demand high-performance data processing capabilities. The article advocates for the strategic integration of PLINQ in developing applications that not only perform faster but are also scalable and robust, thereby meeting the challenges of processing large volumes of data in today’s computing environments.

Modular relaxed indistinguishability and the aggregation problem

<p>The notion of indistinguishability operator plays a central role in a large number of problems that arise naturally in decision-making, artificial intelligence, and computer science. Among the different issues studied for these operators, the aggregation problem has been thoroughly explored. In some cases, the notion of indistinguishability operator can be too narrow and, for this reason, we can find two different extensions of such notion in the literature. On the one hand, modular indistinguishability operators make it possible to measure the degree of similarity or indistinguishability with respect to a parameter. On the other hand, relaxed indistinguishability operators delete the reflexivity condition of classical indistinguishability operators. In this paper, we introduced the notion of modular relaxed indistinguishability operator unifying under the same framework all previous notions. We focused our efforts on the study of the associated aggregation problem. Thus, we introduced the notion of modular relaxed indistinguishability operator aggregation function for a family of t-norms extending the counterpart formulated for classical non-modular relaxed indistinguishability operators. We provided characterizations of such functions in terms of triangle triplets with respect to a family of t-norms. Moreover, we addressed special cases where the operators fulfill a kind of monotony and a condition called small-self indistinguishability. The differences between the modular and the non-modular aggregation problem were specified and illustrated by means of suitable examples.</p>

TVDO: Tchebycheff Value-Decomposition Optimization for Multiagent Reinforcement Learning.

In cooperative multiagent reinforcement learning (MARL), centralized training with decentralized execution (CTDE) has recently attracted more attention due to the physical demand. However, the most dilemma therein is the inconsistency between jointly-trained policies and individually executed actions. In this article, we propose a factorized Tchebycheff value-decomposition optimization (TVDO) method to overcome the trouble of inconsistency. In particular, a nonlinear Tchebycheff aggregation function is formulated to realize the global optimum by tightly constraining the upper bound of individual action-value bias, which is inspired by the Tchebycheff method of multiobjective optimization (MOO). We theoretically prove that, under no extra limitations, the factorized value decomposition with Tchebycheff aggregation satisfies the sufficiency and necessity of individual-global-max (IGM), which guarantees the consistency between the global and individual optimal action-value function. Empirically, in the climb and penalty game, we verify that TVDO precisely expresses the global-to-individual value decomposition with a guarantee of policy consistency. Meanwhile, we evaluate TVDO in the StarCraft multiagent challenge (SMAC) benchmark, and extensive experiments demonstrate that TVDO achieves a significant performance superiority over some SOTA MARL baselines.

Stochastically ordered aggregation operators

In aggregation theory, there exists a large number of aggregation functions that are defined in terms of rearrangements in increasing order of the arguments. Prominent examples are the Ordered Weighted Operator and the Choquet and Sugeno integrals. Following a probability approach, ordering random variables by means of stochastic orders can be also a way to define aggregations of random variables. However, stochastic orders are not total orders, thus pairs of incomparable distributions can appear. This paper is focused on the definition of aggregations of random variables that take into account the stochastic ordination of the components of the input random vectors. Three alternatives are presented, the first one by using expected values and admissible permutations, then a modification for multivariate Gaussian random vectors and a third one that involves a transformation of the initial random vectors in new ones whose components are ordered with respect to the usual stochastic order. A deep theoretical study of the properties of all the proposals is made. A practical example regarding temperature prediction is provided

Limit Theorems for Default Contagion and Systemic Risk

We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network subjected to an exogenous macroeconomic shock. We show that under certain regularity assumptions, the default cascade model can be transformed into a death process problem represented by a balls-and-bins model. We state various limit theorems regarding the final size of default cascades. Under appropriate assumptions on the degree and threshold distributions, we prove that the final sizes of default cascades have asymptotically Gaussian fluctuations. We next state limit theorems for different system-wide wealth aggregation functions, which enable us to provide systemic risk measures in relation to the structure and heterogeneity of the financial network. Lastly, we demonstrate how these results can be utilized by a social planner to optimally target interventions during a financial crisis given a budget constraint and under partial information of the financial network.