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Aggregation, as an operation of cartographic generalization, provides an effective means of abstracting the configuration of building features by combining them according to the scale reduction of the 2D map. Automating this design process effectively helps professional cartographers design both paper and digital maps, but finding the best aggregation result from the numerous combinations of building features has been a challenge. This paper presents a novel approach to assist cartographers in interactively designing the aggregation of building features in scale‐aware map visualization. Our contribution is to provide an appropriate set of candidates for the cartographer to choose from among a limited number of possible combinations of building features. This is achieved by collecting locally optimal solutions that emerge in the course of aggregation operations, formulated as a label cost optimization problem. Users can also explore better aggregation results by interactively adjusting the design parameters to update the set of possible combinations, along with an operator to force the combination of manually selected building features. Each cluster of aggregated building features is tightly enclosed by a concave hull, which is later adaptively simplified to abstract its boundary shapes. Experimental design examples and evaluations by expert cartographers demonstrate the feasibility of the proposed approach to interactive aggregation. [ABSTRACT FROM AUTHOR]

This paper aims to propose a novel multi‐attribute group decision‐making (MAGDM) method based on linguistic Pythagorean fuzzy copula extended power average operator. Existing researches under linguistic Pythagorean fuzzy environment lack of the ability to handle with extreme values and the flexible operational rules. To fill these two gaps, this paper first provides the definition of Archimedean copula and co‐copula operational rules under linguistic Pythagorean fuzzy environment, which can reflect the connection among arguments and provide more choices for experts to express their preferences. Then, we gather the extended power average (EPA) operator to present some new aggregation operators, which can reduce the negative influence of extreme evaluation values. To show the application of the proposed method to MAGDM problems, we apply it to handle a case of takeout O2O platform assessment problem. The numerical case and comparative analysis with other existing methods illustrate that our proposed method is more scientific and flexible. [ABSTRACT FROM AUTHOR]

Some decision‐making problems are required to be analysed using insufficient and vague information under an extended space of fuzziness, considering flexibility in the decision‐making process and the interdependency and interaction between the criteria. To tackle these challenges, a spherical fuzzy set (SFS), which is an extension of the ordinary picture fuzzy set (PFS), can be used to fulfil the requirement of an extended space of fuzziness by quantifying uncertainty. Similarly, the Frank operations can provide flexibility to the decision‐making process due to the involvement of a parameter, whereas the Choquet integral considers all possible interactive characteristics between different criteria. Therefore, this paper integrates these three important concepts to make more sound and realistic decisions by extending the existing arithmetic operation for spherical fuzzy numbers (SFNs) using Frank t‐norm and t‐conorm. In addition, the paper introduces some novel Choquet‐Frank aggregation operators, such as spherical fuzzy Choquet‐Frank averaging (SFCFA) and spherical fuzzy Choquet‐Frank geometric (SFCFG). To demonstrate the effectiveness of the proposed operators, a multi‐criteria decision making (MCDM) problem related to the selection of an enterprise resource planning (ERP) system is analysed for the available five options χ1,χ2,χ3,χ4, and χ5. Sensitivity analysis is performed to investigate the impact of taking variation in parameter values (θ) on aggregated values. Results confirmed that the best alternatives for SFCFA and SFCFG operators are χ3 and χ5, respectively, while χ2 is the worst alternative for both these operators. To show the effectiveness of the proposed operators, a comparative analysis has been performed to compare the results obtained from other existing aggregation operators. Results concluded that the findings resemble most of the existing operators which confirms the feasibility of the proposed operators. [ABSTRACT FROM AUTHOR]

The concept of importance of criteria is used as a central element in several decision making contexts, specifically in value aggregation, e.g. as an input to decision support tools. For example, in the analytic hierarchy process (AHP) decision makers are asked to estimate how much more important one criterion is than another. However, it is not clear how people understand aggregation models based on importance of criteria in decision making situations. The purpose of this descriptive study is to investigate if people find an aggregation model in simple value aggregation tasks which remind of the way AHP elicits the input. Further, the purpose is to investigate if people's tendency to find a model depends on their cognitive abilities. In an exploratory laboratory experiment, participants assessed which of two alternatives is the best, based on information about the importance of two criteria and how good the two alternatives are compared to each other with respect to these criteria. The results confirm that people are willing to use importance of criteria and goodness of alternatives as input in value aggregations and show three main models for aggregation. More participants with higher numeracy applied a clear model compared to those with lower numeracy. None of the identified models was one of AHP's models but one of them reminded of one of the ways input can be aggregated in the AHP. The three models identified in the experiment are based on lexicographic order, multiplication and a combination of multiplication and addition. How the results could be used in a prescriptive context is discussed in the paper. [ABSTRACT FROM AUTHOR]

This paper proposes a method for aggregating individual preferences in the context of uncertainty. Individuals are assumed to abide by Savage's model of Subjective Expected Utility, in which everyone has his/her own utility and subjective probability. Disagreement on probabilities among individuals gives rise to uncertainty at the societal level, and thus society may entertain a set of probabilities rather than only one. We assume that social preference admits a Maxmin Expected Utility representation. In this context, two Pareto-type conditions are shown to be equivalent to social utility being a weighted average of individual utilities and the social set of priors containing only weighted averages of individual priors. Thus, society respects consensus among individuals' beliefs and does not add ambiguity beyond disagreement on beliefs. We also deal with the case in which society does not rule out any individual belief. [ABSTRACT FROM AUTHOR]

This paper proposes a new family of intuitionistic fuzzy information aggregation operators for multiattribute decision making. Such aggregate operators provide an excellent complement to the existing ones. In this study, comparison with existing intuitionistic fuzzy aggregation operators is presented in detail. Properties and special cases of the proposed operators are investigated. Finally, we introduce an approach to intuitionistic fuzzy multiattribute decision making. An example of the recruitment of intern candidates is illustrated to show the feasibility and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is a powerful tool to handle two dimension phenomenon. Dombi operators with operational parameters have outstanding flexibility. This article presents certain aggregation operators under complex Pythagorean fuzzy environment, including complex Pythagorean Dombi fuzzy weighted arithmetic averaging (CPDFWAA) operator, complex Pythagorean Dombi fuzzy weighted geometric averaging (CPDFWGA) operator, complex Pythagorean Dombi fuzzy ordered weighted arithmetic averaging (CPDFOWAA) operator and complex Pythagorean Dombi fuzzy ordered weighted geometric averaging (CPDFOWGA) operator. Moreover, this paper explores some fundamental properties of these operators with appropriate elaboration. A decision‐making numerical example related to the selection of bank to purchase loan is given to demonstrate the significance of our proposed approach. Finally, a comparative analysis with existing operators is given to demonstrate the peculiarity of our proposed operators. [ABSTRACT FROM AUTHOR]

In this paper, we propose new fusion and selection approaches to accurately predict the remaining useful life. The fusion scheme is built upon the combination of outcomes delivered by an ensemble of Gaussian process regression models. Each regressor is characterized by its own covariance function and initial hyperparameters. In this context, we adopt the induced ordered weighted averaging as a fusion tool to achieve such combination. Two additional fusion techniques based on the simple averaging and the ordered weighted averaging operators besides a selection approach are implemented. The differences between adjacent elements of the raw data are used for training instead of the original values. Experimental results conducted on lithium‐ion battery data report a significant improvement in the obtained results. This work may provide some insights regarding the development of efficient intelligent fusion alternatives for further prognostic advances. [ABSTRACT FROM AUTHOR]

Purpose: Tortuosity of corneal nerve fibers acquired by in vivo Confocal Microscopy (IVCM) are closely correlated to numerous diseases. While tortuosity assessment has conventionally been conducted through labor‐intensive manual evaluation, this warrants an automated and objective tortuosity assessment of curvilinear structures. This paper proposes a method that extracts the image‐level features for corneal nerve tortuosity grading. Methods: For an IVCM image, all corneal nerve fibers are first segmented and then, their tortuosity are calculated by morphological measures. The ordered weighted averaging (OWA) approach, and the k‐Nearest‐Neighbor guided dependent ordered weighted averaging (kNNDOWA) approach are proposed to aggregate the tortuosity values and form a set of extracted features. This is followed by running the Wrapper method, a supervised feature selection, with an aim to identify the most informative attributes for tortuosity grading. Results: Validated on a public and an in‐house benchmark data sets, experimental results demonstrate superiority of the proposed method over the conventional averaging and length‐weighted averaging methods with performance gain in accuracy (15.44% and 14.34%, respectively). Conclusions: The simultaneous use of multiple aggregation operators could extract the image‐level features that lead to more stable and robust results compared with that using average and length‐weighted average. The OWA method could facilitate the explanation of derived aggregation behavior through stress functions. The kNNDOWA method could mitigate the effects of outliers in the image‐level feature extraction. [ABSTRACT FROM AUTHOR]

Due to the technological developments around the world, the amount of information that researchers work on increases continuously. This information density contains incomplete and uncertain data that cannot be fully expressed with crisp numbers. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are useful tools to manage such information, but these concepts use a symmetrical and uniform scale to express data, whereas real‐life problems contain nonsymmetrical and non‐uniform information. Intuitionistic multiplicative sets (IMSs) are effective tools for dealing with these real‐life problems. However, IMSs cannot handle real‐life problems completely because indeterminate information depends on membership and non‐membership information of IMSs, which is a restriction for decision makers and also for decision problems. To overcome this limitation, this paper generalizes the IMSs by using simplified neutrosophic set and introduces a novel approach that is called simplified neutrosophic multiplicative sets (SNMSs). Firstly, we define SNMS, show their set‐based operations, and then give a description of simplified neutrosophic multiplicative numbers (SNMNs). Based on SNMNs, we develop two simplified neutrosophic multiplicative aggregation operators on SNMNs that are called simplified neutrosophic multiplicative weighted arithmetic average operator and simplified neutrosophic multiplicative weighted geometric average operator. Furthermore, we define some simplified neutrosophic multiplicative distance measures. Finally, using a model based on water‐filling algorithm for determining criteria weights, we give a numerical example to demonstrate the effectiveness of the introduced concept with the proposed simplified neutrosophic multiplicative simplified neutrosophic multiplicative‐TODIM method. [ABSTRACT FROM AUTHOR]

In group decision-making situations, the decision-makers' opinions are generally characterized by subjectivity, imprecision and vagueness. Such opinions can be represented by fuzzy numbers such as positive trapezoidal fuzzy numbers. Several aggregation methods have been proposed previously; however, there are still deficits which limit their applications. This paper proposes an aggregation method based on centroid measurement which aims to overcome some of the shortcomings. In the paper, a number of axioms are proposed. A numerical example is given at the end to illustrate the application of the proposed aggregation method. [ABSTRACT FROM AUTHOR]

This paper considers a new approach to a priori sparsification of the sparsity pattern of the factorized approximate inverses (FSAI) preconditioner using the so-called vector aggregation technique. The suggested approach consists in construction of the FSAI preconditioner to the aggregated matrix with a prescribed sparsity pattern. Then small entries of the computed ‘aggregated’ FSAI preconditioning matrix are dropped, and the resulting pointwise sparsity pattern is used to construct the low-density block sparsity pattern of the FSAI preconditioning matrix to the original matrix. This approach allows to minimize (sometimes significantly) the construction costs of low-density high-quality FSAI preconditioners. Numerical results with sample matrices from structural mechanics and thin shell problems are presented. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Several aggregation methods, including the EKS, start by calculating bilateral Fisher indices. Prices and quantities are, however, subject to measurement error. This stochastic behavior, which implies both unequal variances, and non-zero correlations, between different Fisher indices, has to be taken into account if optimal estimates of aggregate PPPs are to be derived from the Fisher indices. This paper provides estimates of the variance/covariance structure of the Fisher indices, under two alternative models for stochastic variation at basic heading level: and it applies these formulae to the 1996 OECD data set, illustrating that the Fisher indices for this data set are indeed highly correlated. The paper also establishes a general theoretical result, proving that the EKS is optimal for a particular variance/covariance structure involving non-zero correlations, and hence shows that the standard EKS aggregation method is likely to be near optimal for the 1996 OECD data set. [ABSTRACT FROM AUTHOR]

To address the preferred and nonpreferred degrees of linguistic variables, this paper introduces intuitionistic linguistic preference relations (ILPRs) that apply intuitionistic linguistic variables (ILVs) to denote the decision makers' preferences. To judge the consistency of ILPRs, a consistent concept is introduced, and a consistency index is defined. When ILPRs are unacceptably inconsistent, a method to improve the consistency is introduced. Then, an approach to rank ILVs is introduced. In some situations where ILPRs might be incomplete, the consistency‐based linear programming model is constructed to evaluate the missing values. Considering group decision making, a group consensus index is defined, and its several desirable properties are discussed. Meanwhile, an acceptability‐based consistency and consensus approach is developed, and the associated example is offered to show the efficiency of the proposed procedure. [ABSTRACT FROM AUTHOR]

We address in this paper the problem of scoring alternatives when they are evaluated with respect to several criteria on a finite ordinal scale E. We show that in general, the ordinal scale E has to be refined or shrunk in order to be able to represent the preference of the decision maker by an aggregation operator belonging to the family of mean operators. This paper recalls previous theoretical results of the author giving necessary and sufficient conditions for a representation of preferences, and then focuses on describing practical algorithms and examples. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Microaggregation is a popular statistical disclosure control technique for continuous data. The basic principle of microaggregation is to group the observations in a data set and to replace them by their corresponding group means. However, while reducing the disclosure risk of data files, the technique also affects the results of statistical analyses. The paper deals with the impact of microaggregation on a multiple linear regression in continuous variables. We show that parameter estimates are biased if the dependent variable is used to form the groups. Using this result, we develop a consistent estimator that removes the aggregation bias, and derive its asymptotic covariance matrix. [ABSTRACT FROM AUTHOR]

This paper examines the impact of temporal aggregation on alternative definitions of inflation persistence. Using the CPI and the core PCE deflator of the United States, our results show that temporal aggregation from the monthly to the quarterly to the annual frequency induces persistence in the inflation series. [ABSTRACT FROM AUTHOR]

The present paper presents a generalised class of cost functions suitable for aggregation of firms and considers various flexible functional forms to assess whether they possess desirable aggregation properties. This set of cost functions includes two output functions and subsumes linear and non-linear cost functions employed in existing analyses. While the quadratic and the generalised Leontief and McFadden cost functions satisfy the generalised aggregation condition, the translog cost function and its variants are less capable of possessing desirable aggregation properties. A modified quasi-homothetic translog form is presented that is useful for aggregate analysis. Possible extensions of the generalised aggregation rule are discussed. [ABSTRACT FROM AUTHOR]

The focus of geographical studies in epidemiology has recently moved towards looking for effects of exposures based on data taken at local levels of aggregation (i.e. small areas). This paper investigates how regression coefficients measuring covariate effects at the point level are modified under aggregation. Changing the level of aggregation can lead to completely different conclusions about exposure–effect relationships, a phenomenon often referred to as ecological bias. With partial knowledge of the within-area distribution of the exposure variable, the notion of maximum entropy can be used to approximate that part of the distribution that is unknown. From the approximation, an expression for the ecological bias is obtained; simulations and an example show that the maximum-entropy approximation is often better than other commonly used approximations. [ABSTRACT FROM AUTHOR]

The low‐carbon development of integrated energy systems is achieved via the sharing of multiple energy interactions by park‐level IES (PIES).However, coordinating profit distribution conflicts among complex interactive stakeholders in stochastic scenarios is challenging. Accordingly, this study proposes a novel tri‐layer framework that aggregates different game mechanisms to investigate the interactions between PIESs and coupled energy markets. First, a linkage trading mechanism is proposed by integrating carbon emissions trading and green certificate trading, which establishes a coupled electricity‐carbon‐green certificate market. Consequently, a park aggregation operator acts as an intermediary between PIESs and the coupled market, setting upper‐level purchase and sale prices to guide unit generation in each PIES using the Stackelberg game theory. Subsequently, the Nash game theory is applied to realize cooperative bargaining among PIESs for a fair revenue distribution. Further, the impact of uncertain environments is considered by utilizing stochastic scenario methods and the conditional value‐at‐risk theory. To protect the privacy of each participating agent while improving the convergence speed, a differential evolutionary method is combined with analysis target cascading to solve the framework. Finally, the proposed scheduling method is validated by utilizing a typical case to optimize conflicting PIES interests in multiple scenarios and realize decarbonisation. [ABSTRACT FROM AUTHOR]

The employment of a decision support system for optimizing fund raising strategies is crucial to the management of non-profit organizations. Commonly considered methodologies utilize the organization's donor database in order to gather and analyse information. However, many organizations, especially small- and medium-sized ones, do not own or efficiently manage a database, and consequently, the usual methods are inapplicable. In this paper, a decision support system is developed that is able to identify the most promising fund raising strategies on the basis of the organization's profile. The profile factors of a non-profit organization are analysed and hierarchically organized in a decision tree in order to effectively employ the Choquet integral methodology, which is recommended in these kinds of multi-criteria decision problems. The results obtained in the real operational context show the effectiveness of the proposed system. [ABSTRACT FROM AUTHOR]

An aggregate signature scheme is a digital signature scheme that allows aggregation of n distinct signatures by n distinct users on n distinct messages. In this paper, we present an aggregate signcryption scheme (ASC) that is useful for reducing the size of certification chains (by aggregating all signatures in the chain) and for reducing message size in secure routing protocols. The new ASC scheme combines identity-based encryption and the aggregation of signatures in a practical way that can simultaneously satisfy the security requirements for confidentiality and authentication. We formally prove the security of the new scheme in a random oracle model with respect to security properties IND-CCA2, AUTH-CMA2, and EUF-CMA. [ABSTRACT FROM AUTHOR]

Feature analysis of weak nonlinear signals from geographic spatiotemporal data has received increasing attention. Most existing signal processing methods cannot effectively perform comprehensive feature analysis because of the multiple dimensions and unbalance of spatiotemporal data. We developed a divide–aggregate–explore method for the feature analysis of spatiotemporal data. In our method, strategies for dividing different dimensions are defined for multidimensional analysis, and the tensor–block structure is adopted to reorganize the original data and distinguish differences in dimensions. Then, information‐based data aggregation is used to weaken the impact of dimensional unbalance. Case studies based on climatic reanalysis field data released by the National Oceanic and Atmospheric Administration showed that the proposed method can effectively extract weak propagation signals such as the El Niño–Southern Oscillation and El Niño–Southern Oscillation Modoki. Our method can also reveal more detailed evolutionary characteristics of complex coupling systems in different dimensions compared with classical feature detection methods such as principal component analysis and tensor decomposition. Plain Language Summary: The accurate extraction and pattern analysis of nonlinear, weak, and quasiperiodic signals from geographic spatiotemporal data is an important research direction. However, since most geographic data often has strong spatial heterogeneity, existing signal processing methods cannot effectively perform comprehensive feature analysis owing to the multiple and unbalance of dimensions. This paper introduces the information‐based data aggregation to weaken the impact of dimensional unbalance and uses tensor analysis to conduct the multidimensional analysis. The experiment results verify the correctness and the advantages of our idea. We hope that our approach will provide you with an alternative method that deserves further study. Key Points: Multidimensional feature analysis reveals detailed evolutionary characteristics of complex coupling systemsInformation‐based data aggregation weakens the impact of dimension unbalanceThe proposed method can effectively extract weak propagation signals such as the El Niño–Southern Oscillation [ABSTRACT FROM AUTHOR]

SUMMARY This paper describes multilevel methods for the calculation of the stationary probability vector of large, sparse, irreducible Markov chains. In particular, several recently proposed significant improvements to the multilevel aggregation method of Horton and Leutenegger are described and compared. Furthermore, we propose a very simple improvement of that method using an over-correction mechanism. We also compare with more traditional iterative methods for Markov chains such as weighted Jacobi, two-level aggregation/disaggregation, and preconditioned stabilized biconjugate gradient and generalized minimal residual method. Numerical experiments confirm that our improvements lead to significant speedup, and result in multilevel methods that are competitive with leading iterative solvers for Markov chains. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Security quad and cube (SQC) is a network attack analyzer that is capable of aggregating many different events into a single significant incident and visualizing these events in order to identify suspicious or illegitimate behavior. A network administrator recognizes network anomalies by analyzing the traffic data and alert messages generated in the security devices; however, it takes a lot of time to inspect and analyze them because the security devices generate an overwhelming amount of logs and security events. In this paper, we propose SQC, an efficient method for analyzing network security through visualization. The proposed method monitors anomalies occurring in an entire network and displays detailed information of the attacks. In addition, by providing a detailed analysis of network attacks, this method can more precisely detect and distinguish them from normal events. [ABSTRACT FROM AUTHOR]

Reservation aggregation provides scalability to the IETF Integrated Services (IntServ) by reducing the high number of states stored at internal routers and the number of signaling messages processed at these routers. However, in the case of frequent joining and leaving of individual flows, the latter benefit will be lost due to frequent adjustment of aggregation size. In this paper, to reduce aggregation adjustment frequency, we focus on investigating two critical parameters: aggregation size and the lower threshold. We propose two policies to find out the optimal values of these criteria. One policy called Two Bounded operating Policy (TBP) is parameter-based policy and the other called Resource request Variance Policy (RVP) is measure-based policy. The calculation of these optimal values considers three costs: underutilization cost, signaling cost and holding cost. In our evaluation study, we compare the proposed two policies with two others, Temporal Operating Policy (TOP) and Cardinal Operating Policy (COP). This study shows that our mechanisms outperform the previous propositions in terms of cost and blocking ratio. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the effectiveness of two different Algebraic Multigrid (AMG) approaches to the solution of 4th-order discrete-difference equations for incompressible fluid flow (in this case for a discrete, scalar, stream-function field). One is based on a classical, algebraic multigrid, method (C-AMG) the other is based on a smoothed-aggregation method for 4th-order problems (SA-AMG). In the C-AMG case, the inter-grid transfer operators are enhanced using Jacobi relaxation. In the SA-AMG case, they are improved using a constrained energy optimization of the coarse-grid basis functions. Both approaches are shown to be effective for discretizations based on uniform, structured and unstructured, meshes. They both give good convergence factors that are largely independent of the mesh size/bandwidth. The SA-AMG approach, however, is more costly both in storage and operations. The Jacobi-relaxed C-AMG approach is faster, by a factor of between 2 and 4 for two-dimensional problems, even though its reduction factors are inferior to those of SA-AMG. For non-uniform meshes, the accuracy of this particular discretization degrades from 2nd to 1st order and the convergence factors for both methods then become mesh dependent. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

How to represent geographic space has long been an issue in location modelling. Facilities, demand and/or the region of interest are often abstracted using aggregated points. However, substantial errors can be introduced, and obtained solutions could be dependent on the degree of aggregation. To address this, geographic representation of space is undergoing renewed research interest in spatial analysis and modelling. In this article the maximal coverage problem is studied, with a particular focus on demand coverage representation. Due to the limitations of existing modelling approaches for examining the coverage of space, there exist significant discrepancies between what is modelled and actual geographic coverage. In order to accurately reflect the mechanism of maximal coverage for spatial objects (points, lines or polygons), we introduce a new model explicitly accounting for joint service provided by multiple facilities. The new model can be viewed as an extension of existing approaches, but also a generalisation. An application to warning siren siting is carried out to demonstrate the merits of this new approach. [ABSTRACT FROM AUTHOR]

Model simplification distils essential model structures that cause selected problems and increases the quality and understanding of models. It can also be a step towards building theory-like structures and general representations of case-specific problems in various application domains. In this paper, simplification of a large system dynamics model and validation of the simplified version are illustrated. The original model represents agricultural and environmental problems of irrigation development in southeast Turkey and consists of 14 model sectors and 110 stock variables. Its simplified version with a narrow model boundary and higher level of aggregation is a general representation of its selected dynamics and consists of four model sectors and 17 stock variables only. Analysis of reference behaviours, indirect structural validity tests (structure-oriented behaviour tests) and scenario runs reveal the simplified model as a valid and useful simplification of the original one. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of temporal aggregation when the aggregation frequency is variable and possibly stochastic. The results that we report include, as a particular case, the well-known results on fixed-interval aggregation, such as when monthly data are aggregated into quarters. A variable aggregation frequency implies that the aggregated process will exhibit time-varying parameters and non-spherical disturbances, even when these characteristics are absent from the original model. Consequently, we develop methods for specification and estimation of the aggregate models and show with an example how these methods perform in practice. [ABSTRACT FROM AUTHOR]

Dual hesitant q‐rung orthopair fuzzy (DHq‐ROF) set appears as a powerful tool in compare to other variants of fuzzy sets to deal with uncertainties associated with available information in various real‐life decision‐making cases. In order to make DHq‐ROF aggregation information process flexible, at first some operations viz., addition, multiplication, scalar multiplication, exponential laws based on Schweizer‐Sklar class of t‐conorms and t‐norms are defined. Subsequently, using these operations, weighted average and geometric operators and ordered weighted average and geometric operators are introduced. But weighted average or geometric operators and ordered weighted average or geometric operators consider only the weight of the opinions and the weight of the ordered position of each given opinion respectively. To resolve weights of the arguments, hybrid aggregation operators viz., DHq‐ROF Schweizer‐Sklar hybrid averaging, DHq‐ROF Schweizer‐Sklar hybrid geometric operators are developed and their properties are discussed. Afterwards, a new method to deal with multicriteria group decision making problems under DHq‐ROF environment is framed. To illustrate the proposed method a decision making problem related to investment company selection is considered and solved. To show the advantages of the proposed study, a comparative analysis among the developed and existing studies is discussed. [ABSTRACT FROM AUTHOR]

This article defines ranked soft sets and establishes their fundamental theory. This new model of uncertain knowledge is a non‐numerical yet powerful improvement of soft sets. The model relies on a qualitative improvement of the basic parameterized description posed by soft sets. We define relations between ranked soft sets and some existing models (N‐soft sets, fuzzy soft sets, probabilistic soft sets) that enhance the soft set spirit with the help of additional quantities. Primary contributions to their development include set‐theoretic operations and representation theorems, at a theoretical level; and scores and aggregation operators, at a practical level. Finally we design a multi‐person decision‐making strategy for data in the form of ranked soft sets that takes advantage of these elements. [ABSTRACT FROM AUTHOR]

This paper examines the effects of temporal aggregation on the estimated time series properties of economic data. Theory predicts that temporal aggregation loses information about the underlying data processes. We derive low frequency, quarterly and annual, models implied by high frequency, monthly, structural vector autoregressive (SVAR) models and we find that these losses in information are substantial. It is shown that the accuracy of both the estimates and the forecasts of this class of models improve substantially when monthly data are used. Moreover, the aggregated data show more long-run persistence than the underlying disaggregated data. [ABSTRACT FROM AUTHOR]

The aggregation procedure is a natural way to analyse signals which exhibit long-range-dependent features and has been used as a basis for estimation of the Hurst parameter, H. In this paper it is shown how aggregation can be naturally rephrased within the wavelet transform framework, being directly related to approximations of the signal in the sense of a Haar multiresolution analysis. A natural wavelet-based generalization to traditional aggregation is then proposed: ‘a-aggregation’. It is shown that a-aggregation cannot lead to good estimators of H, and so a new kind of aggregation, ‘d-aggregation’, is defined, which is related to the details rather than the approximations of a multiresolution analysis. An estimator of H based on d-aggregation has excellent statistical and computational properties, whilst preserving the spirit of aggregation. The estimator is applied to telecommunications network data. [ABSTRACT FROM AUTHOR]

The literature of multiple attribute decision making (MADM) is fruitful since there are various and successful applications of different fuzzy set extensions such as intuitionistic, Pythagorean and q‐Rung orthopair fuzzy sets (IFS, PFS and q‐ROFS). Besides their powerful aspects, some definitional limitations are known. In order to eradicate these boundaries regarding the definitions of membership and non‐membership degrees, linear Diophantine fuzzy set (LDFS) concept has been recently emerged. By considering two parameters, LDFS extends the representation area of the previous fuzzy set definitions and provides more extensive human judgement coverage field. In this study, the first distance and entropy measures in the literature have been developed for LDFSs. Their axiomatic definitions are given, and the proofs are shown. Also, thanks to our extensive literature review, we became aware that there is no MADM extension dedicatedly proposed for LDFS. So, the first MADM method extension for LDFS environment has also been developed in this study. A very well‐known MADM approach, TOPSIS, has been extended into LDFS environment for the first time in the literature. The applicability is shown in a healthcare management decision problem and the validity is checked and approved by comparing the alternative rankings LDF‐TOPSIS and the aggregation operators that were obtained from the literature produced. [ABSTRACT FROM AUTHOR]

The aim of the presented paper is to give a multiattribute decision making (MADM) method under the linguistic intuitionistic fuzzy (LIF) environment using the set pair analysis (SPA) theory. LIF set can express the qualitative information in terms of linguistic variables, whereas the connection number (CN) based on the "identity," "discrepancy," and "contrary" degrees of the SPA theory handles the uncertainties and certainties systems. On the basis of these features, we develop some series of linguistic CN (LCN) power weighted and ordered weighted geometric aggregation operator to aggregate the different LCNs. Several properties of the operators are also studied. Afterward, we present a novel MADM method to solve decision‐making problems under LIF set environment and illustrate with several examples to validate it. A comparative analysis is also presented to show the results. [ABSTRACT FROM AUTHOR]

In the age of mobile cloud computing, we are confronted by mobility, diversity of network access types, frequent network disconnection and poor reliability, and security with complex structures. Mobile cloud computing industry decision making is crucially important for countries or societies to enhance the effectiveness and validity of leadership, which can greatly expedite industrialized and large‐scale development. In the case of mobile cloud computing industry decision evaluation, the indispensable issue arises serious inexactness, fuzziness, and ambiguity. Single‐valued neutrosophic set, disposing the indeterminacy portrayed by truth membership T, indeterminacy membership I, and falsity membership F, is a more viable and effective means to seize indeterminacy. The main purpose of the current paper is to investigate the novel operations on single‐valued neutrosophic number (SVNN) based on Dombi Bonferroni mean (DBM) and Dombi geometric Bonferroni mean (DGBM) operator, which have the enormous advantage of high flexibility with adjustable parameters. Moreover, we employ the DBM operator to present single‐valued neutrosophic DBM (SVNDBM) operator, single‐valued neutrosophic weighted DBM (SVNWDBM) operator, single‐valued neutrosophic DGBM (SVNDGBM), operator and single‐valued neutrosophic weighted DGBM (SVNWDGBM) operator for disposing with the aggregation of SVNNs and develop two multiple attribute decision making methods based on SVNWDBM and SVNWDGBM. The validity of algorithms are illustrated by a mobile cloud computing industry decision making issue, along with the sensitivity analysis of diverse parameters on the ranking. Finally, a comparison of the developed with the existing single‐valued neutrosophic decision making methods has been executed for displaying their effectiveness. [ABSTRACT FROM AUTHOR]

In this article, we introduce dual hesitant q‐rung orthopair fuzzy 2‐tuple linguistic set (DHq‐ROFTLS), a new strategy for dealing with uncertainty that incorporates a 2‐tuple linguistic term into dual hesitant q‐rung orthopair fuzzy set (DHq‐ROFS). DHq‐ROFTLS is a better way to deal with uncertain and imprecise information in the decision‐making environment. We elaborate the operational rules, based on which, the DHq‐ROFTL weighted averaging (DHq‐ROFTLWA) operator and the DHq‐ROFTL weighted geometric (DHq‐ROFTLWG) operator are presented to fuse the DHq‐ROFTL numbers (DHq‐ROFTLNs). As Maclaurin symmetric mean (MSM) aggregation operator is a useful tool to model the interrelationship between multi‐input arguments, we generalize the traditional MSM to aggregate DHq‐ROFTL information. Firstly, the DHq‐ROFTL Maclaurin symmetric mean (DHq‐ROFTLMSM) and the DHq‐ROFTL weighted Maclaurin symmetric mean (DHq‐ROFTLWMSM) operators are proposed along with some of their desirable properties and some special cases. Further, the DHq‐ROFTL dual Maclaurin symmetric mean (DHq‐ROFTLDMSM) and weighted dual Maclaurin symmetric mean (DHq‐ROFTLWDMSM) operators with some properties and cases are presented. Moreover, the assessment and prioritizing of the most important aspects in multiple attribute group decision‐making (MAGDM) problems is analysed by an extended novel approach based on the proposed aggregation operators under DHq‐ROFTL framework. At long last, a numerical model is provided for the selection of adequate medication to control COVID‐19 outbreaks to demonstrate the use of the generated technique and exhibit its adequacy. Finally, to analyse the advantages of the proposed method, a comparison analysis is conducted and the superiorities are illustrated. [ABSTRACT FROM AUTHOR]

Accurate prediction of long‐term and short‐term clean energy production is the basis for understanding short‐term clean energy supply capacity, long‐term clean energy development trend and evaluating the effect of energy policies. However, under the circumstances of the large time span, the insufficient data samples and the periodic characteristics of seasonal clean energy production make the traditional grey prediction model prone to produce forecasting deviations. Given this situation, a novel seasonal fractional‐order full‐order time power discrete grey prediction model is initially proposed to deal with long‐term clean energy production sequences featured with nonlinearity and periodicity. Based on the proposed model, we also propose a data‐based algorithm to select the model structure adaptively. To prove the practicability of the new model for nonlinear long‐term development trend, monthly periodic time series and quarterly periodic time series, this article uses the new model to predict annual hydropower capacity in North America, monthly natural gas production in China and quarterly solar power generation in China. And the prediction results are compared with the existing grey models and non‐grey prediction models. Different methods including GM (1,1), DGM (1,1), NGM (1,1), ARGM (1,1), ENGM (1,1), Verhulst, CCRGM (1,1), FOTP‐DGMr (1,1), PFSM (1,1), Holt‐winters model, SARIMA model, SGM, HP‐GM and DGGM are used as benchmarks. In experiments, the MAPE of the proposed model is 2.92%, 2.43%, and 7.87%, respectively. The results of empirical analysis indicate that the proposed model generally outperform the benchmark model as it can well capture nonlinear long‐term development trend and seasonal characteristics. [ABSTRACT FROM AUTHOR]

SUMMARY We found characteristics that can help us predict the convergence or divergence of iterative aggregation-disaggregation methods. We provided two results for spectral radii of asymptotic error propagation matrices: (i) the spectral radius is bounded by unity for symmetric Markov chains and (ii) the spectral radius can be arbitrarily large for a certain class of sparse Markov chains. Surprisingly, permuting states of cyclic Markov chains by algorithms usually used for reducing bandwidth of matrices leads to the latter case. We proposed a sorting method that prevents divergence for this class of Markov chains.Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Predictive models based on the Choquet integral have been applied successfully in machine learning and multi criteria decision making context. The ability of the Choquet integral to recognize and capture non‐linear dependencies and its comprehensibility make it a very appealing tool. Yet, its complexity is often an obstacle to estimate model parameters in the presence of a large number of attributes. The other concern is the so‐called numerical instability, that is, learning the Choquet integral for a high degree of complexity exhibits a numerical instability. This study addresses complexity reduction and presents a novel algorithm in order to enhance the quality of optimization results and computational efficiency of learning predictive models underlying the Choquet integral. [ABSTRACT FROM AUTHOR]

The multiple attribute decision‐making models are empowered with the support of fuzzy sets such as intuitionistic, q‐rung orthopair, Pythagorean, and picture fuzzy sets, and also neutrosophic sets, etc. These concepts generate varying representation opportunities for the decision‐maker's preferences and expertise. Pythagorean and Fermatean fuzzy sets are special cases of q‐rung orthopair fuzzy set when q = 2 and q = 3, respectively. From a geometric perspective, the latter provides a broader representation domain than the former does. In this study, the emerging concept of Fermatean fuzzy set is studied in detail and three well‐known multi‐attribute evaluation methods, namely SAW, ARAS, and VIKOR are extended under Fermatean fuzzy environment. In this manner, the decision‐makers will have more freedom in specifying their preferences, thoughts, and expertise, and the abovementioned decision approaches will be able to handle this new type of data. The applicability of the propositions is shown in determining the best Covid‐19 testing laboratory which is an important topic of the ongoing global health crisis. To validate the proposed methods, a benchmark analysis covering the results of the existing Fermatean fuzzy set‐based decision methods, namely TOPSIS, WPM, and Yager aggregation operators is presented. [ABSTRACT FROM AUTHOR]

Complex spherical fuzzy set, an extended version of spherical fuzzy set, is a very powerful tool to capture fourfold information (typically yes, no, abstain and refusal), in which the range of degrees occurs in the complex plane with unit disk. Through this prominent feature, complex spherical fuzzy sets outperform earlier concepts of fuzzy sets and their extensions. This research article utilizes complex spherical fuzzy sets and prioritized weighted aggregation operators to construct the complex spherical fuzzy prioritized weighted averaging/geometric operators. We present their most noticeable properties. Further, we establish a decision‐making approach that takes full advantage of the aforesaid operators. To explore their superiority and applicability in decision making, we apply our algorithm to a numerical example. Finally, we compare this decision‐making approach with prevailing methods in this context. [ABSTRACT FROM AUTHOR]

This paper specifies and empirically analyzes a continuous-time, linear-quadratic, representative consumer model with time-nonseparable preferences of several forms. Within this framework I show how time aggregation and time nonseparabilities in preferences over consumption streams can interact. The behavior of both seasonally adjusted and unadjusted consumption data is consistent with time-nonseparable preferences if consumption goods are durable and if individuals develop habit over the flow of services from the good. The data do not support a version of the model that ignores time nonseparabilities in preferences and focuses solely upon time aggregation. [ABSTRACT FROM AUTHOR]

This paper presents the problem of aggregation over individual agents as a basic identification problem inherent to interpreting relationships between averaged economic variables. The concept of a complete aggregation structure is introduced, which embodies the correct condition for identification. Several examples of complete aggregation structures are provided by previous work on the aggregation problem in economics. Examples are also provided by work on complete distribution families in statistics, which in turn provide the correct conceptual framework for developing a theory of parameter estimation and tests of specific aggregation assumptions. The potential lack of correspondence between microeconomic behavior and estimated relations between averaged data is illustrated by distribution families obeying linear probability movement, which induce an extreme failure of the completeness property. Certain topics regarding empirical applications of aggregation results are reviewed. [ABSTRACT FROM AUTHOR]

Animal social networks are often used to describe dynamic social systems, where individual behaviour generates network‐level structures that subsequently influence individual‐level behaviour. This interdependence between individual behaviour and group structuring is of central concern for questions concerning the evolution and development of social systems and collective animal behaviour more generally.Various statistical methods exist for estimating network changes through time. One approach, time‐aggregated networks, takes repeated snapshots of interactions within windows of time to generate a time series of networks. However, there remain many analytical hurdles when implementing the time‐aggregated approach. To ameliorate this, we introduce an r package netTS that focuses on three analytical steps for analysing time‐aggregated networks: choosing appropriate time scale using bootstrapping, comparing patterns to relevant null models using permutation and finally building and interpreting statistical models using simulated data. We use simulated data to first highlight these steps, then use observed grooming data from a group of vervet monkeys as an applied example.Our results suggest that the use of bootstrapping and permutation can accurately extract known patterns from simulated data. Using this approach with vervet data suggests that there is consistent social structuring, differing from what would be expected due to chance, and that some individuals are contributing to this structure more than others (i.e. keystone individuals).We demonstrate that bootstrapping, permutation and simulation can aid in constructing and interpreting time‐aggregated networks. We suggest that the use of time‐aggregated networks to quantify patterns of network change can be a useful tool alongside process‐based approaches that seek mechanistic descriptions. Ultimately, by looking at both patterns and processes, dynamic networks can be used to better understand how individual behaviour generates social structures, and in turn how individual behaviour can be influenced by social structures, ultimately leading to a better understanding of the evolution of social behaviour. [ABSTRACT FROM AUTHOR]

The interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS) and complex fuzzy set (CFS) are two generalizations of the fuzzy set (FS) to cope with uncertain information in real decision making problems. The aim of the present work is to develop the concept of complex interval‐valued q‐rung orthopair fuzzy set (CIVq‐ROFS) as a generalization of interval‐valued complex fuzzy set (IVCFS) and q‐rung orthopair fuzzy set (q‐ROFS), which can better express the time‐periodic problems and two‐dimensional information in a single set. In this article not only basic properties of CIVq‐ROFSs are discussed but also averaging aggregation operator (AAO) and geometric aggregation operator (GAO) with some desirable properties and operations on CIVq‐ROFSs are discussed. The proposed operations are the extension of the operations of IVq‐ROFS, q‐ROFS, interval‐valued Pythagorean fuzzy, Pythagorean fuzzy (PF), interval‐valued intuitionistic fuzzy, intuitionistic fuzzy, complex q‐ROFS, complex PF, and complex intuitionistic fuzzy theories. Further, the Analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) method are also examine based on CIVq‐ROFS to explore the reliability and proficiency of the work. Moreover, we discussed the advantages of CIVq‐ROFS and showed that the concepts of IVCFS and q‐ROFS are the special cases of CIVq‐ROFS. Moreover, the flexibility of proposed averaging aggregation operator and geometric aggregation operator in a multi‐attribute decision making (MADM) problem are also discussed. Finally, a comparative study of CIVq‐ROFSs with pre‐existing work is discussed in detail. [ABSTRACT FROM AUTHOR]

In this work, we present conditions to obtain a global‐in‐time existence of solutions to a class of nonlinear viscous transport equations describing aggregation phenomena in biology with sufficiently small initial data in Besov‐Morrey spaces and gradient potential as a Radon measure. We also study the self‐similarity and asymptotic stability of solutions at large times. [ABSTRACT FROM AUTHOR]

Summary Clustering is one of the essential operations in wireless sensor network (WSN) to ensure organized data aggregation followed by energy efficiency. However, obtaining optimal clustering performance is yet an unsolved problem in WSN. Review of existing approaches towards cluster optimization shows that effective balance between energy efficiency and topology control is still missing. Therefore, the proposed system presents a unique topology control mechanism using a novel concept of interstellar orientation toward optimizing the clustering performance in WSN. Adopting an analytical research methodology, the proposed system introduces two interstellar‐based topology control system, which targets the maximum saving of resource consumption of the cluster head. The simulated outcome of the study shows that the proposed topology control system offers significant energy conservation performance in comparison to the existing hierarchical clustering scheme in WSN. [ABSTRACT FROM AUTHOR]

Thus far, limited research has been performed on resilient supplier selection—a problem that requires simultaneous consideration of a set of numerical and linguistic evaluation criteria, which are substantially different from traditional supplier selection problem. Essentially, resilient supplier selection entails key sourcing decision for an organization to gain competitive advantage. In the presence of multiple conflicting evaluation criteria, contradicting decision makers, and imprecise decision‐relevant information (DRI), this problem becomes even more difficult to solve with the classical optimization approaches. Possibility distribution‐based multicriteria decision analysis (MCDA) is a viable alternative approach for handling inherent uncertainty of imprecise DRI associated with the evaluation offered by a group of contradicting decision makers. However, prior research focusing on MCDA‐based supplier selection problem has been lacking in the ability to provide a seamless integration of numerical and linguistic evaluation criteria along with the consideration of multiple decision makers. To address these challenges, we present a comprehensive decision‐making framework for ranking a set of suppliers from resiliency perspective. The proposed algorithm is capable of leveraging imprecise and aggregated DRI obtained from crisp numerical assessments and reliability adjusted linguistic appraisals from a group of decision makers. We adapt two popular tools—single‐valued neutrosophic sets (SVNS) and interval‐valued fuzzy sets (IVFS)—and for the first time, extend them to incorporate both crisp and linguistic evaluations in a group decision‐making platform to obtain aggregated SVNS and IVFS decision matrixes. This information is then used to rank the resilient suppliers by using technique for order preference by similarity to an ideal solution method. We present a case study to illustrate the mechanism of the proposed algorithm. A sensitivity analysis demonstrates the strength of the proposed algorithm to generate alternative ranking scheme with respect to the shifting priorities of evaluation criteria and shows the reliability of the decision‐making framework. [ABSTRACT FROM AUTHOR]