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Accurate freight volume forecasts play a crucial role in supporting regional economies and transportation systems. Nevertheless, the majority of previous studies rely on historical data, which poses challenges in promptly capturing the influence of market changes and emergency situations. To address this challenge, a novel prediction model based on the Baidu search index (BSI) and emergency is proposed, which comprises four distinct stages. In the first stage, we gathered the Baidu search index data and the COVID-19 index to furnish comprehensive, interactive, and timely information for the primary freight volume dataset. In the second stage, seasonal-trend decomposition procedures based on loess (STL) and empirical mode decomposition (EMD) are used to reduce data complexity. Additionally, we utilized boxplot to identify outliers in the remainder component. In the third stage, we employed seasonal naive prediction to forecast the seasonal component, while utilizing a genetic algorithm optimized backpropagation neural network (GABP) to predict other sub-sequences. To improve the prediction accuracy, we applied BPNN for error correction. Finally, to evaluate the performance of the proposed model, China's freight volume is selected as the subject of the study. The results demonstrate that the model incorporating BSI and COVID-19 information can effectively establish a dynamic forecasting system for freight volume. Furthermore, the data preprocessing techniques employed in this study successfully reduce data complexity and enhance the accuracy of prediction. In comparative experiments, the proposed model has been demonstrated to outperform all the contrasted models in terms of forecasting accuracy. [ABSTRACT FROM AUTHOR]

Multiplicative probabilistic linguistic preference relation (MPLPR) has been widely used by decision-makers (DMs) to tackle group decision-making (GDM) problems. However, due to the complexity of the decision-making circumstance and individual subjectivity of DMs, they often provide inconsistent MPLPRs which often lead to unreasonable decision results. To solve this problem, this paper investigates a novel approach to GDM with MPLPRs based on consistency improvement and upgraded multiplicative data envelopment analysis (DEA) cross-efficiency. First, the concept of sequential consistency of MPLPR is defined. Then, a consistency improvement algorithm is proposed, which can convert any unacceptable consistent MPLPR into an acceptable one. Furthermore, we use geometric averages to transform MPLPR into multiplicative preference relation (MPR). Meanwhile, considering the conservative psychology of DMs, an upgraded multiplicative DEA cross-efficiency model based on the pessimistic criterion is constructed, which can derive the priority vector of MPLPR. Therefore, we can obtain the rational ranking results for all alternatives. Finally, a case analysis of emergency logistics under COVID-19 is provided to illustrate the validity and applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

Due to the complexity of the actual group decision-making environment, the probabilities with real values provided by multiplicative probabilistic linguistic term sets may not accurately reflect the decision maker's perspective on practical issues. To solve this issue, we first propose the multiplicative interval-probabilistic linguistic term set and multiplicative interval-probabilistic linguistic preference relation. It is widely acknowledged that group decision-making results derived from preference relations lacking an acceptable level of consistency are often considered unreasonable. Therefore, an optimal consistency adjustment strategy based on the prioritization algorithm is proposed to obtain the acceptable consistent multiplicative interval-probabilistic linguistic preference relations. Then, to derive the objective weights of decision makers, we design a nonlinear programming model based on the novel trust relationship. Furthermore, considering the benevolent mentality of decision makers, the benevolent multiplicative data envelopment analysis cross-efficiency model, which aims to minimize the sum of deviations between other decision-making units and the ideal point, is constructed to obtain the ranking of all alternatives. Finally, we give a case study on the branch location selection of a new energy vehicle company to demonstrate the validity of our suggested method. The merits of our proposed group decision-making method are validated through comparative analysis and discussion. [ABSTRACT FROM AUTHOR]

A city is a carrier of the development of human society; the higher the resilience of a city is, the better it can resist invasion from the outside. Therefore, the evaluation factors affecting resilient cities are of great practical significance in the study of resilient cities. The assessment method with hesitant fuzzy linguistic preference relation (HFLPR) has recently widely used in evaluation problems. However, some existing priority vector solving methods in the assessment method often ignore much decision-making information. Therefore, the aim of this paper is to present a new priority vector solving method for HFLPR by integrating data envelopment analysis (DEA) cross-efficiency and a distance-based priority aggregation (DPA) model. The innovation of this method contains: (1) DEA model is introduced to solve the priority vector of linguistic preference relation (LPR); (2) a DPA model is constructed to obtain the HFLPR's priority vector, which can avoid the loss of decision-making information. For completely additive consistent LPR and incompletely additive consistent LPR, an output-oriented DEA model and DEA cross-efficiency model are introduced to derive its priority vector, respectively. An HFLPR is viewed as being composed of many LPRs, a DPA model is constructed based on the L2 norm to find the priority vector of HFLPR that minimizes the distance among the LPRs' priority vectors. Based on the above, an integrated group decision-making method is proposed and then applied to an illustrative example of the evaluation factors affecting resilient cities to show its performance and advantages by comparing with the existing methods. [ABSTRACT FROM AUTHOR]

Accurate crude oil price forecasting is crucial for maintaining energy economy stability and enhancing investment and operational decision-making. Nowadays, the link prediction model for crude oil prices based on a complex network model has become an emerging and promising approach. However, existing link prediction methods are unable to extract complex information about interval-valued crude oil prices, and fail to consider the impact of multi-source information. Therefore, this paper proposes the link prediction model for interval-valued crude oil prices using complex network and multi-source information, which converts crude oil price interval series into complex networks. Through link prediction, it takes into account both the impact of past interval-crude oil prices on future interval time series and the interference of external real-time information on interval-valued prices. First, news headlines and geopolitical risk indices related to crude oil prices are captured, and search index data and news sentiment scores associated with interval data are analyzed. Subsequently, the interval sequence data and related influencing factors are decomposed and reconstructed respectively. The reconstructed interval center and radius sequence are then converted into a directed network, and node similarity in the network is calculated to generate similar nodes of the interval subsequence as feature values. Finally, multiple machine learning models are employed to acquire the optimal weighted combination prediction with interval prediction values. According to the experimental data, this approach outperforms other benchmark methods in terms of prediction accuracy. • Predictive modeling to transform interval-valued into complex networks is proposed. • A link prediction model based on multi-source information is constructed. • Combining AI, link prediction, and complex networks forms a multidisciplinary mothed. • The proposed model is well validated in predicting interval WTI crude oil prices. • The constructed model can effectively extract multi-scale data features. [ABSTRACT FROM AUTHOR]

Accurate crude oil price forecasting is crucial for maintaining energy economy stability and enhancing investment and operational decision-making. Nowadays, the link prediction model for crude oil prices based on a complex network model has become an emerging and promising approach. However, existing link prediction methods are unable to extract complex information about interval-valued crude oil prices, and fail to consider the impact of multi-source information. Therefore, this paper proposes the link prediction model for interval-valued crude oil prices using complex network and multi-source information, which converts crude oil price interval series into complex networks. Through link prediction, it takes into account both the impact of past interval-crude oil prices on future interval time series and the interference of external real-time information on interval-valued prices. First, news headlines and geopolitical risk indices related to crude oil prices are captured, and search index data and news sentiment scores associated with interval data are analyzed. Subsequently, the interval sequence data and related influencing factors are decomposed and reconstructed respectively. The reconstructed interval center and radius sequence are then converted into a directed network, and node similarity in the network is calculated to generate similar nodes of the interval subsequence as feature values. Finally, multiple machine learning models are employed to acquire the optimal weighted combination prediction with interval prediction values. According to the experimental data, this approach outperforms other benchmark methods in terms of prediction accuracy. • Predictive modeling to transform interval-valued into complex networks is proposed. • A link prediction model based on multi-source information is constructed. • Combining AI, link prediction, and complex networks forms a multidisciplinary mothed. • The proposed model is well validated in predicting interval WTI crude oil prices. • The constructed model can effectively extract multi-scale data features. [ABSTRACT FROM AUTHOR]

Large-scale group decision-making (LSGDM) deals with complex decision- making problems which involve a large number of decision makers (DMs). Such a complex scenario leads to uncertain contexts in which DMs elicit their knowledge using linguistic information that can be modelled using different representations. However, current processes for solving LSGDM problems commonly neglect a key concept in many real-world decision-making problems, such as DMs' regret aversion psychological behavior. Therefore, this paper introduces a novel consensus based linguistic distribution LSGDM (CLDLSGDM) approach based on a statistical inference principle that considers DMs' regret aversion psychological characteristics using regret theory and which aims at obtaining agreed solutions. Specifically, the CLDLSGDM approach applies the statistical inference principle to the consensual information obtained in the consensus process, in order to derive the weights of DMs and attributes using the consensus matrix and adjusted decision-making matrices to solve the decision-making problem. Afterwards, by using regret theory, the comprehensive perceived utility values of alternatives are derived and their ranking determined. Finally, a performance evaluation of public hospitals in China is given as an example in order to illustrate the implementation of the designed method. The stability and advantages of the designed method are analyzed by a sensitivity and a comparative analysis. [ABSTRACT FROM AUTHOR]

This study designs a novel decision support model to address group decision-making (GDM) problems with Pythagorean fuzzy linguistic information. To do so, a new concept of Pythagorean fuzzy linguistic preference relations (PFLPRs) is first introduced to describe fuzzy and uncertain information, where the Pythagorean fuzzy linguistic values (PFLVs) are represented by the linguistic membership degree and linguistic non-membership degree. Then, we also give the definitions of multiplicative consistency of PFLPRs, consistency index (CI), individual consensus degree (IGD) and group consensus degree (GCD). Subsequently, a consistency-adjustment approach is proposed to convert unacceptable multiplicative consistent PFLPRs into acceptable ones, as well as, derive the optimal normalized Pythagorean fuzzy priority weight vector (PFPWV) for alternatives. Furthermore, we design two algorithms in group decision support model. The first algorithm is used to check the multiplicative consistency of original PFLPRs and transform the unacceptable multiplicative consistent PFLPRs into the acceptable ones. The second algorithm is designed to aid the GCD to achieve the predefined level. The most innovative features of the proposed decision support model are following two points. One is that the GCD reaches the predefined level, while each PFLPR still keeps multiplicative consistency. The other is that it can preserve decision makers' original preference information as much as possible. Finally, we give a numerical example to illustrate validity and practicality of this proposed approach. [ABSTRACT FROM AUTHOR]

It is widely accepted that an effective carrier-selective contact is indispensable for high performance crystalline silicon (c-Si) solar cells. However, the properties of these carrier-selective contact materials significantly differ from c-Si in terms of band gap, work function, lattice constant. Consequently, this gives rise to challenges such as band discontinuity and suspended bonds at the interface, which subsequently impact the specific carrier transport process and potentially lead to a reduction primarily in the fill factor at the device level. Titanium nitride (TiN) and titanium oxynitride (TiOxNy) have been employed as an electron-selective contact in both c-Si and perovskite solar cells, demonstrating their effectiveness in enhancing the performance of these devices. Based on the detailed characterizations of the band alignment, the carrier transport mechanisms are analyzed using multiple models, and the theoretical results are basically self-consistent through the verification of variable temperature experiments. These analytical methods can also provide solutions for analyzing the band structure and transport mechanism of diverse heterojunctions, ultimately contributing to the design and optimization of semiconductor heterojunction devices. Carrier-selective contact technology plays a critical role in achieving high-performance photovoltaic devices, but intrinsic limitations within this widely used technology limit further advances in efficiency. Using a combination of experimental characterization, theoretical modeling, and variable temperature experiments, the authors investigate carrier transport mechanisms in silicon heterojunction solar cells and determine that thermal emission dominates the carrier transport process in TiN/n-Si heterojunction. [ABSTRACT FROM AUTHOR]

Faced with complex decision problems, distribution linguistic preference relation (DLPR) is an effective way for decision-makers (DMs) to express preference information. However, due to the complexity of the decision-making environment, DMs may not be able to provide complete linguistic distribution for all linguistic terms in DLPRs, which results in incomplete DLPRs. Therefore, in order to solve group decision-making (GDM) with incomplete DLPRs, this paper proposes expected consistency-based model and multiplicative DEA cross-efficiency. For a given incomplete DLPRs, we first propose an optimization model to obtain complete DLPR. This optimization model can evaluate the missing linguistic distribution and ensure that the obtained DLPR has a high consistency level. And then, we develop a transformation function that can transform DLPRs into multiplicative preference relations (MPRs). Furthermore, we design an improved multiplicative DEA model to obtain the priority vector of MPR for ranking all alternatives. Finally, a numerical example is provided to show the rationality and applicability of the proposed GDM method. [ABSTRACT FROM AUTHOR]

Considering the influence of undesirable outputs in environmental assessments of the practical production process, this paper proposes a DEA cross-efficiency method and fuzzy preference relation based on semi-disposability of undesirable outputs for environmental assessments, which combines self-evaluation with peer-evaluation and avoids potentially unrealistic weighting scheme. We first develop a new input-oriented DEA model based on semi-disposability of undesirable outputs. Then, the corresponding DEA cross-efficiency method is proposed to evaluate the homogeneous decision-making units (DMUs) and the additive fuzzy preference relation is constructed using the DEA cross-efficiency scores. An output-oriented DEA model is adopted to derive the priority vector from the constructed additive fuzzy preference relation. Furthermore, we summarize the specific procedures for environmental assessments based on DEA cross-efficiency and fuzzy preference relation. Finally, the practical example of industrial environment assessment of the Yangtze River Economic Belt is provided to show the applicability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes an integrated approach to group decision making with interval fuzzy preference relations using data envelopment analysis (DEA) and stochastic simulation. A novel output-oriented CCR DEA model is proposed to obtain the priority vector for the consistency fuzzy preference relation, in which each of the alternatives is viewed as a decision-making unit. Meanwhile, we design a consistency adjustment algorithm for the inconsistent fuzzy preference relation. Furthermore, we build an optimization model to get the weights of each fuzzy preference relation based on maximizing group consensus. Then, an input-oriented DEA model is introduced to obtain the final priority vector of the alternatives. Finally, a stochastic group preference analysis method is developed by analyzing the judgments space, which is carried out by Monte Carlo simulation. A numerical example demonstrates that the proposed method is effective. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new triangular fuzzy series combination forecasting method based on triangular fuzzy discrete difference equation forecasting model and PSO-SVR, and use the developed forecasting method to power load forecasting. First, we propose a triangular fuzzy discrete difference equation (TFDDE) forecasting model to predict the triangular fuzzy series, which can accurately predict the fluctuating trend and is suitable for small sample data. Then, the support vector regression optimized by particle swarm optimization (PSO-SVR) is adopted to further improve the forecast result of TFDDE forecasting model, in which the parameters of support vector regression are optimally obtained by particle swarm optimization algorithm so as to avoid the blindness of artificial selection. Finally, the practical example of load forecasting of US PJM power market is employed to illustrate the proposed forecasting method. The experimental results show that the proposed forecasting method produces much better forecasting performance than some existing triangular fuzzy series models. The proposed combination forecasting method, which fully capitalizes on the time series forecasting model and intelligent algorithm, makes the triangular fuzzy series prediction more accurate than before and has good applicability. This is the first attempt of employing discrete difference equation theory for the triangular fuzzy series forecasting. [ABSTRACT FROM AUTHOR]

The accurate forecasting of electric vehicles (EVs) sales is crucial for reasonably deploying charging infrastructure, improving industrial policies, and securing energy supply for transportation systems. However, most of the forecasting models are based on historical sales data, which results in a certain lag. Although some researchers further consider exploiting the Internet Search Index with high dimensions, they often ignore the extraction of nonlinear features in the process of dimension reduction. Therefore, a novel combination forecasting model based on multi-angle feature extraction and sentiment analysis is proposed. First, we collect Internet search index, online reviews, and sales volume data, thereby considering real-time information. Second, sentiment analysis is adopted to quantify online reviews. Meanwhile, a multi-angle feature extraction method is developed, which can extract the multi-frequency features from the Internet search index. Third, the decomposition methods are performed on the sequences. Finally, EVs sales prediction results are obtained through combination forecasting. To verify the effectiveness and stability of the proposed model, four groups of comparison experiments are conducted. As shown in the empirical results, the proposed model has higher prediction accuracy, which indicates that multi-source information fusion and multi-angle feature extraction enhance the forecasting performance and adaptability of the model. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of operators called the ordered quasi-modular averaging (OQMA) operators based on the ordered modular averaging (OMA) operators. It is shown that the OQMA operators are monotonic, bounded, idempotent, commutative and quasi-comonotone modular. Moreover, we introduce the generalized ordered modular averaging (GOMA) operator, which is a special case of the OQMA operator. Some special cases of the GOMA operator are discussed. An orness measure to reflect the or-like degree of the GOMA operator is proposed. We further extend the GOMA operator to the generalized ordered hybrid modular (GOHM) operator, which focuses not only on the degree of importance with respect to input arguments but also their serial positions. Finally, a new method based on the GOHM operator for multi-attribute group decision making is presented and a numerical example shows that the developed approach is feasible. [ABSTRACT FROM AUTHOR]

Accurate carbon price forecasting is essential to reduce carbon dioxide emissions and slow down global warming. However, a key issue in the carbon trading market is the diversity and uncertainty of external factors. Some studies began to focus on the impact of a single external factor, but few of them considered the application of multi-source information on carbon prices. In addition, the selection of the decomposition method is still controversial, making carbon price forecasting inefficient and unstable. Therefore, this paper proposes a carbon price forecasting method based on multi-source information fusion (MSIF) and hybrid multi-scale decomposition (HMSD). First, MSIF can provide complete, interactive, and timely information for raw carbon prices, including historical data, influencing factors (coal prices, oil prices), and unstructured data (Baidu index, social media sentiment). Second, HMSD is used to completely extract the internal features of multi-source information and avoid the problem of decomposition method selection. Third, due to the linear and nonlinear characteristics of carbon prices, a combination strategy based on Holt, ARIMA, SVR, BPNN, and LSTM can achieve satisfactory results. Finally, to evaluate the effectiveness of the proposed framework, seven types of comparative experiments (based on historical data, influencing factors, Baidu index, and sentiment analysis) are carried out. The results show that MSIF is superior to single-source information in improving carbon price forecasting performance. Furthermore, the HMSD is stronger than the single multi-scale decomposition method in information extraction. Therefore, the proposed hybrid framework is a state-of-the-art carbon price forecasting approach. [ABSTRACT FROM AUTHOR]

Exploring the influence of atmospheric turbulence on remote sensing based on filament-induced fluorescence is still challenging. In this study, we applied artificial turbulence during remote filamentation and recorded the enhanced backward fluorescence of nitrogen. At the strongest turbulence, the nitrogen fluorescence signal was higher than that obtained when no turbulence was applied. The air turbulence introduces random noise in the laser profile, which is subsequently amplified by self-focusing effect and causes multiple filamentation. Moreover, by lowering the threshold for multiple filaments generation, turbulence led to an increase in the number of filaments, thereby enhancing fluorescence. [ABSTRACT FROM AUTHOR]

In this paper, we develop the generalized linguistic weighted logarithm averaging (GLWLA) operator and the generalized linguistic ordered weighted logarithm averaging (GLOWLA) operator in the group decision making under the linguistic surrounding. Then some properties of the families of the GLOWLA operator by different weighting vector are investigated. Furthermore, we present the generalized linguistic ordered weighted hybrid logarithm averaging (GLOWHLA) operator, which extends the GLOWLA operator. We also construct a nonlinear goal programming model to determine GLOWHLA weights from observational linguistic variable values under partial weight information. Finally, a numerical example is given to illustrate the new approach to evaluating university faculty for tenure and promotion, which indicates the feasibility and effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

Harmonic mean is suitable to aggregate negative indicators. In order to improve the flexibility of harmonic mean for modeling many situations, the ordered weighted harmonic averaging (OWHA) operator is extended to provide a new class of operators called the generalized OWHA (GOWHA) operators, and investigate some desirable properties of them. When different parameter of the GOWHA operator is employed, various conventional aggregation operators can be deduced, such as the ordered weighted averaging (OWA) operator and the ordered weighted geometric averaging (OWGA) operator. We further demonstrate that the OWHA operator and the GOWHA operator exhibit monotonicity with respect to the weighting vector. Furthermore, we introduce the generalized hybrid harmonic averaging (GHHA) operator, which can reflect the importance degrees of both the given arguments and the ordered position of the arguments. Finally, a new approach on the basis of the GHHA operator is presented in an example of an investment project with group decision making. [ABSTRACT FROM AUTHOR]

• The interval-valued carbon price forecasting model is proposed. • A hybrid interval multi-scale decomposition method is developed. • Combination strategies can capture the complex features of carbon prices. • The proposed approach can improve the forecasting accuracy significantly. Forecasting carbon price accurately is of great significance to ensure the healthy development of the carbon market. However, due to the non-linearity, non-stationarity, and dynamic uncertainty of interval-valued carbon price, there are many challenges to forecast the interval-valued carbon price precisely and stably. Therefore, this paper proposes a combination forecasting model based on the hybrid interval multi-scale decomposition method and its application to forecasting interval-valued carbon prices. First, three interval multi-scale decomposition methods, including interval discrete wavelet transform method (IDWT), interval empirical mode decomposition method (IEMD), and interval variational mode decomposition method (IVMD), are developed to decompose the interval-valued carbon price into interval trend and residuals. Second, Generalized autoregressive conditional heteroskedasticity (GARCH), auto-regressive integrated moving average model (ARIMA), support vector regression model (SVR), backpropagation neural network (BPNN), and long short-term memory networks (LSTM) are used to forecast the interval trend and residuals. Third, through interval-valued reconstruction, the results of each single forecasting model for three different decomposition methods are obtained respectively. Finally, the combination forecasting results are obtained by the LSTM, which is employed as an ensemble tool. The empirical analysis results show that our proposed model is significantly superior to some benchmark models in terms of accuracy and stability, and is an effective model for forecasting interval-valued carbon prices. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Quasi-OWA operator to the case in which the input argument is a continuous valued interval and present the continuous Quasi-OWA (C-QOWA) operator, which generalizes a wide range of continuous operators such as the continuous ordered weighted averaging (C-OWA) operator, the continuous generalized OWA operator (C-GOWA) and the continuous generalized ordered weighted logarithm aggregation (C-GOWLA) operator. Then an orness measure to reflect the or-like degree of the C-QOWA operator is proposed. Moreover, some desirable properties of the C-QOWA operator associated with its orness measure are investigated. In addition, we apply the C-QOWA operator to the aggregation of multiple interval arguments and obtain the weighted C-QOWA operator, the ordered weighted C-QOWA (OWC-QOWA) operator, the combined C-QOWA (CC-QOWA) operator. Finally, a CC-QOWA operator-based approach for multi-attribute group decision making problem is presented, and a numerical example shows that the developed approach is feasible and the results are credible. [ABSTRACT FROM AUTHOR]

• Two axiomatic notions for information measures are introduced. • Two novel methods for information measures are established. • A convergent group consensus reaching process is developed. • An empirical application is provided to show the advantages. For practical group decision-making (GDM) problems, DMs play varying degrees of importance. Thus, determining the weight of decision makers (DMs) is one of the key issues in GDM. Additionally, it is known that information measures methods have been a growing focus in recent years. Therefore, under the probabilistic linguistic fuzzy information environment, a group consensus reaching approach with the help of information measures is designed. First, two axiomatic notions regarding to entropy and similarity measures for probabilistic linguistic term sets (PLTSs) are introduced. Then, in line accordance with logarithmic function, two novel methods of entropy and similarity measures with PLTSs are established, which is followed by the determination of the weight vector of DMs by using probabilistic linguistic fuzzy entropy. Subsequently, based on probabilistic linguistic fuzzy entropy and similarity measures, we develop a group consensus reaching process (CRP), which is convergent and able to enhance the group consensus level. Moreover, the proposed group CRP can calculate the weight vector with the initial probabilistic linguistic evaluation information of DMs. Finally, for displaying the applicability and merits of the developed group CRP, the numerical example, sensitivity analysis and comparative analysis are provided. It's worth noting that our proposed measure fully utilizes the elements of the original probabilistic linguistic preference relationships (PLPRs), which can reduce the systematic error of the entire decision model, thereby making the results more reflective of the original decision information from DMs. The novelties of this paper are as follows: (1) The proposed novel way can estimate the degree of importance of DMs by the mean fuzzy entropy of PLPRs; (2) We construct two formulas about fuzzy entropy and similarity measures for PLTSs and proof these formulas, which are both reasonable and effective. [ABSTRACT FROM AUTHOR]

The filamentation process under atmospheric turbulence is critical to its remote-sensing application. The effects of turbulence intensity and location on the spatial distribution of femtosecond laser filaments in the air were studied. The experimental results show that the nonlinear effect of the filament can restrain the beam wander. When the turbulence intensity was 3.31 × 10 − 13   cm − 2 / 3 , the mean deviation of the wander of the filament center was only 27% of that of the linear transmitted beam. The change in turbulence location would lead to a change in the standard deviation of the beam centroid drift. Results also show that the filament length would be shortened, and that the filament would end up earlier in a turbulent environment. Since the filamentation-based LIDAR has been highly expected as an evolution multitrace pollutant remote-sensing technique, the study promotes our understanding of how turbulence influences filamentation and advances atmospheric remote sensing by applying a filament. [ABSTRACT FROM AUTHOR]

Probabilistic linguistic term set (PLTS) is highly useful for decision-makers (DMs) to describe qualitative and uncertain information in the decision-making process. This paper proposes a novel probabilistic linguistic decision-making method with consistency improvement algorithm and data envelopment analysis (DEA) cross-efficiency. Firstly, we put forward the concept of order consistency of probabilistic linguistic preference relation (PLPR). The order consistency is helpful for DMs to make quick and efficient decision in certain situations. Then, based on the defined multiplicative consistency of PLPR, we develop a consistency improvement algorithm to transform the unacceptable multiplicative consistent PLPRs into the acceptable ones. Furthermore, a DEA model is established to derive the priority weight vector of alternatives from the acceptable multiplicative consistent PLPR. Meanwhile, for the alternatives that have equal priority weights, we use a DEA cross-efficiency model to further differentiate and obtain the final ranking of alternatives. Finally, a numerical example of emergency logistics distribution selection is given to illustrate the effectiveness and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

The conventional approaches to constructing Prediction Intervals (PIs) always follow the principle of 'high coverage and narrow width'. However, the deviation information has been largely neglected, making the PIs unsatisfactory. For high-risk forecasting tasks, the cost of forecast failure may be prohibitive. To address this, this work introduces a multi-objective loss function that includes Prediction Interval Accumulation Deviation (PIAD) within the Lower Upper Bound Estimation (LUBE) framework. The proposed model can achieve the goal of 'high coverage, narrow width, and small bias' in PIs, thus minimizing costs even in cases of prediction failure. A salient feature of the LUBE framework is its ability to discern uncertainty without explicit uncertainty labels, where the data uncertainty and model uncertainty are learned by Deep Neural Networks (DNN) and a model ensemble, respectively. The validity of the proposed method is demonstrated through its application to the prediction of carbon prices in China. Compared with conventional uncertainty quantification methods, the improved interval optimization method can achieve narrower PI widths. [ABSTRACT FROM AUTHOR]

With the rapid increase in efficiency of organic-inorganic hybrid solar cells of Si-poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS), their poor stability has become an important factor limiting its further development. Here, we demonstrate that the moisture in the air is the main cause for the performance degradation of the hybrid heterojunction solar cells (HHSCs) and innovatively discovered the effect of the Ag electrodes on the degradation of HHSCs. When exposed to air, the growth of the thin oxide layer on the interface of n-Si/PEDOT:PSS and the formation of silver sulfide (Ag 2 S) on the Ag/PEDOT:PSS interface together caused the increase in the series resistance (Rs) of the HHSCs. The increase in Rs decreases the fill factor (FF) of the HHSCs and thus leads to the degradation of the cell performance. • The moisture in the air is the main cause for the performance degradation of the PEDOT:PSS/Si hybrid heterojunction solar cells. • The effect of the Ag electrode on the performance degradation is investigated. • The formation of Ag 2 S on the Ag/PEDOT:PSS interface caused the increase of R s and thus leads to the degradation of the cell performance. [ABSTRACT FROM AUTHOR]

As one of the most useful tools, fuzzy preference relations (FPRs) can cope with the situations in which the experts are more comfortable providing their evaluation information with numerical values. Consistency-improving process and deriving the reliable priority weight vector for alternatives are two significant and challenging issues in decision making with FPRs. This paper investigates a novel decision-making model with FPRs on the basis of consistency local adjustment strategy and data envelopment analysis (DEA). Firstly, a new approach is proposed to generate the multiplicative consistent FPRs. Subsequently, a convergent consistency-improving algorithm for FPRs is developed to transform the unacceptable multiplicative consistent FPRs into the acceptable ones. In the consistency-improving process for FPRs, the local adjustment strategy is presented to employ decision-maker original evaluation information sufficiently. In order to determine the priority weight vector for alternatives, a novel fuzzy DEA model is constructed. Furthermore, a decision-making model with FPRs is designed to derive the reliable decision-making results. Finally, a numerical example of selecting the most important influence factor for fog–haze is provided, and the comparison with existing approaches is made to validate the rationality and effectiveness of the developed model. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a multi-attribute group decision making (MAGDM) with picture fuzzy sets based on ELECTRE TRI method, i.e., an ELECTRE TRI based group decision making with picture fuzzy information is given. The MAGDM with picture fuzzy information based on picture fuzzy ELECTRE TRI outranking method is divided into three stages, i.e., the group decision information aggregation stage, determination of parameters and ELECTRE TRI outranking based outranking stage. A novel comparison law for picture fuzzy sets is introduced. In the group decision information aggregation stage, the concept of picture fuzzy normalized weighted Bonferroni mean (PFNWBM) is developed. The developed decision procedure is further applied to the assessment of energy security. The numerical example shows that the developed group decision procedure is feasible and valid. [ABSTRACT FROM AUTHOR]

Recently, graph-based neural networks have been investigated in hyperspectral image (HSI) classification to address the limited global feature representation capability issue of HSI classification methods based on convolutional neural networks (CNN). However, most of the existing graph-based neural networks for HSI classification methods either characterize the relation information by the pair-wise modeling or rely on the CNNs to extract the local spectral–spatial features. To solve this problem, in this paper, a concise hypergraph convolutional network (HGCN) is proposed for semi-supervised HSI classification. To effectively and efficiently capture the global and local features of HSI, the hypergraph model is established on superpixel level which characterizes the spectral affinities rather than the spatial distance. The designed hypergraph model not only incorporates the local homogeneity and complex correlations of HSI but also consumes little computation. Two hypergraph convolution layers are designed to propagate and update the features of nodes. To construct an end-to-end architecture, a mapping matrix is defined for pixels encoding and superpixels decoding. The proposed method is hinged on the goodness the clustering algorithm used in superpixel segmentation and the experiments has shown that the clustering algorithm affects the effectiveness of proposed method. Thus, we give a strategy for selecting the segmentation parameter. The comparison experiments conducted on four real-world benchmark HSI data sets demonstrate that the proposed method provides more stable and effective classification performance than some state-of-the-art deep approaches with very limited training samples. The overall accuracies are 95.42% on Indian Pines, 98.48% on Kennedy Space center, 98.23% on Salinas Valley and 96.91% on Pavia University. [ABSTRACT FROM AUTHOR]

Interval type-2 trapezoidal fuzzy (IT2TrF) number is a powerful tool to depict fuzzy information. Information measures methods have received more and more attention in recent years as they play an important role in decision-making theory. A new multi-attribute decision-making (MADM) method supported by IT2TrF information measures is investigated in this paper under the IT2TrF information environment. Firstly, three axiomatic definitions of IT2TrF information measures are introduced, which include information entropy, similarity measure and cross-entropy. Secondly, with the help of the exponential function, we formulate some information measure formulas, which are followed by the proofs that the exponential entropy, exponential similarity measure and exponential cross-entropy fit the three axiomatic definitions. Subsequently, a novel IT2TrF MADM method is designed, in which the IT2TrF exponential entropy and cross-entropy are utilized to generate the attribute weights, the IT2TrF exponential similarity measure is employed to obtain the closeness degree of the ideal solution and derive the most satisfying solution. Lastly, we provide a numerical example of corporate investment to demonstrate the applicability and feasibility of the proposed MADM method. The robustness and merits of the developed MADM method are highlighted by the comparative analysis. [ABSTRACT FROM AUTHOR]

Complex and uncertain decision-making environment increasingly requires the collaborations of participants, the exchange and interaction of knowledge of different actors can effectively promote and improve the decision-making process. Collaborative decision-making (CDM), a prevailing decision-making method, is extensively studied by scholars, in which different actors can communicate mutually and then reach a common goal. Hence, in view of the advantages and usefulness of CDM, an overview is conducted for showing the state of the art of CDM, pointing out the current issues and indicating the future research directions. To achieve those goals, firstly, the bibliometric analysis is implemented to briefly review the previous research topics. Then, the definitions, comparisons, weights and consensus concerning CDM are recalled, which are followed by the summarization of methodologies used for solving CDM problems. Subsequently, the current research directions and popular application areas are highlighted. Finally, the challenges and potential research directions are concluded from five perspectives. • The main research topics of CDM is explored with bibliometric analysis. • The main research contents and approaches of CDM are summarized. • The current research directions of CDM are presented. • The popular application areas of CDM are summarized. • The limitations and future research directions of CDM are pointed out. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate a novel approach to group decision making (GDM) based on multiplicative DEA cross-efficiency and stochastic acceptability analysis with hesitant fuzzy linguistic preference relations (HFLPRs), which can avoid information distortion and obtain more credible decision-making results. First, a transform function is defined, which can extract effective information of the hesitant fuzzy linguistic term set (HFLTS) sufficiently. Then, an optimization model is proposed to derive the occurring probabilities of the elements in the HFLTS. It can avoid the normalization process of HFLPRs and simulate the element-selection process of decision makers (DMs). Moreover, a Maximum Log DEA Cross Efficiency model is proposed to evaluate the relative efficiency of each alternative from HFLPR. We further develop the stochastic weight space acceptability analysis method to solve the GDM problem and a step-by-step procedure is presented. Finally, numerical examples are given to illustrate the validity and applicability of the proposed method. This is the first attempt of employing the multiplicative DEA cross-efficiency to the GDM with HFLPRs. [ABSTRACT FROM AUTHOR]

Representing features at multiple scales is of great significance for hyperspectral image classification. However, the most existing methods improve the feature representation ability by extracting features with different resolutions. Moreover, the existing attention methods have not taken full advantage of the HSI data, and their receptive field sizes of artificial neurons in each layer are identical, while in neuroscience, the receptive field sizes of visual cortical neurons adapt to the neural stimulation. Therefore, in this paper, we propose a Res2Net with spectral-spatial and channel attention (SSCAR2N) for hyperspectral image classification. To effectively extract multi-scale features of HSI image at a more granular level while ensuring a small amount of calculation and low parameter redundancy, the Res2Net block is adopted. To further recalibrate the features from spectral, spatial and channel dimensions simultaneously, we propose a visual threefold (spectral, spatial and channel) attention mechanism, where a dynamic neuron selection mechanism that allows each neuron to adaptively adjust the size of its receptive fields based on the multiple scales of the input information is designed. The comparison experiments on three benchmark hyperspectral image data sets demonstrate that the proposed SSCAR2N outperforms several state-of-the-art deep learning based HSI classification methods. [ABSTRACT FROM AUTHOR]

K -means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to the non-convexity of the model formulations, expectation-maximization (EM) type algorithms converge to different local optima with different initializations. Recent discoveries have identified that the global solution of K -means cluster centroids lies in the principal component analysis (PCA) subspace. Based on this insight, we propose PCA-guided effective search for K -means. Because the PCA subspace is much smaller than the original space, searching in the PCA subspace is both more effective and efficient. Extensive experiments on four real world data sets and systematic comparison with previous algorithms demonstrate that our proposed method outperforms the rest as it makes the K -means more effective. [ABSTRACT FROM AUTHOR]

With the acceleration of urban modernization, the temporal variability in air pollution has become increasingly significant. Predicting average daily pollutant concentrations no longer suffices for decision-making in public health and environmental management. Therefore, this paper proposes the TCN-LSTM-Attn model, a hybrid PM 2.5 interval concentration prediction model based on decomposition reconstruction and attention mechanism. Firstly, the interval grey incidence analysis (IGIA) and the bivariate ensemble empirical mode decomposition (BEEMD) algorithm were respectively used for feature selection affecting PM 2.5 concentration and decomposition of input variables. Subsequently, considering the uneven distribution of components in various influencing factors and the high computational complexity of the model, an interval reconstruction coefficient (RCI) and evolutionary clustering algorithm (ECA) effectively clustered these components. Finally, the proposed TCN-LSTM-Attn model generated the corresponding prediction results. An empirical study evaluated the model using air quality datasets from three environmental monitoring sites in different geographical locations in Beijing. The evaluation results demonstrated that compared to the benchmark interval prediction models, the model proposed in this paper exhibited substantial improvements across all five interval evaluation criteria, with average reductions of 15.19%, 15.30%, 32.07%, 16.63%, and 33.87%, respectively. These results highlight superior performance in terms of prediction accuracy and stability across the board. The integrated attention mechanism hybrid model proposed in this paper supports routine urban air quality warnings. • The interval-value PM 2.5 decomposition and reconstruction methods are studied. • The TCN-LSTM-Attn model is proposed to enhance the precision of PM 2.5. • The proposed model considers the factors influencing PM 2.5 concentration. • The proposed model outperforms several benchmark models in empirical analysis. [ABSTRACT FROM AUTHOR]

We develop a new distance measure called the continuous ordered weighted distance (COWD) measure by using the continuous ordered weighted averaging (COWA) operator in the interval distance. We study some properties and different families of the COWD measure. We further generalize the COWD measure. The prominent characteristics of the COWD measure are that it is not only a generalization of some widely used distance measures and the continuous generalized OWA operator, but also it can deal with interval deviations in aggregation on interval arguments by using a controlled parameter. The desirable characteristics make the COWD measure be suitable to wide range situations, such as decision making, engineering and economics. In the end, we develop the new approach to group decision making in investment selection. [ABSTRACT FROM AUTHOR]

In this paper, we present a new operator called the generalized ordered weighted multiple averaging (GOWMA) operator based on a minimization problem with penalty function, which unifies the geometric mean and the generalized ordered weighted averaging operator with the generalized ordered weighted harmonic averaging operator in the same formulation. We study different properties and families of the GOWMA operator and develop a generalization of this operator called the generalized hybrid multiple averaging operator. To determine the GOWMA operator weights, we propose the generalized least squares method which does not follow a regular distribution. Finally, we give a numerical example of an investment selection to illustrate the application of the GOWMA operator to multiple attribute group decision making. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a new operator called the generalized ordered weighted logarithmic proportional averaging (GOWLPA) operator based on an optimal model, which is an extension of the generalized ordered weighted logarithm averaging (GOWLA) operator. The key advantage of the GOWLPA operator is not only that it is an aggregation operator with theoretic basis on aggregation, but also that the weighting vector of the GOWLPA operator depends on the input arguments. We analyze some properties and families of the GOWLPA operator and further develop generalizations of this operator including the generalized hybrid logarithmic proportional averaging (GHLPA) operator and the quasi ordered weighted logarithmic proportional averaging (QOWLPA) operator. To determine the GOWLPA operator weights, we propose the generalized logarithm chi-square method (GLCSM) which does not follow a regular distribution. Finally, we give a numerical example of an investment selection to illustrate the application of the GOWLPA operator to multiple attribute group decision making. [Copyright &y& Elsevier]

Abstract: We present a new aggregation operator called the generalized ordered weighted exponential proportional averaging (GOWEPA) operator, which is based on an optimal model. We study some properties and different families of the GOWEPA operator. We also generalize the GOWEPA operator. The key advantage of the GOWEPA operator is that it is an aggregation operator with theoretic basis on aggregation. Moreover, we propose an orness measure of the GOWEPA operator and indicate some properties of this orness measure. Furthermore, we introduce the least exponential squares method (LESM) to determine the GOWEPA operator weights based on its orness measure. In the end, we develop an application of the new approach in a case of group decision making in investment selection. [Copyright &y& Elsevier]

The development of distribution linguistic provides a new research idea for linguistic information group decision-making (GDM) problems, which is more flexible and convenient for experts to express their opinions. However, in the process of using distribution linguistic fuzzy preference relations (DLFPRs) to solve linguistic information GDM problems, there are few studies that pay attention to both internal consistency adjustment and external consensus of experts. Therefore, this study proposes a fresh decision support model based on consistency adjustment algorithm and consensus adjustment algorithm to solve GDM problems with distribution linguistic data. Firstly, we review the concept of DLFPRs to describe the fuzzy linguistic evaluation information, and then we present the multiplicative consistency of DLFPRs and a new consistency measurement method based on the distance, and investigate the consistency adjustment algorithm to ameliorate the consistency level of DLFPRs. Subsequently, the consensus degree measurement is carried out, and a new consensus degree calculation method is put forward. At the same time, the consensus degree adjustment is taken the expert cost into account to make it reach the predetermined level. Finally, a distribution linguistic fuzzy group decision making (DLFGDM) method is designed to integrate the evaluation linguistic elements and obtain the final evaluation information. A case of the evaluation of China's state-owned enterprise equity incentive model is provided, and the validity and superiority of the proposed method are performed by comparative analysis. [ABSTRACT FROM AUTHOR]

In the context of small sample and poor information, the data often change rapidly and interact with multiple factors which make it a challenge to analyse and predict multivariate sequences efficiently. Due to the fact that real systems usually show fractional order characteristics, the aim of this paper is to consider the approach improving the forecast results of multivariate interval grey prediction model via exploiting fractional accumulation. Noting that fractional accumulation could disturb the exponential law, the connotation prediction method is introduced to balance the disturbance. Correspondingly, a fractional connotation prediction method is constructed. In addition, traditional background value coefficient is optimized by using the particle swarm optimization algorithm (PSO). Therefore, a multivariate interval grey fractional accumulative connotation prediction model with optimized background value coefficient is constructed, in which the interval grey number time series are transformed into kernel series and radius series. Finally, the developed model is applied to clean energy prediction in China to verify the feasibility and validity. [Display omitted] • A multivariate interval grey prediction model via fractional accumulation is bulit. • The dynamic background value is optimized by integral mean value theorem and PSO. • The developed model is applied to model clean energy datum in China. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a novel type of soft set called basic uncertain information soft set (BUISS), which combines the notion of basic uncertain information and soft set theory. Since basic uncertain information can measure the quality of datum by using the degree of certainty, the developed BUISS provides a novel extension of soft set. In this paper, set operations and comparison law of basic uncertain information are also developed. Then, operations on BUISSs include set operations, 'AND' operation and 'OR' operation are defined. Besides, the Jaccard similarity between two BUISSs is introduced. The properties of the operations and similarity measure are studied. Theoretically, a multi-criteria group decision making (MAGDM) problem under basic uncertain information environment is analysed by using BUISSs. Two decision algorithms based on level BUISS and the aggregation of ϵ -approximate elements are proposed. Finally, an assessment of natural gas security in China is investigated to illustrate the feasibility and validity of the developed decision approaches. • Introducing set operations of basic uncertain information and their properties. • Developing a novel soft set called basic uncertain information soft set by combining the concept of basic uncertain information and soft set. • Proposing the set operations and similarity between basic uncertain information soft sets. • Developing two multi-criteria group decision making algorithms. [ABSTRACT FROM AUTHOR]

• A unified validity index framework for the hierarchical clustering is proposed. • The deficiencies of the measurements in the existing validity indexes are improved. • The incompatibility of similarity between the clustering and validation is solved. • The proposed indexes can handle various sorts of data sets. Clustering validation and identifying the optimal number of clusters are of great importance in expert and intelligent systems. However, the commonly used similarity measures for validating are not versatile to measure the complex data structure, in reality, some of which are not as effective as that of the used clustering algorithm which gives the clustering results. This paper studies the validity indexes for the hierarchical clustering algorithm and proposes a unified validity index framework. For the single-linkage agglomerative hierarchical clustering we propose two efficient synthetical clustering validity (SCV) indexes using the minimum spanning tree to calculate the intra-cluster compactness to overcome the deficiencies of the measurements in the existing validity indexes. For the general hierarchical clustering, a self-adaptive similarity measure strategy and two generalized synthetical clustering validity (GSCV) indexes, which are the extension of the proposed SCV indexes, are developed. The proposed SCV and GSCV indexes constitute a unified validity index framework, where SCV index is a special case of GSCV index, can avoid the incompatibility of the similarity measure between the clustering and validation. The experimental comparisons with the state-of-the-art validity indexes on artificial and real-world data sets demonstrate the efficiency of the proposed validity indexes in discovering the true number of clusters and dealing with various sorts of data sets, including imbalanced data sets. [ABSTRACT FROM AUTHOR]

Abstract In order to deal with non-stationary and nonlinear carbon price series, a hybrid forecasting approach is proposed in this study, which is incorporated variational mode decomposition (VMD), mode reconstruction (MR) and optimal combined forecasting model (CFM). The proposed approach introduces a new modes reconstruction method by using evolutionary clustering algorithm, and utilizes optimal combined model to forecast the reconstructed modes. The major steps of developed method can be summarized as: Firstly, carbon price is decomposed into several modes via VMD model, and the modes are obtained adaptively. Secondly, the comprehensive contribution index (CCI) of each mode is calculated and modes are further reconstructed by evolutionary clustering algorithm according to CCI. Then, a new sub-series called virtual modes (V-Modes) is defined and obtained. Thirdly, the optimal combined forecasting model is developed to forecast the V-Modes. In the end, the final forecasting results are obtained by summing the forecasts of V-Modes. For illustration and comparison, the carbon price data from Shenzhen and Hubei Province in China are shown as numerical examples. The empirical results confirm that the proposed approach outperforms benchmark models in terms of some statistical measures and robustness. Therefore, the proposed hybrid approach can be utilized as an effective model for the forecasting of carbon price. Highlights • A series of data modes for the carbon price is obtained based on VMD model. • The modes are reconstructed based on evolutionary clustering algorithm. • The optimal combined model is proposed to forecast the reconstructed modes. • The proposed model can improve the forecasting accuracy significantly. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to linguistic multiple attribute decision-making problems with interactive unbalanced linguistic assessment information by unbalanced linguistic generalized Heronian mean aggregation operators. First, some generalized Heronian mean aggregation operators with unbalanced linguistic information are proposed, involving the unbalanced linguistic generalized arithmetic Heronian mean operator and the unbalanced linguistic generalized geometric Heronian mean operator. For the situation that the input arguments have different degrees of importance, the unbalanced linguistic generalized weighted arithmetic Heronian mean operator and the unbalanced linguistic generalized weighted geometric Heronian mean operator are developed. Then we investigate their properties and some particular cases. Finally, the effectiveness and universality of the developed approach are illustrated by a low-carbon tourist instance and comparison analysis. A sensitivity analysis is performed as well to test the robustness of proposed methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel iterative two-stage method to suppress salt and pepper noise. In the first phase, a multilevel weighted graphs model for image representation is built to characterize the gray or color difference between the pixels and their neighbouring pixels at different scales. Then the noise detection is cast into finding the node with minimum node strength in the graphs. In the second phase, we develop a method to determine the order-inducing variables and weighted vectors of the induced generalized order weighted average (IGOWA) operator to restore the detected noise candidate. In the proposed method, the two stages are not separate, but rather alternate. Simulated experiments on gray and color images demonstrate that the proposed method can remove the noise effectively and keep the image details well in comparison to other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

2-tuple linguistic preference relations (2-TLPRs) are useful tools for addressing decision-making issues where the decision makers (DMs) are inclined to apply linguistic variables to express evaluation information. To retain the DM's initial preference information as much as possible, this paper provides a 2-tuple linguistic decision-making method that incorporates a consistency adjustment algorithm and a 2-tuple linguistic data envelopment analysis (DEA) model. As two important aspects of decision-making, it is worthy to further study the improvements in consistency and weight generation for alternatives with 2-TLPRs. In this paper, in order to adjust the consistency of an original 2-TLPR to a predetermined level, a convergent consistency-improving algorithm is first presented, and we employ a minimum adjustment strategy to preserve the DM's initial evaluation information. A 2-tuple linguistic DEA model is then developed to generate a vector of weights for the alternatives and we can derive reliable decision-making results. Finally, we provide a numerical example that can identify the most influential factor in Fog–haze weather to indicate the applicability of the 2-tuple linguistic decision-making method. The comparative analysis highlights the advantages and effectiveness of the 2-tuple linguistic decision-making method. [ABSTRACT FROM AUTHOR]

• Acoustic method was adopted to quantitatively measure the long-distance filamentation. • A simple physical model was presented to analyze the spatial distribution of filament. • The onset and length of filament can be conveniently obtained from the model. • The increase of the filament length can be obtained for longer pulse with more energy. The promising application of femtosecond laser filamentation in atmospheric remote sensing brings imperative demand for diagnosing and controlling the spatiotemporal dynamics of long-distance filamentation. Here, the acoustic method was adopted to quantitatively diagnose the long-distance filamentation of femtosecond pulses manipulated by energy and temporal domain. The onset and length of filament can be conveniently obtained from a simple analytic formula based on reasonable approximation and further demonstrated by the experimental results. The influence of pulse energy and initial pulse chirp under three different focal lengths (∼10 m, 20 m, and 30 m) on the filamentation in the air were studied experimentally. These findings provide a guiding significance for the optimal control of the long-distance propagation of filament, thereby laying a firm foundation for femtosecond laser-based atmospheric remote sensing. [ABSTRACT FROM AUTHOR]