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The purpose of the development of the paper is to construct probabilistic interval-valued hesitant fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) model and to improve some preliminary aggregation operators such as probabilistic interval-valued hesitant fuzzy averaging (PIVHFA) operator, probabilistic interval-valued hesitant fuzzy geometric (PIVHFG) operator, probabilistic interval-valued hesitant fuzzy weighted averaging (PIVHFWA) operator, probabilistic interval-valued hesitant fuzzy ordered weighted averaging (PIVHFOWA) operator, probabilistic interval-valued hesitant fuzzy weighted geometric (PIVHFWG) operator and probabilistic interval-valued hesitant fuzzy ordered weighted geometric (PIVHFOWG) operator to cope with multicriteria group decision-making (MCGDM) problems in an efficient manner.

(1) To design probabilistic interval-valued hesitant fuzzy TOPSIS model. (2) To improve some of the existing aggregation operators. (3) To propose the Hamming distance, Euclidean distance, Hausdorff distance and generalized distance between probabilistic interval-valued hesitant fuzzy sets (PIVHFSs).

The results of the proposed model are discussed in comparison with the aggregation-based method from the related literature and found the effectiveness of the proposed model and improved aggregation operators.

A case study concerning the healthcare facilities in public hospital is addressed.

The notion of the proposed distance measure is used as rational tool to extend TOPSIS model for probabilistic interval-valued hesitant fuzzy setting.

The purpose of this paper is to study a fractional grey model FAGM(1,1,t^α) based on the GM(1,1,t^α) model and the fractional accumulated generating operation, and then predict the national health expenditure, the government health expenditure and the out-of-pocket health expenditure of China.

The presented univariate grey model is systematically studied by using the grey modelling technique, the fractional accumulated generating operation and the trapezoid approximation formula of definite integral. The optimal system parameters r and α are evaluated by the particle swarm optimisation algorithm.

The expressions of the time response function and the restored values of this model are derived. The GM(1,1), NGM(1,1,k,c) and GM(1,1,t^α) models are particular cases of the FAGM(1,1,t^α) model with deterministic r and α. Compared with other forecasting models, the results of the FAGM(1,1,t^α) model have higher precision.

The superiority of the new model has high potential to be used in the medicine and health fields and others. Results can provide a guideline for government decision making.

The univariate fractional grey model FAGM (1,1,t^α) successfully studies the China’s health expenditure.

This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.

Vibration fatigue of railway bogie arising from the wheel/rail high frequency vibration has become the main concern of railway operators. Previous reviews usually focused on the formation mechanism of wheel/rail high frequency vibration. This paper thus gives a critical review of the vibration fatigue of railway bogie owing to the short-pitch irregularities-induced high frequency vibration, including a brief introduction of short-pitch irregularities, associated high frequency vibration in railway bogie, typical vibration fatigue failure cases of railway bogie and methodologies used for the assessment of vibration fatigue and research gaps.

The results showed that the resulting excitation frequencies of short-pitch irregularity vary substantially due to different track types and formation mechanisms. The axle box-mounted components are much more vulnerable to vibration fatigue compared with other components. The wheel polygonal wear and rail corrugation-induced high frequency vibration is the main driving force of fatigue failure, and the fatigue crack usually initiates from the defect of the weld seam. Vibration spectrum for attachments of railway bogie defined in the standard underestimates the vibration level arising from the short-pitch irregularities. The current investigations on vibration fatigue mainly focus on the methods to improve the accuracy of fatigue damage assessment, and a systematical design method for vibration fatigue remains a huge gap to improve the survival probability when the rail vehicle is subjected to vibration fatigue.

The research can facilitate the development of a new methodology to improve the fatigue life of railway vehicles when subjected to wheel/rail high frequency vibration.

This paper aims to first apply more advanced anisotropic yield criterions as Yld91 and Yld2004 to spherical indentation simulations, and investigate plastic anisotropy identified from indentation simulations following different yield criterions (Hill48, Yld91, Yld2004) to discover laws. It also aims to compare the difference in plastic anisotropy identified from indentation on three yield criterions and evaluate the applicability of plastic anisotropy.

This paper uses indentation simulations on different yield criterions to identify plastic anisotropy. First, the trust-region techniques based on the nonlinear least-squares method are used to determine anisotropy coefficients of Yld91 and Yld2004. Then, Yld91 and Yld2004 are implemented into ABAQUS software using user-defined material (UMAT) subroutines with the proposed universal structure. Finally, through considering comprehensively the key factors, the locations of the optimal data acquisition points in indentation simulations on different yield criterions are determined. And, the identified stress–strain curves are compared with experimental data.

This paper discovers that indentation on Yld2004 is able to fully identify difference in equivalent plastic strain between 0° and 90° directions when indentation depth h_t is relatively smaller. And, this research demonstrates conclusively that plastic anisotropy identified from indentation on Yld2004 and Yld91 is more applicable at larger strains than that on Hill48, and that on Yld2004 is more applicable than that on Yld91, overall. In addition, the method on the determination of the locations of the optimal data acquisition points is demonstrated to be also valid for anisotropic material.

This paper first investigates plastic anisotropic properties and laws identified from indentation simulations following more advanced anisotropic yield criterions and provides reference for later research.

Given that the use of Google Trends data is helpful to improve forecasting performance, this study aims to investigate whether the precision of forecast combination can benefit from the use of Google Trends Web search index along with the encompassing set.

Grey prediction models generate single-model forecasts, while Google Trends index serves as an explanatory variable for multivariate models. Then, three combination sets, including sets of univariate models (CUGM), all constituents (CAGM) and constituents that survive the forecast encompassing tests (CSET), are generated. Finally, commonly used combination methods combine the individual forecasts for each combination set.

The tourism volumes of four frequently searched-for cities in Taiwan are used to evaluate the accuracy of three combination sets. The encompassing tests show that multivariate grey models play a role to be reckoned with in forecast combinations. Furthermore, the empirical results indicate the usefulness of Google Trends index and encompassing tests for linear combination methods because linear combination methods coupled with CSET outperformed that coupled with CAGM and CUGM.

With Google Trends Web search index, the tourism sector may benefit from the use of linear combinations of constituents that survive encompassing tests to formulate business strategies for tourist destinations. A good forecasting practice by estimating ex ante forecasts post-COVID-19 can be further provided by scenario forecasting.

To improve the accuracy of combination forecasting, this research verifies the correlation between Google Trends index and combined forecasts in tourism along with encompassing tests.

過去的研究顯示 Google 搜尋趨勢資料有助於改善旅遊需求預測的準確度，本研究就此進一步探討 Google 搜尋趨勢網頁搜尋指標與涵蓋性檢定的使用對於組合預測準確度所造成的影響。

本研究以 Google 搜尋趨勢指標做為多變量灰色預測模式的解釋變數，並以單變量與多變量灰色模式產生各別預測值。在分別產生由所有的單變量模式 (CUGM)所有的模式 (CAGM), 以及經過涵蓋性檢定所留存下來之模式 (CSET) 所組成之集合後，就各別的組合集以常用的組合方法產生預測值。

以台灣的四個熱搜旅遊城市的旅遊人數進行三個組合集的預測準確度分析。涵蓋性檢定顯示多變量灰色模式在組合預測中扮演重要的角色，而結果亦呈現線性組合方法在 CSET優於在 CUGM 與 CAGM 的準確度，突顯搜尋趨勢指標與涵蓋性檢定對於線性組合方法的有用性。

藉由 Google 搜尋趨勢網頁搜尋指標與涵蓋性檢定，旅遊部門應可透過線性組合方法的預測規劃旅遊目的地的經營策略。新冠疫情下於各季的事前預測亦可結合情境預測具體呈現。

為提升組合預測在旅遊需求的預測準確度，本研究結合涵蓋性檢定以分析 Google 搜尋趨勢指標與組合預測準確度之間的關聯性。

旅遊需求,涵蓋性檢定,Google 搜尋趨勢,灰色預測,組合預測

研究型论文

Dado que el uso de los datos de Google Trends es útil para mejorar la precisión de las predicciones, este estudio examina si el uso del índice de búsqueda web de Google Trends combinado con la agregación de relevancia puede mejorar la precisión del predictor.

El modelo predictivo gris genera predicciones bajo un único modelo, mientras que el modelomultivariado utiliza el indicador Google Trends como variable explicativa. Se generaron tresensamblajes generales, incluido el Modelo armónico único (CUGM), los ensamblajes de todos loscomponentes (CAGM) y la prueba de presencia de componentes con predicción (CSET). Laspredicciones individuales encada grupo luego se combinan utilizando métodos de correlación deuso común.

Utilizando el número de turistas en las cuatro ciudades más investigadas de Taiwán, los tresgrupos combinados se clasificaron según su precisión. Las pruebas incluidas muestran que losmodelos multivariados en escala de grises son importantes para la predicción. Además, losresultados de las pruebas muestran que el índice de Google Trends y las pruebas que incluyenmétodos de suma lineal son útiles porque los métodos combinados con CSET funcionan majorque los métodos combinados con CSET. CAGM y VCUG.

La industria de viajes puede usar el índice de búsqueda web de Google Trends para desarrollarestrategias comerciales para atracciones basadas en un conjunto lineal de componentes.

Con el objetivo de mejorar la precisión de los pronósticos agregados, este estudio investiga larelación entre el índice de tendencias de Google y las expectativas generales de viaje junto con laevidencia global.

Demanda de viajes, Experiencia global, Tendencias de Google, Predicción gris

Trabajo de investigación

Electricity consumption prediction has been an important topic for its significant impact on electric policies. Due to various uncertain factors, the growth trends of electricity consumption in different cases are variable. However, the traditional grey model is based on a fixed structure which sometimes cannot match the trend of raw data. Consequently, the predictive accuracy is variable as cases change. To improve the model's adaptability and forecasting ability, a novel fractional discrete grey model with variable structure is proposed in this paper.

The novel model can be regarded as a homogenous or non-homogenous exponent predicting model by changing the structure. And it selects the appropriate structure depending on the characteristics of raw data. The introduction of fractional accumulation enhances the predicting ability of the novel model. And the relative fractional order r is calculated by the numerical iterative algorithm which is simple but effective.

Two cases of power load and electricity consumption in Jiangsu and Fujian are applied to assess the predicting accuracy of the novel grey model. Four widely-used grey models, three classical statistical models and the multi-layer artificial neural network model are taken into comparison. The results demonstrate that the novel grey model performs well in all cases, and is superior to the comparative eight models.

A fractional-order discrete grey model with an adaptable structure is proposed to solve the conflict between traditional grey models' fixed structures and variable development trends of raw data. In applications, the novel model has satisfied adaptability and predicting accuracy.

The proposed model can emphasize the priority of new information and can extract messages from the first pair of original data. The comparison results show that the proposed model can improve the traditional grey model.

The grey multivariate model with fractional Hausdorff derivative is firstly put forward to enhance the forecasting accuracy of traditional grey model.

The proposed model is used to predict the air quality composite index (AQCI) in ten cities respectively.

The effect of population density on AQCI in cities with poor air quality is not as significant as that of the cities with better air quality.

The purpose of this paper is to develop a novel multivariate fractional grey model termed GM(a, n) based on the classical GM(1, n) model. The new model can provide accurate prediction with more freedom, and enrich the content of grey theory.

The GM(α, n) model is systematically studied by using the grey modelling technique and the forward difference method. The optimal fractional order a is computed by the genetic algorithm. Meanwhile, a stochastic testing scheme is presented to verify the accuracy of the new GM(a, n) model.

The recursive expressions of the time response function and the restored values of the presented model are deduced. The GM(1, n), GM(a, 1) and GM(1, 1) models are special cases of the model. Computational results illustrate that the GM(a, n) model provides accurate prediction.

The GM(a, n) model is used to predict China’s total energy consumption with the raw data from 2006 to 2016. The superiority of the GM(a, n) model is more freedom and better modelling by fractional derivative, which implies its high potential to be used in energy field.

It is the first time to investigate the multivariate fractional grey GM(α, n) model, apply it to study the effects of China’s economic growth and urbanization on energy consumption.

The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods and to deal with high Rayleigh number for the natural convection problem.

The paper introduces a novel characteristic variational multiscale (C-VMS) finite element method which combines advantages of both the characteristic and variational multiscale methods within a variational framework for solving the incompressible natural convection problem with variable density. The authors chose the conforming finite element pair (P₂, P₂, P₁, P₂) to approximate the density, velocity, pressure and temperature field.

The paper gives the stability analysis of the C-VMS method. Extensive two-dimensional/three-dimensional numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

Extensive 2D/3D numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

This paper aims to provide a framework of the supervised hyperspectral classification, to study the traditional flowchart of hyperspectral image (HIS) analysis and processing. HSI technology has been proposed for many years, and the applications of this technology were promoted by technical advancements.

First, the properties and current situation of hyperspectral technology are summarized. Then, this paper introduces a series of common classification approaches. In addition, a comparison of different classification approaches on real hyperspectral data is conducted. Finally, this survey presents a discussion on the classification results and points out the classification development tendency.

The core of this survey is to review of the state of the art of the classification for hyperspectral images, to study the performance and efficiency of certain implementation measures and to point out the challenges still exist.

The study categorized the supervised classification for hyperspectral images, demonstrated the comparisons among these methods and pointed out the challenges that still exist.