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Ranking and comparing grey numbers represent a very important decision-making procedure in any given grey environment. The purpose of this paper is to study the existing approaches of ordering interval grey numbers in the context of decision making by surveying existing definitions.

Different methods developed for comparing grey numbers are presented along with their disadvantages and advantages in terms of comparison outcomes. Practical examples are employed to show the importance and necessity of using appropriate methods to compare grey numbers.

Most the available methods are not suitable for pointing out which number is larger when the nuclei of the grey numbers of concern are the same. Also, these available methods are also considered in terms of partial order and total order. Kernel and degree of greyness of grey numbers method is more advantageous than other methods and almost eliminates the shortcomings of other methods.

Different methods for ranking grey numbers are presented where each of them has disadvantages and advantages. By using different methods, grey interval numbers are compared and the results show that some methods cannot make grey number comparisons in some situations. The authors intend to find a method that can compare grey numbers in any situation. The findings of this research can prevent errors that may occur based on inaccurate comparisons of grey numbers in decision making. There are various research studies on the comparison of grey numbers, but there is no research on the comparison of these methods and their disadvantages, advantages or their total or partial order.

This study aims to investigate how source attractiveness (including platform credibility, product appeal and streamer attractiveness) and information quality impact viewers’ cognition and flow state. Additionally, it examines how these factors influence the development of consumer attitudes and behaviors toward livestreamed tourism shopping, as well as the moderating roles of perceived risk and personal characteristics.

A sequential mixed-methods research design was used. In addition to a literature review, 15 interviews were conducted to identify measurement items for the subsequent questionnaire survey. Sample 1 (n = 209) was used to refine these measurement items, whereas Sample 2 (n = 227) was used to evaluate the measurement model and test the proposed hypotheses.

Findings reveal that source attractiveness (streamer attractiveness, tourism product attractiveness and platform credibility) and information quality significantly influence customers’ behavior formation, with cognition and flow state acting as mediators. Findings further confirm the moderating effect of perceived risk in a livestreamed shopping environment.

The findings provide new insights into how consumers select livestreamed shopping platforms. As viewers assess the credibility and trustworthiness of each component to form their perception of the overall platform’s credibility, companies should market their products through credible platforms, studios and stores with extensive reach. It is also critical to collaborate with streamers who are sincere, trustworthy, knowledgeable and professional. Since perceived risk lowers consumer behavioral intentions, live streamers, platforms and merchants should offer convincing and credible arguments to alleviate viewers’ perceived risks.

This study advances the literature on livestreamed shopping by broadening the conceptualization of source attractiveness to include three dimensions: streamer attractiveness, product attractiveness and platform attractiveness. Furthermore, it differentiates itself from existing studies by integrating and adopting multidimensional measurements of cognition (perceived usefulness and ease of use) and flow state (control, enjoyment, curiosity and concentration).

本研究旨在探讨信息源吸引力(平台可信度、产品吸引力和主播吸引力)和信息质量如何影响旅游购物直播观众的认知和心流体验。本研究进一步探讨了这些因素如何影响旅游直播购物消费者的态度与行为。本研究还检验了感知风险和个人特征的调节作用。

采用顺序混合研究方法。基于文献和15次深度访谈确定了问卷调查中使用的测量项目。样本1 (n= 209)用于净化测量项目。样本2 (n= 227)用于评估测量模型并验证假设。

信息源吸引力(主播吸引力、旅游产品吸引力和平台可信度)和信息质量显著影响消费者行为, 其中认知和心流起中介作用。研究结果进一步证实了感知风险的调节作用。

研究结果为消费者如何选择直播购物平台提供了新的见解。由于观众对每个组成部分的可信度进行评估, 从而形成他们对整个平台可信度的看法, 因此公司应该通过可靠的平台、直播间和具有广泛影响力的店铺来营销他们的产品。与真诚、值得信赖、知识渊博、专业的主播合作也至关重要。由于感知风险会降低消费者的行为意愿, 因此主播、平台和商家应该提供令人信服和可信的论据, 以减轻观众的感知风险。

本研究将信息源吸引力的概念扩展到三个维度：主播吸引力、产品吸引力和平台可信度, 从而丰富了直播购物相关研究。通过整合并采用认知（感知有用性和感知易用性）和心流体验（控制、愉悦、好奇和沉浸）的多维测量, 本研究进一步区别于现有研究。

Este estudio investiga cómo el atractivo de la fuente (incluida la credibilidad de la plataforma, el atractivo del producto y el atractivo del emisor) y la calidad de la información influyen en la cognición y el estado de flujo de los espectadores. Además, examina cómo influyen estos factores en el desarrollo de las actitudes y los comportamientos de los consumidores hacia las compras turísticas retransmitidas en directo, así como los papeles moderadores del riesgo percibido y las características personales.

Se empleó un método de investigación mixto secuencial. Además de una revisión bibliográfica, se realizaron 15 entrevistas para identificar los ítems de medición para la posterior encuesta por cuestionario. La muestra 1 (n = 209) se utilizó para refinar estos ítems de medición, mientras que la muestra 2 (n = 227) se utilizó para evaluar el modelo de medición y probar las hipótesis propuestas.

Resultados revelan que el atractivo de la fuente (atractivo del emisor, atractivo del producto turístico y credibilidad de la plataforma) y la calidad de la información influyen significativamente en la formación del comportamiento de los clientes, con la cognición y el estado de flujo actuando como mediadores. Resultados confirman además el efecto moderador del riesgo percibido en el entorno de las compras en directo.

Los Resultados aportan nuevos conocimientos sobre cómo seleccionan los consumidores las plataformas de compras en directo. Dado que los espectadores evalúan la credibilidad y la fiabilidad de cada componente para formarse su percepción de la credibilidad global de la plataforma, las empresas deberían comercializar sus productos a través de plataformas, estudios y tiendas creíbles con un amplio alcance. También es fundamental colaborar con streamers que sean sinceros, dignos de confianza, informados y profesionales. Dado que el riesgo percibido disminuye las intenciones de comportamiento de los consumidores, los streamers en directo, las plataformas y los comerciantes deben ofrecer argumentos convincentes y creíbles para aliviar los riesgos percibidos por los espectadores.

Este estudio hace avanzar la literatura sobre las compras en directo ampliando la conceptualización del atractivo de la fuente para incluir tres dimensiones: el atractivo del streamer, el atractivo del producto y el atractivo de la plataforma. Además, se diferencia de los estudios existentes al integrar y adoptar mediciones multidimensionales de la cognición (utilidad percibida y facilidad de uso) y el estado de flujo (control, disfrute, curiosidad y concentración).

This paper aims to study the boundary disturbance rejection control design for a flexible Timoshenko robot arm to diminish external disturbances and achieve desired angle tracking, with system vibration and elastic deformation considered.

This study introduces disturbance observer and disturbance rejection mechanism into the boundary control design for flexible Timoshenko robot arm systems. The uniform bounded stability of controlled systems is proved via Lyapunov analysis without any simplification of the infinite-dimensional system dynamics.

The proposed boundary disturbance rejection control scheme can effectively suppress vibrations and shear deformations, achieve the required angular positioning and reject external disturbances. Numerical simulations developed by the finite difference method are adapted to demonstrate the validity of the designed controller.

The originality of this study is to design boundary disturbance rejection control to suppress vibrations and shear deformations for the flexible Timoshenko robot arm, thereby improving the performance and control accuracy of the system.

Intuitionistic linguistic fuzzy information (ILFI), characterized by linguistic terms and intuitionistic fuzzy sets (IFSs), can easily express the fuzzy information in the process of muticriteria decision making (MCDM) and muticriteria group decision making (MCGDM) problems. The purpose of this paper is to provide an overview of aggregation operators (AOs) and applications of ILFI.

First, some meaningful AOs for ILFI are summarized, and some extended MCDM approaches for intuitionistic uncertain linguistic variables (IULVs), such as extended TOPSIS, extended TODIM, extended VIKOR, are discussed. Then, the authors summarize and analyze the applications about the AOs of IULVs.

IULVs, characterized by linguistic terms and IFSs, can more detailed and comprehensively express the criteria values in the process of MCDM and MCGDM. Therefore, lots of researchers pay more and more attention to the MCDM or MCGDM methods with IULVs.

The authors summarize and analyze the applications about the AOs of IULVs Finally, the authors point out some possible directions for future research.

Due to social transformation in China, more than 100,000,000 people are migrating within the country. Many parents are forced to leave their children behind when they migrate. In 2008, 58,000,000 children were living as left‐behind children, mainly in the rural parts of China (Zhang, 2009).Migration and its accompanying stressors may affect the mental health of the left‐behind children. This unique literature review of Chinese literature summarises the present state of knowledge and reviews the influential factors. Possible approaches to intervention and system reforms are discussed.A literature review was performed of published studies between 2001 and 2008. Databases used were Fujian Medical University Library Interface, Chinese National Knowledge Infrastructure, Wanfang Data, and VIP Information. The Chinese word for ‘left‐behind’ was used as a key word. Books, book chapters, monographs and studies on caring were searched electronically and by hand. Altogether, 53 items were found, discussed and grouped together. Migration affected the mental health of the left‐behind children in a passive way, especially their emotions and social behaviour.There is still controversy over how serious mental health problems are among children who have been left behind. Life events, personality, coping strategies and social suppor t can be regarded as four main factors that are predictive of mental health, which provides theoretical guidance for intervention. Suppor t and prevention of mental health problems in schools, in families and in primary care should be developed and studied.

Emotions, understood as evolving mental states, are pivotal in shaping individuals“' decision-making, especially in ambiguous information evaluation, probability estimation of events, and causality analysis. Public–private partnership (PPP) projects represent a confluence of “economic–environmental–social” dimensions, wherein stakeholder behavior follows the sequential progression of “cognition–emotion–action.” Consequently, comprehending the effects of emotional shifts on stakeholder's decision-making processes is vital to fostering the sustainability of PPP projects.

The paper utilizes rank-dependent expected utility and evolutionary game theory to systematically examine the influence of emotional factors on stakeholders' behavior and decision-making processes within PPP projects. The paper integrates three emotional state functions—optimism, pessimism and rationality—into the PPP framework, highlighting the intricate interactions among the government, private sector, surrounding public and the media. Furthermore, the paper amalgamates the evolutionary pathways of environmental rights incidents with the media's role. Through equilibrium analysis and numerical simulation, the paper delves into the diverse interplay of emotions across different phases of the environmental rights incident, assessing the impact of these emotions on the evolutionary game's equilibrium results.

Emotions significantly influence the microlevel decisions of PPP stakeholders, adapting continually based on event dynamics and media influences. When the private sector demonstrates optimism and the surrounding public leans toward rationality or pessimism, the likelihood of the private sector engaging in speculative behavior escalates, while the surrounding public refrains from adopting a supervisory strategy. Conversely, when the private sector is pessimistic and the public is optimistic, the system fails to evolve a stable strategy. However, when government regulation intensifies, the private sector opts for a nonspeculative strategy, and the surrounding public adopts a supervisory strategy. Under these conditions, the system attains a relatively optimal state of equilibrium.

The paper develops a game model to examine the evolutionary dynamics between the surrounding public and private sectors concerning environmental rights protection in waste incineration PPP projects. It illuminates the nature of the conflicting interests among project participants, delves into the impact of emotional factors on their decision-making processes and offers crucial perspectives for the governance of such partnerships. Furthermore, this paper provides substantive recommendations for emotional oversight to enhance governance efficacy.

With respect to the multiple-attribute decision-making problem with subjective preference for a certain attribute whose weight-value range have been given over other attributes whose weight values are unknown, a method based on the mean value of the grey number is proposed to analyse the decision-making problem. This method is used to choose a supply-chain partner under the condition that the decision makers have a preference for a certain attribute of various alternatives. The paper aims to discuss these issues.

First, the middle value of the preferred attribute’s weight-value range is supposed to be its weight value according to the content of the mean value of the grey number. Second, to reflect the decision maker’s subjective preference information, an improved optimisation model that requests the minimum deviation between the actual and expected numerical value of each attribute is constructed to assess the attributes’ weights. Third, the correlated degree and the correlation matrix, which are determined by the weight values of all attributes, are used to rank all the alternatives.

This paper provides a method for making a decision when decision makers have a preference for a certain attribute from an array of various alternatives, and the range of the certain attribute’s weight value is given but the weight value of the other attributes is unknown. When applied to supply-chain partner selection, this method proves feasible and effective.

This method is feasible and effective when applied to supply-chain partner selection, and can be applied to other kinds of decision-making problems. This means it has significant theoretical importance and extensive practical value.

Based on the mean value of the grey number, an optimisation model is built to determine the importance degree of each attribute, then the correlated degree of each alternative is combined to rank all the alternatives. This method can suit the decision makers’ subjective preference for a certain attribute well.

This study aims to reveal the triggering mechanism and boundary conditions of tourists’ cross-border travel anxiety (CBTA) from different crisis information sources.

Drawing on the heuristic-systematic model (HSM), this study constructs a theoretical formation path of tourists’ CBTA. Based on competence-based and moral-based crises, hypotheses were examined through three situational experiments, targeting Chinese and Malaysian potential tourists.

Organization-released crisis information triggers higher tourists’ CBTA than government ones, with perceived uncertainty mediating it. Crisis communication message appeals (CCMAs) (rational vs emotional) negatively moderate the above relationships. Rational CCMAs work for governmental crisis communication, while emotional CCMAs work for organizational ones.

This study proposes a heuristic cross-border tourism crisis information dissemination strategy for destination management organizations and highlights the advantages of CCMAs in preventing secondary crises.

This study reexamines the cause-and-effect and the intervention mechanisms of tourists’ reactions to crisis information, which expands the cross-border tourism crisis management research and the application of the HSM in such a context.

本研究旨在从不同的危机信息源中揭示游客跨境旅行焦虑的触发机制和边界条件。

本研究借鉴启发式-系统式模型（HSM）, 构建了游客跨境旅游焦虑的理论形成路径。基于能力型和道德型目的地危机事件, 以中国及马来西亚潜在游客为例, 通过三组情境实验验证所提出的假设。

与政府发布的危机信息相比, 组织发布的危机信息会引发更高的游客跨境旅游焦虑, 而感知不确定性会对该路径起到中介作用。危机沟通信息诉求（理性vs.感性）对上述关系起负向调节作用。理性的信息诉求适用于政府危机沟通, 而感性的信息诉求适用于组织危机沟通。

本研究为目的地管理组织提出了启发式跨境旅游危机信息传播策略, 并强调了危机沟通信息诉求在预防二次危机方面的优势。

本研究重新审视了游客对危机信息反应的因果关系和干预机制, 拓展了跨境旅游危机管理研究和HSM在此背景下的应用。

Este estudio pretende revelar el mecanismo desencadenante y las condiciones límite de la ansiedad de los turistas ante los viajes transfronterizos (CBTA) a partir de diferentes fuentes de información sobre crisis (CIS).

Basándose en el modelo heurístico-sistemático (HSM), este estudio construye una vía teórica de formación de la CBTA de los turistas. A partir de las crisis basadas en la competencia y en la moral, se examinaron las hipótesis mediante tres experimentos situacionales, dirigidos a turistas potenciales chinos y malayos.

La información sobre crisis difundida por organizaciones desencadena una mayor CBTA de los turistas que la gubernamental, con la incertidumbre percibida como mediadora. Los recursos de los mensajes de comunicación de crisis (CCMA) (racionales frente a emocionales) moderan negativamente las relaciones anteriores. Los CCMA racionales funcionan para la comunicación de crisis gubernamental, mientras que los CCMA emocionales para las organizativas.

Los resultados proponen que las organizaciones de gestión de destinos (OGD) deberían considerar estrategias heurísticas a la hora de difundir información sobre crisis turísticas transfronterizas. Prestar atención al efecto diferencial de las CCMA ayuda a prevenir crisis secundarias.

Este estudio reexamina la causa-efecto y los mecanismos de intervención de las reacciones de los turistas a la información sobre crisis, lo que amplía la investigación sobre la gestión de crisis turísticas transfronterizas y la aplicación de la HSM en dicho contexto.