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The uncertainty of the interval variable is represented by interval factor, and the interval variable is described as its mean value multiplied by its interval factor. Based on interval arithmetic rules, an analytical method of interval finite element for uncertain structures but not probabilistic structure or fuzzy structure is presented by combining the interval analysis with finite element method. The static analysis of truss with interval parameters under interval load is studied and the expressions of structural interval displacement response and stress response are deduced. The influences of uncertainty of one of structural parameters or load on the displacement and stress of the structure are examined through examples and some significant conclusions are obtained.

We compare methods to measure comovement in business cycle data using multi-level dynamic factor models. To do so, we employ a Monte Carlo procedure to evaluate model performance for different specifications of factor models across three different estimation procedures. We consider three general factor model specifications used in applied work. The first is a single-factor model, the second a two-level factor model, and the third a three-level factor model. Our estimation procedures are the Bayesian approach of Otrok and Whiteman (1998), the Bayesian state-space approach of Kim and Nelson (1998) and a frequentist principal components approach. The latter serves as a benchmark to measure any potential gains from the more computationally intensive Bayesian procedures. We then apply the three methods to a novel new dataset on house prices in advanced and emerging markets from Cesa-Bianchi, Cespedes, and Rebucci (2015) and interpret the empirical results in light of the Monte Carlo results.

The application of the traditional failure mode and effects analysis (FMEA) technique has been widely questioned in evaluation information, risk factor weights and robustness of results. This paper develops a novel FMEA framework with extended MULTIMOORA method under interval-valued Pythagorean fuzzy environment to solve these problems.

This paper introduces innovatively interval-value Pythagorean fuzzy weighted averaging (IVPFWA) operator, Tchebycheff metric distance and interval-value Pythagorean fuzzy weighted geometric (IVPFWG) operator into the MULTIMOORA submethods to obtain the risk ranking order for emergencies. Finally, an illustrative case is provided to demonstrate the practicality and feasibility of the novel fuzzy FMEA framework.

The feasibility and validity of the proposed method are verified by comparing with the existing methods. The calculation results indicate that the proposed method is more consistent with the actual situation of project and has more reference value.

The research results can provide supporting information for risk management decisions and offer decision-making basis for formulation of the follow-up emergency control and disposal scheme, which has certain guiding significance for the practical popularization and application of risk management strategies in the infrastructure projects.

A novel approach using FMEA with extended MULTIMOORA method is developed under IVPF environment, which considers weights of risk factors and experts. The method proposed has significantly improved the integrity of information in expert evaluation and the robustness of results.

The healthcare system is regarded as one of the most critical service industries. The surgical unit is the heart of hospitals in that any failures directly affect the safety of patients, so they should be managed thoroughly. It is an intricate multi-attributes decision-making problem with uncertainty. Uncertain information in the form of fuzzy sets theory has been applied widely to describe the different aspects of system uncertainty. This study aims to present a new methodology to manage the healthcare system failures due to the multi-attributes decision-making process.

This study introduces a new risk evaluation methodology by failure mode and effect analysis (FMEA) and MULTIMOORA method. Group decision-making process in this methodology is presented under uncertain information in the form of interval-valued hesitant fuzzy linguistic sets (IVHFLSs). IVHFLSs encompass both qualitative and quantitative interpretation of experts to reflect their preferences, as well the ability and flexibility of derivation of linguistic information by several linguistic terms increase. To avoid the different ranking order of MULTIMOORA approaches, a new interval multi-approaches multi-attribute methodology, namely, technique of precise order preference (TPOP), is extended to provide precise ranking order.

The application and precision of proposed integrated IVHFL-MULTIMOORA methodology with TPOP is examined in a case study of healthcare systems. The results indicate the superiority of proposed methodology to prioritize and assess the failures as well as handling system uncertainty.

This study addresses the challenges of an organization to prioritize potential failures by implementing FMEA method. Moreover, this paper contributes to making the manager's ability in decision-making. The value of this study can be discussed in two aspects. First and foremost, this study provides a new FMEA-based methodology to rank failures precisely. The results prove that the proposed methodology is more robust to changes of different ranking order methods, applied by FMEA. On the other hand, using the capability of IVHFLSs allows collecting accurate information in an ambiguous and uncertain environment.

The purpose of this paper is to introduce an interval finite element method (IFEM) to simulate the temperature field of mass concrete under multiple influence uncertainties e.g. environmental temperature, material properties, pouring construction and pipe cooling.

Uncertainties of the significant factors such as the ambient temperature, the adiabatic temperature rise, the placing temperature and the pipe cooling are comprehensively studied and represented as the interval numbers. Then, an IFEM equation is derived and a method for obtaining interval results based on monotonicity is also presented. To verify the proposed method, a non-adiabatic temperature rise test was carried out and subsequently simulated with the method. An excellent agreement is achieved between the simulation results and the monitoring data.

An IFEM method is proposed and a non-adiabatic temperature rise test is simulated to verify the method. The interval results are discussed and compared with monitoring data. The proposed method is found to be feasible and effective.

Compared with the traditional finite element methods, the proposed method taking the uncertainty of various factors into account and it will be helpful for engineers to gain a better understanding of the real condition.

This study aims to propose the adoption of artificial neural network (ANN)-based prediction intervals (PIs) to give more reliable prediction of labour productivity using historical data.

Using the proposed PI method, various sources of uncertainty affecting predictions can be accounted for, and a PI is proposed instead of a less reliable single-point estimate. The proposed PI consists of a lower and upper bound in which the realization of the predicted variable, namely, labour productivity, is anticipated to fall with a defined probability and represented in terms of a confidence level (CL).

The proposed PI method is implemented on a case study project to predict labour productivity. The quality of the generated PIs for the labour productivity is investigated at three confidence levels. The results show that the proposed method can predict the value of labour productivity efficiently.

This study is the first attempt in construction management to undertake a shift from deterministic point predictions to interval forecasts to improve the reliability of predictions. The proposed PI method will help project managers obtain accurate and credible predictions of labour productivity using historical data. With a better understanding of future outcomes, project managers can adopt appropriate improvement strategies to enhance labour productivity before commencing a project.

Point predictions provided by traditional deterministic ANN-based forecasting methodologies may be unreliable due to the different sources of uncertainty affecting predictions. The current study proposes ANN-based PIs as an alternative and robust tool to give a more reliable prediction of labour productivity using historical data. Using the proposed method, various sources of uncertainty affecting the predictions are accounted for, and a PI is proposed instead of a less reliable single point estimate.

Today, social media is counted as an integral part of marketing strategies, which has led to a paradigm change in this field. As reported, social media marketing has been growing over the recent five years and is predicted to be exponentially growing in the future. However, despite the huge promise and intention to adopt social media marketing strategies by organisations, there remain challenges regarding the successful implementation of these new marketing programmes. Accordingly, marketing managers’ awareness of the success factors of social media marketing is essential to return investment in this area. Due to the little research been accomplished in this field, this paper aims to identify the success factors of social networks’ marketing and to rank the factors by using of interval best-worst method (BWM).

To serve the research aims, an extant literature review is accomplished and a focus group approach is conducted to identify the main success factors and sub-factors. To analyse the focus group discussions, a qualitative content analysis approach is applied. Interval BWM is used to calculate the weights of each identified factor.

In the final framework, six main success criteria, including strategy, process, technology, content, performance evaluation and people are identified, for each sub-criteria are developed. The interval BWM results suggest the content criterion as the most important success factor in developing a social media marketing strategy.

First, this research provides a comprehensive insight into the success factors and best practices of social media marketing. This is the first to draw on the critical factors affecting the success of social media marketing, considering people in the organisation such as top management, employees and customers, strategy, process and performance evaluation focussing on the change management requirements for applying social media marketing and technology as the technical factor of the adoption process, simultaneously. Identifying critical success factors of social media marketing will help marketing managers to avoid falling into the trap of developing social media strategies based on less important areas and ignoring the critical ones. Besides, owing to the limited resources of organisations in implementing social media marketing strategies, prioritising and weighing the success factors will lead to a focus on more important areas.

Whilst the related studies have mostly concentrated on the capabilities and activities required to conduct social media marketing and the few research investigated the critical success factors most concentrated on the customer and the content-related factors, the finding of this research goes beyond that and suggests technical, process and human aspects simultaneously in the implementation process in a holistic view.

Aim to the limitations of grey relational analysis of interval grey number, based on the generalized greyness of interval grey number, this paper tries to construct a grey angle cosine relational degree model from the perspective of proximity and similarity.

Firstly, the algorithms of the generalized greyness of interval grey number and interval grey number vector are given, and its properties are analyzed. Then, based on the grey relational theory, the grey angle cosine relational model is proposed based on the generalized greyness of interval grey number, and the relationship between the classical cosine similarity model and the grey angle cosine relational model is analyzed. Finally, the validity of the model in this paper is illustrated by the calculation examples and an application example of related factor analysis of maize yield.

The results show that the grey angle cosine relational degree model has strict theoretical basis, convenient calculation and is easy to program, which can not only fully utilize the information of interval grey numbers but also overcome the shortcomings of greyness relational degree model. The grey angle cosine relational degree is an extended form of cosine similarity degree of real numbers. The calculation examples and the related factor analysis of maize yield show that the model proposed in this paper is feasible and valid.

The research results not only further enrich the grey system theory and method but also provide a basis for the grey relational analysis of the sequences in which the interval grey numbers coexist with the real numbers.

The paper succeeds in realizing the algorithms of the generalized greyness of interval grey number and interval grey number vector, and the grey angle cosine relational degree, which provide a new method for grey relational analysis.

Various factors may influence project finance when a multi-sourced debt financing strategy is used for financing capital investments, in general, and public infrastructure investments, in particular. Traditional indicators lack comprehensive consideration of the influences of many internal and external factors, such as investment structure, financing mode and credit guarantee structure, which exist in the financing decision making of BOT projects. An effective approach is, thus, desired. The paper aims to discuss these issues.

This paper develops a financial model that uses an interval number to represent the uncertain factors and, subsequently, conducts a standardization of the interval number. Decision makers determine the weight of each objective through the analytic hierarchy process. Through the optimization procedure, project investors and sponsors are provided with a strategy regarding the optimal amount of debt to be raised and the insight on the risk level based on the net present value, as well as the probability of bankruptcy for each different period of debt service.

By using an example infrastructure project in China and based on the comprehensive evaluation, comparison and ranking of the capital structures of urban public infrastructure projects using the interval number method, the final ranking can help investors to choose the optimal capital structure for investment. The calculation using the interval number method shows that X2 is the optimal capital structure plan for the BOT project of the first stage of Tianjin Binhai Rail Transit Z4 line. Therefore, investors should give priority to selecting a capital contribution ratio of 45 per cent for this investment.

In this paper, some parameters, such as depreciation life, construction period and concession period, are assumed to be deterministic parameters, although the interval number model has been introduced to analyze the uncertainty indicators, such as total investment and passenger flow, of BOT rail transport projects. Therefore, more of the above deterministic parameters can be taken as uncertainty parameters in future research so that calculation results fit actual projects more closely.

This model can be used to make the optimal investment decision for a project by determining the impact of uncertainty factors on the profitability of the project in its lifecycle during the project financial feasibility analysis. Project sponsors can determine the optimal capital structure of a project through an analysis of the irregular fluctuation of the unpredictable factors in project construction such as construction investment, operating cost and passenger flow. The model can also be used to examine the effects of different capital investment ratios on indicators so that appropriate measures can be taken to reduce risks and maximize profit.