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By using small reference samples, the calculation method of confidence value and prediction method of confidence interval for multi-input system are investigated. The purpose of this paper is to offer effective assessing methods of confidence value and confidence interval for the simulation models used in establishing guidance and control systems.

In this paper, first, an improved cluster estimation method is proposed to guide the selection of the small reference samples. Then, based on analytic hierarchy process method, the new calculation method of the weight of each reference sample is derived. By using the grey relation analysis method, new calculation methods of the correlation coefficient and confidence value are presented. Moreover, the confidence interval of the sample awaiting assessment is defined. A new prediction method is derived to obtain the confidence interval of the sample awaiting assessment which has no reference sample. Subsequently, by using the prediction method and original small reference samples, Bootstrap resampling method is used to obtain more correlation coefficients for the sample to reduce the probability of abandoning the true.

The grey relational analysis is used in assessing the confidence value and interval prediction. The numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Based on the selected small reference samples, new calculation methods of the correlation coefficient and confidence value are presented to assess the confidence value of model awaiting assessment. The calculation methods of maximum confidence interval, expected confidence interval and other required confidence intervals are presented, which can be used in assessing the validities of controller and guidance system obtained from the model awaiting assessment.

PM10 is one of the most dangerous air pollutants which is harmful to the ecological system and human health. Accurate forecasting of PM10 concentration makes it easier for the government to make efficient decisions and policies. However, the PM10 concentration, particularly, the emerging short-term concentration has high uncertainties as it is often impacted by many factors and also time varying. Above all, a new methodology which can overcome such difficulties is needed.

The grey system theory is used to build the short-term PM10 forecasting model. The Euler polynomial is used as a driving term of the proposed grey model, and then the convolutional solution is applied to make the new model computationally feasible. The grey wolf optimizer is used to select the optimal nonlinear parameters of the proposed model.

The introduction of the Euler polynomial makes the new model more flexible and more general as it can yield several other conventional grey models under certain conditions. The new model presents significantly higher performance, is more accurate and also more stable, than the six existing grey models in three real-world cases and the case of short-term PM10 forecasting in Tianjin China.

With high performance in the real-world case in Tianjin China, the proposed model appears to have high potential to accurately forecast the PM10 concentration in big cities of China. Therefore, it can be considered as a decision-making support tool in the near future.

This is the first work introducing the Euler polynomial to the grey system models, and a more general formulation of existing grey models is also obtained. The modelling pattern used in this paper can be used as an example for building other similar nonlinear grey models. The practical example of short-term PM10 forecasting in Tianjin China is also presented for the first time.

The purpose of this paper is to construct a multi-relational network for an online sharing platform in the age of the sharing economy, to identify the factors impacting users’ product adoption behavior and to predict consumers’ purchases of user-generated products on the platform.

The study conducted multi-relational network analyses of five different sub-networks in identifying influential factors for e-book adoption. Meanwhile, the study adopted machine learning methods with different classification algorithms and feature sets to predict users’ purchasing behaviors.

The authors found that an individual’s adoption of a product was correlated with his or her purchasing habits and collaboration with others on the online sharing platform. Through the inclusion of network features, the authors were able to build a predictive model that forecasted consumers’ purchases of user-generated e-books with reasonable accuracy.

The interdisciplinary approach used in the study can serve as a good reference for identifying factors impacting the product adoption behavior of users in the online sharing platform, through employing different sociological and computational methods.

The outcome of the study has provided important managerial implications, especially for the design of social commerce platform in the age of the sharing economy.

The authors verified the social influence impacting consumers’ product adoption behavior and shed light on the value of collaboration in the age of the sharing economy.

The study was the first to identify user-generated e-book adoption on an online sharing platform from a multi-relational network perspective. The idea and the approach supplied a new method of behavioral analysis in the context of a sharing economy.