Air pollution forecasting plays a vital role in environment pollution warning and control. Air pollution forecasting studies can also recommend pollutant emission control strategies to mitigate the number of poor air quality days. Although various literature works have focused on the decomposition-ensemble forecasting model, studies concerning the endpoint effect of ensemble empirical mode decomposition (EEMD) and the forecasting model of sub-series selection are still limited. In this study, a hybrid forecasting approach (EEMD-MM-CFM) is proposed based on integrated EEMD with the endpoint condition mirror method and combined forecasting model for sub-series. The main steps of the proposed model are as follows: Firstly, EEMD, which sifts the sub-series intrinsic mode functions (IMFs) and a residue, is proposed based on the endpoint condition method. Then, based on the different individual forecasting methods, an optimal combined forecasting model is developed to forecast the IMFs and residue. Finally, the outputs are obtained by summing the forecasts. For illustration and comparison, air quality index (AQI) data from Hefei in China are used as the sample, and the empirical results indicate that the proposed approach is superior to benchmark models in terms of some forecasting assessment measures. The proposed hybrid approach can be utilized for air quality index forecasting.

Accurate carbon price index prediction can delve deeply into the internal law of carbon price changes, provide helpful information to managers and decision makers, as well as improve the carbon market system. Nevertheless, existing methods for combination forecasting typically arbitrarily choose a certain set of single forecasting models. However, a particular selection of forecasting models do not apply to all data sets due to the nonlinearity and nonsmoothness of the carbon trading price series. Therefore, choosing suitable single forecasting models for the combination is crucial. Considering the limitations of the current study, this study constructs a combined carbon trading forecasting model based on Lasso regression and optimal integration. By invoking the Lasso regression model, we can select suitable single forecasting models for combination forecasting based on the variation patterns of different training sets. Meanwhile, ARIMA, NARNN, LSTM, and 11 other single forecasting models are screened in this study, including both traditional statistical forecasting models and artificial intelligence forecasting models. First, the carbon price index is predicted using 11 single prediction models. Furthermore, given the multi-collinearity of the single prediction series, this study employs Lasso regression to reduce the dimensions of the single prediction models, which are then used to construct an optimal combination prediction model. Finally, the proposed model is applied to SZA-2017 and SZA-2019 carbon price data in Shenzhen. The results demonstrate that the model developed in this study outperforms other benchmark prediction models in terms of prediction error and direction accuracy, showing the efficacy of the proposed method.

The aim of this paper is to study the conversions between Pythagorean fuzzy sets and Atanassov's intuitionistic fuzzy sets. Besides, an ORESTE method based on multi-attribute decision making with Pythagorean fuzzy sets is developed by utilising the developed conversions. In this paper, according to the geometric representations of Pythagorean fuzzy sets and Atanassov's intuitionistic fuzzy sets, two types of conversions between the two fuzzy sets are constructed, which are further used to derive information measures include entropy and cross-entropy measures of Pythagorean fuzzy sets. Then, by combining with the ORESTE method, a direct decision procedure for multi-attribute decision making with Pythagorean fuzzy information is developed. Finally, a numerical example of the evaluation of regional energy efficiency is shown to illustrate the feasibility and validity of the developed decision procedure.

In group decision making with social network analysis (SNA), determining the weights of experts and constructing the consensus-reaching process (CRP) are hot topics. With respect to the generation of weights of experts, this paper firstly develops a distributed linguistic trust propagation operator and a path order weighted averaging (POWA) operator to explore the trust propagation and aggregation between indirectly connected experts, and the weights of experts can be derived by using relative node in-degree centrality in a complete distributed linguistic trust relationship matrix. Then, three levels of consensus are proposed, in which the most inconsistent evaluation information in distributed linguistic trust decision-making matrices can be pinpointed. Subsequently, the distance between experts’ evaluation information and collective evaluation information is designed to be applied as the adjustment cost in CRP. Finally, a novel feedback mechanism supported by the minimum adjustment cost is activated until the group consensus degree reaches the predefined threshold. The novelties of this paper are as follows: (1) the proposed POWA considers the trust value as well as the propagation efficiency of trust path when aggregating the trust relationship in SNA; (2) the consensus reaching mechanism can gradually improve the value of group consensus degree by continuously adjusting the most inconsistent evaluation information.