Extended belief rule-based model for environmental investment prediction with indicator ensemble selection
Introduction
Due to increasing pollution emission and ecological damage, government and society have recently paid greater attention to environmental protection [13]. The resulting investments have grown annually to ensure that urgent pollution control and ecological remediation have targeted effect. The greatest impact typically depends on the ability of environment managers to formulate effective investment schemes for achievable environmental managements [6], [25]. For the sake of facilitating implementation of effective investment schemes, many environmental investment prediction models have been proposed based on environmental indicators and experts' knowledge, while the challenge is still how to build reliable prediction models based on various environmental indicators.
The use of representative environmental indicators to monitor management effectiveness is often identified as one of the successful factors for effectively predicting environmental investments, as they can indicate improvement opportunities on accurate investment planning. In previous studies, many methods have been used for environmental indicator selection, e.g., principal component analysis (PCA)-based method [24] and correlation-based feature selection (CFS)-based method [16]. However, they mainly focused on a single indicator selection method, which has its own advantages as well as weaknesses on indicator selection for different kinds of environmental investment problems. This results in the undesired outcome that irrelevant indicators are selected for environmental investment prediction modeling. Making effective indicator selection is the challenge that must be considered to propose a new environmental investment prediction model.
Based on the selected environmental indicators, a certain decision-making methodology and historical environmental data could be included to construct an investment prediction model, e.g., time series forecasting-based [6], [12] and input-output relationship-based models [16], [24]. It is worth noting that the specialty of investment prediction models would inherit from the selected decision-making methodology, so the use of a specific decision-making methodology must take into consideration human involvement for environmental managements, which indicates that environment managers can embed experts' knowledge into the modeling of environmental investment prediction and also know exactly well how the model predict outcomes for investments. As a result, environment managers can have greater confidence to formulate an investment scheme according to the predicted environmental investments.
As discussed above on investment prediction modeling, two critical challenges can be summarized as follows: 1) the use of a single method to select indicators is the main way to screen indicator information in previous studies, but the difference of indicator selection methods will increase the probability of the information loss of representative indicators; 2) since environmental management requires human involvement, the modeling of investment prediction must have the feature of white-box design and the prediction process of the model must be explainable for environment managers.
To overcome the two challenges on investment prediction modeling, a new environmental investment prediction model is proposed on the basis of extended belief rule-based (EBRB) model and indicator ensemble selection (IES) and the new model is called the IES-EBRB model, in which the EBRB model is a white-box designed decision-making model proposed by Liu et al. [10] and has the ability on using experts' knowledge to enhance data analytics for autonomous decision making; the IES is an extension of ensemble learning [2] to cooperatively integrate different kinds of indicator selection methods for selecting indicators, so representative indicators can be accurately selected for investment prediction modeling. Accordingly, the proposed IES-EBRB model has the following advantages:
- (1)
The IES-EBRB model is an unlocking structure so that any kind of indicator selection methods can be added and used together to rank the relative importance of different environmental indicators. In other words, environmental indicators can be sorted according to the various perspectives derived from the advantages of different indicator selection methods.
- (2)
Three ranking combination functions are introduced to integrate the rankings of each indicator, which are obtained from different kinds of indicator selection methods. According to the combined ranking of all indicators, the indicators with top ranking are selected as representative indicators and thus used for the construction of an investment prediction model.
- (3)
The IES-EBRB model can be regarded as a data-driven and knowledge-driven hybrid model, because its extended belief rule can be generated from historical data and revised according to experts' knowledge. Hence, experienced managers can embed experts' knowledge into the IES-EBRB model to enhance its ability on investment prediction.
- (4)
The IES-EBRB model imports the benefits from the EBRB model so that it not only has a high interpretability due to the explainable processes of generating extended belief rules and predicting environment investments, but also is easy to achieve a low complexity because the total number of extended belief rules in the IES-EBRB model does not increase exponentially with the increasing number of indicators and/or referential values.
In order to demonstrate the effectiveness of the proposed IES-EBRB model, a real case regarding actual environmental investment data derived from 2005 to 2018 in 31 China provinces is used to illustrate the development procedure of the proposed IES-EBRB model and also provide the comparative analysis of some existing time series forecasting-based and input-output relationship-based investment prediction models.
The remainder of this work is as follows: Section 2 is the literature review and outlines the challenges of previous environmental investment prediction modeling. Section 3 introduces the basic methodology of conventional EBRB model. Section 4 proposes the IES-EBRB model for environmental investment prediction. Section 5 provides a case study to perform model validation. Section 6 concludes this study.
Section snippets
Literature review and challenges
In this section, the previous studies of the application of the EBRB model and modeling of environmental investment prediction are reviewed, and then the challenges of these studies are summarized to illustrate the necessity of this study.
Basic methodologies of the EBRB model
The EBRB model [10] is an advanced rule-based system extended from the belief rule-based (BRB) system [20] by embedding belief structures into the IF part of belief rules. The extended belief rules therefore have ability to represent hybrid information of experts' knowledge and historical data under uncertainty.
Suppose that there are M antecedent attributes () with each attribute having reference values () and one consequent attribute D with N consequents ().
An improved EBRB model using IES for environmental investment prediction
In this section, the procedure of IES to select indicators is proposed in Section 4.1, followed by the introduction of the EBRB modeling based on the selected indicators in Section 4.2. Finally, the framework of the new model for environmental investment prediction, called the IES-EBRB model, is provided in Section 4.3.
Case study of environmental investment prediction in China
In order to verify the effectiveness of the proposed IES-EBRB model, the actual environmental data of 31 provinces in mainland China were used to perform an empirical case study. The introduction of data source and model setting is in Section 5.1, the development of the IES-EBRB model is in Section 5.2, and the comparative analysis is in Section 5.3.
Conclusions
In this study, a new model called IES-EBRB was proposed for environmental investment prediction. The components of the IES-EBRB model combine the IES procedure and EBRB modeling, where the former process can select representative environmental indicators based on various indicator selection methods, and the latter provides a white-box modeling mechanism for constructing prediction models using experts' knowledge and historical data. The main conclusions of this study can be further summarized
CRediT authorship contribution statement
Fei-Fei Ye: Writing - original draft, Conceptualization, Methodology, Data curation, Formal analysis. Suhui Wang: Formal analysis, Writing - review & editing, Supervision. Peter Nicholl: Writing - review & editing, Supervision. Long-Hao Yang: Investigation, Writing - review & editing, Supervision. Ying-Ming Wang: Writing - review & editing, Supervision, Conceptualization, Investigation, Validation.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research is supported by the National Natural Science Foundation of China (Nos. 61773123, 71701050, 71801050, and 71872047), the Humanities and Social Science Foundation of the Ministry of Education of China (Nos. 20YJC630188, 19YJC630022, and 20YJC630229), and the Social Science Foundation of Fujian Province, China (No. FJ2019C032).
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