Development, Application and Challenges of Set Pair Analysis in Environmental Science from 1989 to 2020: A Bibliometric Review

Set pair analysis is a new intelligent algorithm for dealing with complex uncertain problems, and it is widely used in environmental science because of its concise structure and scalability of results. However, it is still unclear about the development stage distribution of set pair analysis in environmental science and the specific development and application in key areas. Therefore, based on the method of bibliometrics, this paper studies the development, application and challenges of set pair analysis in environmental science over the past 32 years (1989–2020). The analysis found that in terms of time dimension, the development process of set pair analysis is divided into three stages: the initial stage (1989–2011); the rapid development stage (2012–2015); the steady development stage (2016 to present). In terms of specific fields, this article focuses on the development and application of set pair analysis in the three fields of ecology, water resources, and atmospheric environmental science. It is found that set pair analysis is mainly used for environmental assessment, diagnosis and prediction. In particular, the development of partial connection numbers is a new research trend of set pair analysis, which plays an important role in environmental assessment, diagnosis and prediction. However, the current set pair analysis also has the shortcomings of strong subjectivity, an imperfect theoretical system, and unbalanced development at home and abroad. Only when these deficiencies are solved, can the development of set pair analysis in environmental science be further promoted.

Integrated Flood Risk Assessment System Based on the Set Pair Analysis and Variable Fuzzy Sets for Cascade Dams

Flood-caused dam break is an important dam safety problem. Dam flood risk assessment based on an appropriate assessing method is hence essential for reducing dam-break flood damages and losses. In this research, a comprehensive flood risk assessment system for cascade dams was developed by combining the set pair analysis (SPA) and variable fuzzy sets (VFS) theory (namely SPA-VFS for short), and expressing the flood risk as a product of hazard and vulnerability, which were quantified by selected indicators. In the case study of the Dadu river basin, reservoir capacity, dam height, dam age, gross domestic product (GDP) density, population density, and predicted damage were selected as the evaluation indicators, and the evaluation results derived the flood risk classes of each studied dam. The study indicates that the proposed SPA-VFS-based flood risk assessment model is simple and feasible, which enables its further application in flood risk analysis and evaluation, and its extension in the risk assessment of other natural disasters.

Dynamic evaluation of regional water resources carrying capacity based on set pair analysis and partial connection number

In order to describe the micro motion between the connection number components and seek a more applicable evaluation model, quantitatively evaluate and analyze regional water resources carrying capacity (WRCC). Firstly, an evaluation index system and grade standards of regional WRCC were constructed. Then, a method for determining the connection number was proposed, which considered the micro motion between the connection number components in system structure. Finally, built an evaluation model based on set pair analysis (SPA) and partial connection number (PCN) that used subtraction set pair potential (SPP) to identify vulnerability factors, and identification results were compared with total partial connection number (TPCN). The model was applied to Huaibei City, Anhui Province, China. The results showed that: the WRCC grade value was between 2 and 3 that was poor; the support and regulation subsystem grade value was between 2 and 3, and the pressure subsystem grade value was between 1 and 2. SPP identified that the support force and regulation force subsystem were the vulnerable subsystems. Eight indexes such as water resources per capita, rate of ecological water consumption and density of population were the main indicators causing the poor WRCC, which were in good agreement with the local measured data. In addition, the SPP and TPCN are compared to further verify rationality of the connection number determination method and reliability of the identification results. The model established in this paper has strong applicability and can also be used for the dynamic evaluation of other resources, environment and ecological carrying capacity. The results in this study can provide a scientific basis for water resources management and decision-making.

A Heuristic Projection Pursuit Method Based on a Connection Cloud Model and Set Pair Analysis for Evaluation of Slope Stability

Determining the projection direction vector (PDV) is essential to the projection pursuit evaluation method for high-dimensional problems under multiple uncertainties. Although the PP method using a cloud model can facilitate interpretation of the fuzziness and randomness of the PDV, it ignores the asymmetry of the PDV and the fact that indicators are actually distributed over finite intervals; it quickly falls into premature defects. Therefore, a novel PP evaluation method based on the connection cloud model (CCM) is discussed to remedy these drawbacks. In this approach, adaptive numerical characteristics of the CCM are adopted to represent the randomness and fuzziness of the candidate PDV and evaluation indicators. Meanwhile, to avoid complex computing and to accelerate the convergence speed of the optimization procedure, an improved fruit fly optimization algorithm (FOA) is set up to find the rational PDV. Alternatively, candidate PDVs are mutated based on the mechanism “pick the best of the best” using set pair analysis (SPA) and chaos theory. Furthermore, the applicability and reliability are discussed based on an illustrative example of slope stability evaluation and comparisons with the neural network method and the PP evaluation method based on the other FOAs and the genetic algorithm. Results indicate that the proposed method with simpler code and quicker convergence speed has good global ergodicity and local searching capabilities, and can better explore the structure of high-dimensional data with multiple uncertainties and asymmetry of the PDV relative to other methods.

Research on Slope Stability Evaluation Based on Improved Set Pair Analysis Method: A Case of Tonglvshan Open-Pit Mine

In this paper, combined with fuzzy analytic hierarchy process (FAHP), information entropy theory, and set pair analysis (SPA) theory, an improved set pair analysis model (EFAHP-SPA) for open-pit mine slope stability evaluation based on entropy method and FAHP is proposed. Taking the east-side slope of Tonglvshan north open-pit mine in Daye as an example, the proposed method is verified. First, an open-pit mine slope stability evaluation index system with 14 indicators in 4 categories, namely the topography and geomorphology, geological structure, hydrogeology, and other factors, have been constructed. Second, the objective weight and subjective weight of each evaluation index are calculated by entropy and fuzzy analytic hierarchy process, and then the comprehensive weight of the evaluation index is estimated based on subjective weight and objective weight. Afterward, the single-index connection degree between the evaluation index and the evaluation standard of the secondary subsystem is evaluated considering the improved set pair analysis theory, and the comprehensive connection degree of the system is obtained by combining it with the comprehensive weight of each evaluation index. Finally, the confidence criterion is established to discern the risk grade of slope stability in the east-side slope of the north open pit in Daye Tonglvshan mine. Moreover, case studies and comparisons of the proposed model with fuzzy comprehensive evaluation method and Entropy-SPA model were performed to confirm the validity and reliability. The results show that the evaluation results of the proposed EFAHP-SPA model are consistent with the actual situation of open-pit mines and the evaluation results of entropy-SPA model and are somewhat different from those of fuzzy comprehensive evaluation method. It indicates that the proposed EFAHP-SPA evaluation model can objectively evaluate the slope stability of the open-pit mine.