Agriculture contributes extensively to the economic development of countries; however, it is one of the main water-consuming industries. Revealing the characteristics and network structure of agricultural water use efficiency (AWUE) is conducive to green and coordinated development of agriculture. Considering that analyzing the variation of AWUE is helpful to calculating the AWUE, this study aims to calculate the total water consumption coefficient of the agricultural sector in the Yangtze River Economic Belt (YEB) by using the China interregional input-output tables in 2012 and 2017. The gravity model was modified to deduce the spatial correlation network of agricultural total water consumption coefficient (ATWCC), and the social network analysis method was used to analyze the network structural characteristics. The results show that: (1) compared to 2012, the AWUE of YEB in 2017 improved, with a decrease of ATWCC from 532.5 to 387.5 m³/10,000-yuan, account for 27.2%; (2) The network relevance of ATWCC of YEB’s 11 provinces (cities) enhanced, the rank relationship within the network and the network structure was relatively stable; (3) The spatial correlation network formed several network centers, Zhejiang and Jiangsu in the eastern coastal area were the main destinations of the spatial spillover of the spatial correlation network.

In the era of big data, the data is updating in real-time. How to prepare the data accurately and efficiently is the key to mining association rules. In view of the above questions, this paper proposes a dynamic horizontal union algorithm of multiple interval concept lattices under the same background of the different attribute set and object set. First, in order to ensure the integrity of the lattice structure, the interval concept lattice incremental generation algorithm was improved, and then interval concept was divided into existing concept, redundancy concept and empty concept. Secondly, combining the characteristics of the interval concept lattice, the concept of consistency of interval concept lattice was defined and it is necessary and sufficient for the horizontal union of the lattice structure. Further, the interval concepts united were discussed, and the principle of horizontal unions was given. Finally, the sequence was scanned by the traversal method. This method increased the efficiency of horizontal union. A case study shows the feasibility and efficiency of the proposed algorithm.

Water and energy are essential resources that flow between different regions in economic activities, forming a complex network that profoundly impacts sustainable development. Revealing network structural resilience allows for the identification of weak links, thus enhancing the capacity for sustainable development. This study employs a resilience-based method to examine changes in virtual water-energy transfers, combining input–output tables and total resource consumption coefficients (TRCC) to investigate the structural resilience of the virtual water-energy network. Case studies were conducted in the Yangtze River Economic Belt (YEB) in 2012 and 2017. The results show that the virtual water flow rate decreased by 28.66%, while that of virtual energy increased by 4.88% in YEB. The virtual energy network’s structural resilience is better than that of the virtual water network and shows significant improvement in later periods. The virtual water network structure has a clear hierarchical structure, while the virtual energy network structure is relatively flat. The transmission and connectivity of the two networks do not differ significantly, but the virtual energy network’s transmission is superior to that of the virtual water network. There is a significant improvement in the virtual energy network’s agglomeration in the later stages, while there is no significant change in the virtual water contact network.

An interval concept lattice is an expansion form of a classical concept lattice and a rough concept lattice. It is a conceptual hierarchy consisting of a set of objects with a certain number or proportion of intent attributes. Interval concept lattices refine the proportion of intent containing extent to get a certain degree of object set, and then mine association rules, so as to achieve minimal cost and maximal return. Faced with massive data, the structure of an interval concept lattice is more complex. Even if the lattice structures have been united first, the time complexity of mining interval association rules is higher. In this paper, the principle of mining association rules with parameters is studied, and the principle of a vertical union algorithm of interval association rules is proposed. On this basis, a dynamic mining algorithm of interval association rules is designed to achieve rule aggregation and maintain the diversity of interval association rules. Finally, the rationality and efficiency of the algorithm are verified by a case study.