In this paper, we regard the membership degree and the non-membership degree of the intuitionistic fuzzy set (IFS) as a whole and propose a new approach to measuring the correlation degree between the IFSs in finite sets. Like the computational process of the correlation coefficient between the real number variables, we first define the deviation of the intuitionistic fuzzy numbers, the variance of the IFS, and the covariance of the IFSs; then propose the formula to get the correlation coefficient between the IFSs. The proposed method not only reflects the symbol attribute of the correlation degree between the IFSs (the value of the correlation coefficient lies in the interval [–1, 1]), but also makes sure the integrity of the IFS is maintained. Several examples are given to show the feasibility and advantages of the proposed method. Moreover, we extend this approach to the interval-valued intuitionistic fuzzy set (IVIFS) case.

For the past few years, China’s urbanization process has been in a state of rapid and variable development. With many migrants flowing from rural to urban area, the change in the urban structure and the trend of the economic development has led to a rapid development of the real estate market. However, the conflict between the migrants and the local low- and middle-income groups in respect of demand for basic housing has become a concern. Based on Chinese time-series data from 2008 to 2018, this study establishes an evaluation indicator system to consider the influence of urbanization, housing prices, and affordable housing and analyzes the comprehensive development level and coordination relationship using the methods of range standardization, entropy weight model, and coupling coordination. The results show that the comprehensive development levels of housing prices and affordable housing are both in a state of fluctuating growth. From 2008 to 2018, the coupling degree between urbanization, housing prices, and affordable housing was high, while the coupling coordination degree between the three subsystems increased from reluctant coordination to satisfactory coordination; this clearly shows that the relationships between urbanization, housing prices, and affordable housing are mutually coupled and promoted. Furthermore, based on the coupling coordination relationships between the three subsystems, this study discusses the sustainable development of urbanization and provides some suggestions for regional government. The conclusions have practical significance for China and other developing countries to coordinate housing prices and affordable housing in the process of rapid urbanization.

The real estate market is vital for national economic development, and it is of great significance to research an early warning method to identify an abnormal status of the real estate market. In this study, a real estate early warning system based on the PSO-LSSVR model was created to train and test the indicator data of Beijing from 2000 to 2020, and to predict the early warning indicator of the Beijing real estate market from 2021 to 2030. The results showed that the warning status of the Beijing real estate market went from a fluctuation status to a stable “Normal” status from 2000 to 2020, and the warning status is expected to be more stable under a “Normal” status in the next decade under the same political and economic environment. The PSO-LSSVR model was found to have accurate prediction ability and demonstrated generalization ability. Furthermore, the warning status of the Beijing real estate market was analyzed in combination with national historical policies. Based on the results, this paper proposes policy recommendations to promote the healthy and sustainable development of the real estate market.

Beginning with real estate financial risk and risk energy theory, combined with empirical research, this article analyzes real estate financial markets in different stages and calculates the profit and loss (the ratio of the release of risk energy to the risk energy) in order to judge whether the risk energy has exceeded the system tolerance and to play a warning role. First, this article analyzes uncertain factors in the real estate market, builds a real estate supply and demand network, determines system risk characteristics, corresponding profit and loss categories, quantitative and qualitative factors, and the risk of energy release and the collapse of boundary conditions. The real estate market is approached using both univariate and multivariate analyses, dividing the real estate market into three stages and probing mergers and transformation conditions for different levels of risk. Finally, the authors analyze whether the financial risk energy released by real estate market exceeds the capacity of the system by calculating probability, risk, which play a warning role.

This paper addresses the issue of the impact of the competitive behaviors of long-rental apartment firms on the rents of long-rental apartments and ordinary rental housing and introduces a dynamic gaming approach to the housing rental market domain to reveal changes in the long-term complexity of rents of long-rental apartments and ordinary rental housing caused by the competitive behavior of long-rental apartment firms. Through numerical simulation, it is found that the adoption of smaller rent adjustment strategies by firms is important for maintaining system stability, while the changes in reference effect behavior of landlords and service quality and differences in demand share have moderating effects on system stability. The enhanced reference effect of landlords, the improvement of service quality, and the increase of the difference in demand share between the two long-rental apartments help to mitigate the disruption of system stability by the increase of the adjustment factor of the firms. The decentralized long-lease apartment firms, which occupy a higher proportion of the market, are able to exert a major impact on the rent of general rental housing by taking advantage of the market, while the difference in the demand share between the two firms is the main reason for the change in the rent of long-rental apartments.

In this paper, we construct an evolutionary game model of government and real estate operators (long-term apartment rental companies) in the housing rental market in the context of financial institutions and public participation in regulation and analyze the effects of different regulatory levels of financial institutions and the public on the evolutionary results through model solving and numerical simulation. The results show that, under five different levels of supervision, financial institutions and the public have different evolutionary and stable strategies; financial institutions’ participation in supervision can effectively reduce the cost of government supervision and promote the government’s evolution towards strict supervision. It is difficult for real estate operators to evolve naturally towards keeping their promises when the probability of the social public or financial institutions participating in regulation is low. Only when the probability of social public and financial institutions participating in regulation reaches a certain level will real estate operators be inclined to keep their promises.