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The purpose of this paper is to explore a new grey relational analysis model to measure the coupling relationship between the indicators for the water environment status assessment. Meanwhile, the model deals with the problem that the changing of indicator order may result in the changing of the degree of grey relation.

The binary index submatrix of the sample matrix is given first. Then the product of the matrix and its own transpose is used to measure the characteristics of the index and the coupling relationship between the indicators. Thirdly, the grey relational coefficient is defined based on the matrix norm, and a grey coupling relational analysis model is proposed.

The paper provides a novel grey relational analysis model based on the norm of matrix. The properties, normalization, symmetry, relational order invariance to the multiplicative, are studied. The paper also shows that the model performs very well on the water environment status assessment in the eight cities along the Yangtze River.

The model in this paper has supplemented and improved the grey relational analysis theory for panel data.

Accurate foreign tourist arrivals forecasting can help public and private sectors to formulate scientific tourism planning and improve the allocation efficiency of tourism resources. This paper aims to address the problem of low prediction accuracy of Chinese inbound tourism demand caused by the lack of valid historical data.

A novel hybrid Chinese inbound tourism demand forecasting model combining fractional non-homogenous discrete grey model and firefly algorithm is constructed. In the proposed model, all adjustable parameters of the fractional non-homogenous discrete grey model are optimized simultaneously by the firefly algorithm.

The data sets of annual foreign tourist arrivals to China are used to verify the validity of the proposed model. Experimental results show that the proposed method is effective and can be used as a useful predictor for the prediction of Chinese inbound tourism demand.

The method proposed in this paper is effective and can be used as a feasible approach for forecasting the development trend of Chinese inbound tourism.