A new method of the relative membership degree calculation in variable fuzzy sets for water quality assessment

The wide application of variable fuzzy sets theory (VFST) in water quality evaluation indicates that the calculation process of relative membership degree (RMD) is complicated and laborious. The traditional method of calculating RMD repeatedly reuses the relative membership degree function (RMDF), and lacks an effective means to estimate the reliability of the calculation. These problems increase the difficulty of water quality evaluation. Based on the principle of variable fuzzy sets, this research finds some data characteristics of RMD and further demonstrates its inevitability. A new method was developed using a combination of these data characteristics and the traditional method of RMD calculation. By empirical analysis of water quality evaluation, the new method exhibited stable reliability and efficient performance compared with the traditional method. The primary advantages include the following: (i) simplification of the calculation of RMD and reduction in the computation burden for RMDF, (ii) verification of the calculation result of RMD and development of a scientific basis for testing evaluation results, and (iii) improvement of the calculation accuracy of RMD.