2.2 Method
Osculating value method is an optimization method which determines the water quality by
the osculating values ordering of different water samples and the quality standards of
different ranks. The steps are as follows (Wu et al., 2010):
(1) Set up standardized dimensionless matrix
Assuming there are m samples and p standard ranks and in each sample or standard ranks
there are n indices to be considered. Then we can get an initial matrix C =c (ij) (m + p) × n,
where, c (ij) is the observed values of samples or the standard limits of corresponding ranks, i
= 1, 2 … (m + p) and j = 1, 2 …n.
Because in the initial matrix, complex relation such as the different dimensions, different
order of magnitude or sometimes different unites exists, the initial matrix must be
standardized. The initial matrix is standardized with formula (2).