Grey Relational Analysis Functions

A collection of functions for performing grey relational analysis, including calculation of grey correlation degree and evaluation based on grey correlation. These functions are designed for decision-making and data analysis by measuring the relational degree between sequences.

Usage

grey_corr(ref, cmp, rho = 0.5, w = NULL)

grey_corr_topsis(X, w, index = NULL, rho = 0.5)

Arguments

ref

Numeric vector, the reference sequence for grey_corr.

cmp

Numeric matrix or data frame, the comparison sequences for grey_corr.

rho

Numeric scalar, the distinguishing coefficient (default = 0.5).

w

Numeric vector, weights for weighted correlation (default = equal weights).

X

Numeric matrix or data frame, the decision matrix for grey_corr_topsis.

index

Character vector indicating indicator direction: Use "+" for positive indicators (higher is better), "-" for negative indicators (lower is better), and NA for already rescaled indicators (no rescaling will be applied). If index = NULL (default), all indicators are treated as NA, meaning no rescaling is performed.

Value

grey_corr

Returns a numeric vector of grey correlation degrees for each comparison sequence.

grey_corr_topsis

Returns a numeric vector of relative closeness (grey correlation degrees).

Details

These functions implement grey relational analysis for evaluating relationships between sequences or decision alternatives:

grey_corr

Computes the grey correlation degree between a reference sequence (ref) and comparison sequences (cmp) using the distinguishing coefficient (rho) and optional weights (w).

grey_corr_topsis

Evaluates a decision matrix (X) by normalizing it, applying weights (w), computing grey correlation with the ideal sequence. Direction of indicators can be specified via index.

Examples

# Grey correlation degree
ref = c(0.9, 0.8, 0.7)
cmp = data.frame(
  x1 = c(0.9, 0.7, 0.8),
  x2 = c(0.8, 0.9, 0.7),
  x3 = c(0.7, 0.8, 0.9)
)
grey_corr(ref, cmp, rho = 0.5)
#>        x1        x2        x3 
#> 0.6666667 0.6666667 0.5555556 

# Grey correlation evaluation
X = data.frame(x1 = c(8, 7, 6), x2 = c(150, 180, 200), x3 = c(60, 80, 100))
w = c(0.3, 0.4, 0.3)
idx = c("+", "+", "+")
grey_corr_topsis(X, w, idx, rho = 0.5)
#> [1] 0.4642511 0.4421740 0.4642511