TOPSIS Method for Multi-Criteria Decision Making

Implements the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to rank alternatives based on multiple criteria. The function normalizes the decision matrix using L2 norm, applies weights, and computes relative closeness to the ideal solution.

Usage

topsis(X, w = NULL, index = NULL)

Arguments

X

A numeric matrix or data frame where rows represent alternatives and columns represent criteria.

w

A numeric vector of weights for each criterion. Must be non-negative and sum to 1. If not provided, equal weights are used.

index

A character vector indicating the direction of each indicator: Use "+" for positive indicators (higher is better), "-" for negative indicators (lower is better). If index = NULL (default), all indicators are treated as "+".

Value

A named numeric vector of relative closeness scores (in 0, 1) for each alternative. Higher values indicate better alternatives. Names are taken from rownames(X) or default to "Sample1", "Sample2", etc.

Details

The TOPSIS method ranks alternatives by:

1. Normalizing the decision matrix using L2 norm normalization.

2. Applying weights to form a weighted normalized matrix.

3. Identifying positive and negative ideal solutions based on indicator directions.

4. Computing Euclidean distances to ideal solutions.

5. Calculating relative closeness as S0 / (S0 + Sstar), where S0 is the distance to the negative ideal and Sstar is the distance to the positive ideal.

This implementation supports both positive and negative indicators via the index parameter.

Examples

A = data.frame(
  X1 = c(2, 5, 3),  # "+"
  X2 = c(8, 1, 6)   # "-"
)
w = c(0.6, 0.4)
idx = c("+","-")
topsis(A, w, idx)
#> [1] 0.0000000 1.0000000 0.3111391