Decision.TOPSIS

This function applies the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method in order to rank alternatives based on multiple criteria. It normalizes the data, applies weights, calculates the distance to the ideal and anti-ideal solutions, and computes a Closeness Coefficient (CC) for each alternative. The result is a ranked table of alternatives.

Syntax

Decision.TOPSIS(
    tbl as table,
    alternativesColumn as text,
    weights as record
) as table

Parameters

• table: The input table containing alternatives and their evaluation across multiple criteria.
• alternativesColumn: The name of the column that identifies each alternative.
• weights: A record where each field name corresponds to a criterion column in the table, and each field value is the weight (importance) of that criterion.

Return Value

A ranked table of alternatives ordered by the closeness coeficient (CC).

Remarks

• The function performs the following steps:
  • Normalization of each criterion using Euclidean norm.
  • Weighting of normalized values using the provided weights.
  • Calculation of Positive Ideal Solution (PIS) and Negative Ideal Solution (NIS).
  • Distance to PIS ($D^{+}$) and Distance to NIS ($D^{-}$) for each alternative.
  • Closeness Coefficient (CC): $CC = \frac{D^{-}}{D^{+} + D^{-}}​$
  • Ranking: Alternatives are sorted by CC in descending order. Ties receive the same rank.
• If both $D^{+}$ and $D^{-}$ are zero, CC is set to 0.5.
• This method is widely used in multi-criteria decision analysis (MCDA), especially when criteria have different units or scales.

Example

Ranking alternatives with three criteria.

let
    Source = #table(
        {"Alternative", "Cost", "Quality", "Speed"}, {
        {"A", 300, 80, 60},
        {"B", 250, 70, 75},
        {"C", 400, 90, 50}
    }),
    Weights = [Cost = 0.4, Quality = 0.3, Speed = 0.3],
    Result = Decision.TOPSIS(Source, "Alternative", Weights)
in
    Result

Result

Alternative	Cost	Quality	Speed	CC	RANKING
C	400	90	50	0.74	1
B	250	70	75	0.26	2
A	300	80	60	0.26	3

References

• Hwang, C.L. and Yoon, K. (1981) Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag, New York. http://dx.doi.org/10.1007/978-3-642-48318-9
• Madanchian M, Taherdoost H. A comprehensive guide to the TOPSIS method for multi-criteria decision making. Sustainable Social Development 2023; 1(1): 2220. doi: 10.54517/ssd.v1i1.2220