Decision matrix

Rank options on several criteria with TOPSIS and VIKOR, set the weights directly or by AHP, and see with SMAA-2 how the ranking holds when the weights are uncertain.

The example ranks four flats on rent, commute, floor area and energy use. Change a score or a weight and see whether the winner holds, or type in your own table.

Made-up flats to show the methods. Edit any cell, or paste a table from a spreadsheet.

Options by criteria
Option

Weights

Rent, €/month25 %

Commute, min25 %

Floor area, m²25 %

Energy use, kWh/m²·yr25 %

The weights share 100 %: raising one lowers the others.

TOPSIS

Closeness
1Flat B0.683
2Flat D0.611
3Flat A0.464
4Flat C0.282

VIKOR

$Q$ $S$ $R$
1Flat D0.050.410.18
2Flat A0.290.510.17
3Flat B0.750.500.25
4Flat C1.000.590.25

No single winner: Flat D, Flat A form the compromise set, because the lead in $Q$ is under $1/(m-1)$ = 0.33.

When the weights are uncertain: SMAA-2

Every set of weights is equally likely.

Rank acceptability: the share of weights that puts each option at each rank
Option	Rank 1	Rank 2	Rank 3	Rank 4	Holistic
Flat D	42 %	28 %	28 %	3 %	0.69
Flat B	37 %	19 %	4 %	40 %	0.50
Flat A	5 %	32 %	63 %	<1 %	0.47
Flat C	16 %	22 %	5 %	57 %	0.33

Central weights: the typical weights that make each option first
Option	Rent	Commute	Floor area	Energy use
Flat D	19 %	24 %	41 %	17 %
Flat B	15 %	34 %	11 %	40 %
Flat A	42 %	14 %	9 %	34 %
Flat C	58 %	12 %	18 %	13 %

Method

Every method works on the table as costs: a criterion where higher is better is negated first. TOPSIS (Hwang and Yoon 1981) normalizes each column by its length and ranks by closeness to the ideal option against the anti-ideal one. VIKOR (Opricovic and Tzeng 2004) ranks by $Q$ , a mix ( $v=0.5$ ) of the weighted sum of shortfalls $S$ and the largest single shortfall $R$ , and proposes one option only if it leads clearly and is stable.

AHP (Saaty 1990) turns one judgement per pair of criteria, on the 1 to 9 scale, into weights: the principal eigenvector of the comparison matrix. The consistency ratio divides the consistency index by the random index, the mean index of random comparison matrices; the published tables of that index differ slightly between sources, so here it is estimated from 100,000 random matrices per size (0.525, 0.881, 1.108 and 1.247 for 3 to 6 criteria).

SMAA-2 (Lahdelma and Salminen 2001) scores each option by a weighted sum of its criteria, each scaled from the worst option (0) to the best (1), for 10,000 weight vectors drawn from what is known about the weights, with a fixed seed so a link always gives the same numbers. Rank acceptability is the share of those weights that puts an option at each rank; central weights are the average weights where it comes first; holistic acceptability weighs the ranks linearly, from 1 for first to 0 for last.

References Code

Assumptions and limits

All three methods assume the criteria can be traded against each other and treat each one as linear between its worst and best values. They rank only the options in the table: adding or removing one can change the order of the others.

The flats are made up to show the methods. A teaching tool, not decision advice; everything stays in your browser.

Cite

@software{guven_decision,
  author = {Güven, Murat},
  title  = {Decision matrix},
  year   = {2026},
  url    = {https://likemaestro.github.io/tools/decision}
}

References

Hwang, C.-L., & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications – A State-of-the-Art Survey. Springer. doi:10.1007/978-3-642-48318-9
Lahdelma, R., & Salminen, P. (2001). SMAA-2: Stochastic multicriteria acceptability analysis for group decision making. Operations Research, 49(3), 444–454. doi:10.1287/opre.49.3.444.11220
Opricovic, S., & Tzeng, G.-H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445–455. doi:10.1016/S0377-2217(03)00020-1
Saaty, T. L. (1990). How to make a decision: The analytic hierarchy process. European Journal of Operational Research, 48(1), 9–26. doi:10.1016/0377-2217(90)90057-I

Decision matrix

WeightsHow much each criterion counts. Set them directly, or answer one question per pair of criteria and let AHP work them out.

TOPSISRanks by closeness to an ideal option made of the best value on every criterion, against an anti-ideal made of the worst. 1 would be the ideal itself.

VIKORQQQ mixes SSS, the weighted sum of how far an option falls short of the best on each criterion, and RRR, its largest single shortfall. Lower is better for all three.

When the weights are uncertain: SMAA-2Instead of one set of weights, 10,000 sets drawn from what you know about them. Each ranks the options; the table counts how often each option lands at each rank.