Raquel Dourado Coutinho, Marcos dos Santos



Multicriteria Decision Analysis (MCDA) and the AHP-TOPSIS-2N method.

The objective of MCDA is to assist in decisions with multiple criteria. Multicriteria methods can be useful in several problems in business and even in personal life. AHP-TOPSIS-2N is a hybrid method build from the AHP (Analytic Hierarchy Process) and TOPSIS-2N (Technique for Order of Preference by Similarity to Ideal Solution - with two normalizations).

AHP-TOPSIS-2N uses the AHP to calculate the criteria weights and uses TOPSIS twice to generate rankings, each time with a different kind of normalization. This can allow the comparison of results and the analysis of the robustness. A consistency ratio is calculated, and when it is higher than 10%, it is required to check judgments on criteria comparison.


As an example, this vignette uses a case of row material supplier evaluation. The goal is to choose among A, B, and C suppliers based on the product cost, product quality (1 to 5), and the lead time. Below we have the decision matrix (alternatives x criteria).

Alternatives Cost Quality Lead Time
A1 1100 5 25
A2 850 3.5 10
A3 950 4 30

After defining the decision matrix, it’s time to define a matrix with a pairwise comparison of the criteria, using the Saaty scale (1-9).

Cost Quality Lead Time
Cost 1 1 3
Quality 1 1 5
Lead Time 1/3 1/5 1

The criteria comparison matrix can be read like this: “Cost is so important as Quality, Cost has moderate importance over Lead Time, Quality has strong importance over Lead Time.”


# define the decision matrix
decision<-matrix(c(1100, 5, 25,
                   850, 3.5, 10,
                   950, 4, 30), ncol=3, byrow=TRUE)

rownames(decision)<- c("A1", "A2", "A3")

#define criteria matrix with pairwise comparison
criteria<-matrix(c(1, 1, 3,
                   1, 1, 5,
                   1/3, 1/5, 1), ncol=3, byrow=TRUE)

# define each criterion objective
minmax<-c("min", "max", "min")

# associate the objects to the function arguments and run the function
ahptopsis2n(decision=decision, criteria=criteria, minmax=minmax)
#> [[1]]
#>            [,1]
#> [1,] 0.02505497
#> [[2]]
#>       values ranking
#> A1 0.5754562       1
#> A2 0.4553086       2
#> A3 0.3517222       3
#> [[3]]
#>       values ranking
#> A1 0.5374991       1
#> A2 0.4669885       2
#> A3 0.4359941       3

As we can see, the result is a list with a consistency ratio and two data frames with priority sorting of the alternatives.


De Souza, L. P., Gomes, C. F. S. and De Barros, A. P. (2018). Implementation of New Hybrid AHP–TOPSIS-2N Method in Sorting and Prioritizing of an it CAPEX Project Portfolio. International Journal of Information Technology & Decision Making. DOI: 10.1142/S0219622018500207.

Saaty, T.L. The Analytic Hierarchy Process. McGraw-Hill, New York. (1980)