# SAPEVO-M Example

## Introduction

##### Multicriteria Decision Analysis (MCDA) and SAPEVO-M method.

MCDA aims to help with the decision process when there is more than one criterion. Multicriteria methods can be useful in individual or group decisions in business or other fields.

SAPEVO-M is a group ordinal method that uses decision-makers’ preferences among criteria and alternatives. The ordinal preferences are transformed into cardinal using a scale to define the intensity from -3 to 3. SAPEVO-M is an acronym for Simple Aggregation of Preferences Expressed by Ordinal Vectors Group Decision Making.

## Example

This vignette uses, as an example, a case of internet service provider evaluation. The goal is to select among A, B, and C companies based on cost, rating, and speed.

Below we have the decision matrix (alternatives x criteria).

Alternatives Cost Rating Speed
A1 100 7.81 120
A2 150 8.96 200
A3 130 5.78 300

We start getting the criteria pairwise comparison from the decision-makers, two in this example.

#### Criteria pairwise comparison

decision-maker 1

Cost Rating Speed
Cost 0 2 1
Rating -2 0 -2
Speed -1 2 0

decision-maker 2

Cost Rating Speed
Cost 0 3 -2
Rating -3 0 -3
Speed 2 3 0

Considering the decision-maker 2 example, this comparison matrix can be read like this: “Cost is absolutely more important than Rating, Speed is much more important than Cost, Speed is absolutely more important than Rating.”

After this, we get the alternative pairwise comparison - for each criterion - from the two decision-makers.

#### Alternative pairwise comparison

Cost Criterion

decision-maker 1

A1 A2 A3
A1 0 2 1
A2 -2 0 -2
A3 -1 2 0

decision-maker 2

A1 A2 A3
A1 0 3 2
A2 -3 0 -2
A3 -2 2 0

Rating Criterion

decision-maker 1

A1 A2 A3
A1 0 0 1
A2 0 0 2
A3 -1 -2 0

decision-maker 2

A1 A2 A3
A1 0 -1 2
A2 1 0 3
A3 -2 -3 0

Speed Criterion

decision-maker 1

A1 A2 A3
A1 0 -1 -1
A2 1 0 -1
A3 1 1 0

decision-maker 2

A1 A2 A3
A1 0 -2 -3
A2 2 0 -3
A3 3 3 0
library(sapevom)

criteria<- c("Cost", "Rating", "Speed")
alternatives<- c("A1", "A2", "A3")

listofmatrices<-list(matrix(c(0,2,1,-2,0,-2,-1,2,0),
byrow=TRUE, ncol=3, dimnames=list(criteria)),
matrix(c(0,3,-2,-3,0,-3,2,3,0),
byrow=TRUE, ncol=3, dimnames=list(criteria))
)

listoflistsofmatrices<-list(list(matrix(c(0,2,1,-2,0,-2,-1,2,0),
byrow=TRUE, ncol=3, dimnames=list(alternatives)),
matrix(c(0,3,2,-3,0,-2,-2,2,0),
byrow=TRUE, ncol=3, dimnames=list(alternatives))),
list(matrix(c(0,0,1,0,0,2,-1,-2,0),
byrow=TRUE, ncol=3, dimnames=list(alternatives)),
matrix(c(0,-1,2,1,0,3,-2,-3,0),
byrow=TRUE, ncol=3, dimnames=list(alternatives))),
list(matrix(c(0,-1,-1,1,0,-1,1,1,0),
byrow=TRUE, ncol=3, dimnames=list(alternatives)),
matrix(c(0,-2,-3,2,0,-3,3,3,0),
byrow=TRUE, ncol=3, dimnames=list(alternatives)))
)

sapevom(criteriaEvaluations= listofmatrices, alternativesEvaluations= listoflistsofmatrices)
#> []
#>       Cost     Rating      Speed
#> 1.63636364 0.01350649 1.71428571
#>
#> []
#>      values rank
#> A1 3.292537    2
#> A2 1.507532    3
#> A3 5.415584    1

As a result, we have a list with criteria weights and alternative ordering.

#### Reference

GOMES, C. F. S., DOS SANTOS, M., TEIXEIRA, L. F. H. S. B., SANSEVERINO, A. M. and BARCELOS, M.R. S. (2020). SAPEVO-M: a group multicriteria ordinal ranking method. Pesquisa Operacional. 40. 1-20. DOI: 10.1590/0101-7438.2020.040.00226524.