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MCDM Methods

Step-by-Step Algorithms

PIPRECIA Method

Pivot Pairwise Relative Criteria Importance Assessment

2017 Sanja Stanujkić et al. 4 Steps

PIPRECIA (Pivot Pairwise Relative Criteria Importance Assessment) is a subjective criteria-weighting method used in MCDM. It determines the relative importance of criteria by comparing each criterion with a pivot criterion and assessing whether its importance is lower, equal, or higher than the previous criterion.

Video Demonstration

Step-by-Step Algorithm

Calculated cell
Source cells in formula
1

Order the criteria

Arrange the criteria according to the decision-maker's perceived importance. Select a pivot criterion as the starting/reference criterion.

$$ C_1,C_2,\ldots,C_n $$

For each criterion \(C_j\), determine its relative importance compared with the previous criterion \(C_{j-1}\). This assessment is represented by \(S_j\).

$$ S_j=\frac{\text{importance of}C_j} {\text{importance of}C_{j-1}}, \qquad j=2,\ldots,n $$

Starting from the second criterion, assess its relative importance compared with the previous criterion :

$$ S_j=\begin{cases} >1, & \text{if} C_j \text{ is more important than} C_{j-1},\\=1, & \text{if} C_j \text{ is equally important},\\ <1, & \text{if} C_j \text{ is less important than} C_{j-1}. \end{cases} $$

For the first criterion :

$$ S_1=1 $$
CriterionRelative Importance (\(S_j\))
$C_1$1
$C_2$1.5
$C_3$0.5
$C_4$1

The criteria are ordered according to their perceived importance, and \(S_j\) expresses the relative importance of each criterion compared with the criterion immediately preceding it.

2

Calculate the coefficient \(k_j\)

Formula

Calculate the coefficient for each criterion :

$$ k_j=\begin{cases} 1, & s_j=1,\\ 2-s_j, & s_j\neq1. \end{cases} $$
CriterionCoefficient (\(k_j\))
$C_1$1
$C_2$0.5
$C_3$1.5
$C_4$1

The coefficient \(k_j\) transforms the relative importance assessment into a value suitable for calculating the recalculated weight.

3

Initial weight

Formula

Starting with \(q_1=1\), calculate the initial weight :

$$ q_1=1 $$
$$ q_j=\frac{q_{j-1}}{k_j}, \qquad j=2,\ldots,n $$
CriterionInitial Weight (\(q_j\))
$C_1$1
$C_2$2
$C_3$1.3333
$C_4$1.3333

The \(q_j\) values accumulate the relative importance assessments throughout the sequence of criteria.

4

Weights of criteria

Formula

Normalize the initial weights to obtain the final PIPRECIA weights :

$$ w_j=\frac{q_j} {\displaystyle\sum_{j=1}^{n}q_j} $$

The final weights satisfy :

$$ \sum_{j=1}^{n}w_j=1 $$
CriterionFinal Weight (\(w_j\))
$C_1$0.1765
$C_2$0.3529
$C_3$0.2353
$C_4$0.2353
Sum1.0000

PIPRECIA Algorithm Flowchart