# CPP.mb: CPP with multiple perspectives for decision-making, based on... In CPP: Composition of Probabilistic Preferences (CPP)

## Description

The algorithm evaluates alternatives by integrating the CPP-Tri, the CPP-Malmquist, the CPP-Gini, the alternatives' market values and the CPP by axes. The CPP-mb was originally applied in sports science to evaluate players' performance.

## Usage

 `1` ```CPP.mb(t1, t2, m, q, s) ```

## Arguments

 `t1` Decision matrix of Alternatives (rows) and Criteria (columns) in the moment '1'. Benefit criteria must be positive and cost criteria negative. `t2` Decision matrix of Alternatives (rows) and Criteria (columns) in the following moment '2'. Benefit criteria must be positive and cost criteria negative. `m` Vector of alternatives' market values. `q` Vector of quantiles, indicating the classes' profiles. `s` Shape of a Beta PERT distribution, as described in the package 'mc2d'. There is no default value, however the higher the shape the higher the kurtosis, which emulates the precision of data.

## Value

Class assigns the alternatives to classes, defined by the indicated profiles. The list of classes also shows the decision matrices to be modeled by CPP-PP. CPP-mb indicates the final scores per class.

## References

Sant'Anna, Annibal P. (2015). Probabilistic Composition of Preferences: Theory and Applications, Springer.

Lewis, Michael. (2004) Moneyball: The art of winning an unfair game. WW Norton & Company.

Gaviao, Luiz O. & Lima, Gilson B.A. (2017) Support decision to player selection: an application of the CPP in soccer, Novas Edições Acadêmicas [in Portuguese].

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```## Decision matrix of the previous moment '1'. Alt.1 = c(2,30,86,-5) Alt.2 = c(4,26,77,-12) Alt.3 = c(3,22,93,-4) Alt.4 = c(6,34,65,-10) Alt.5 = c(5,31,80,-8) Alt.6 = c(6,29,79,-9) Alt.7 = c(8,37,55,-15) Alt.8 = c(10,21,69,-11) t1 = rbind(Alt.1,Alt.2,Alt.3,Alt.4,Alt.5,Alt.6,Alt.7,Alt.8) ## Decision matrix of the following moment '2'. Alt.1 = c(3,29,82,-3) Alt.2 = c(6,28,70,-8) Alt.3 = c(2,20,99,-8) Alt.4 = c(5,31,62,-14) Alt.5 = c(9,27,73,-5) Alt.6 = c(4,33,85,-13) Alt.7 = c(9,39,59,-10) Alt.8 = c(8,19,77,-9) t2 = rbind(Alt.1,Alt.2,Alt.3,Alt.4,Alt.5,Alt.6,Alt.7,Alt.8) m = c(100,120,150,140,90,70,110,130) # Market values q = c(0.65,0.35) # quantiles of class profiles s = 4 # Shape CPP.mb(t1,t2,m,q,s) ```

CPP documentation built on May 2, 2019, 1:34 p.m.